Tomás Alonso Albi. January, 1, 2004 revision.

PRACTICES ON OBSERVATIONAL ASTRONOMY

0 ...Introduction. abajo1 ...Example of guide of practices on Observational Astronomy. abajo

2 ...Additional exercises. abajo3 ...Relationship of files of the program. Possible updates. abajo

4 ...APENDIX I: Constellations. abajo5 ...APENDIX II: Catalogs of deep sky objects.abajo

6 ...APENDIX III: Classification of deep sky objects.abajo

7 ...Development process. New modifications. abajo

8 ...References. abajo9 ...Additional references. abajo10 ...Legal warning. abajo

0. INTRODUCTION arriba The program Practices on Observational Astronomy is specially designed for the teaching of Astronomy to level of schools and universities. It is the second reversion of a program that, logically, it will be improved and enlarged with the time in some aspects, with the idea of incorporating all the opinions and possible comments. Because I should say that the biggest defect of this program is that it represents only my own vision of what exercises I believe that one could do in the academic teaching of the Astronomy. Since I know no other programs with those to compare, as a student I've tried to take care of the program so that this defect is not noticed in excess. Even this way, in this revised version, the program allows to do interesting exercises, especially in the relative thing to eclipses, the simulation of the firmament, and the dynamics of the Solar System. To use the program it is only necessary to execute the file 'Ucm - departmento de astrofisica.exe'. A PC with processor Pentium 166 Mhz, 32 MBytes of RAM, and Windows 95 (W2000 is recommended) should be used as minimum (I have checked the program successfully even in a Pentium 100 MHz). The program has been designed to be used in any old computer, because this kind of computers are typically used in classrooms.

A screen configuration with 1024x768 pixels is recommended (800x600 is the minimum), as well as the option of to automaticaly ocultate the bar, to display the program in full screen mode. It will be very useful to open the file 'Configuracion', in order to adapting the program as much as possible to your preferences (follow the instructions in the archive to change the language to English). You can use the configuration program, but this is only recommended for advanced users. Also, there are text files in the subdirectories Eclipses, Observaciones, and Imagenes which are configurable. In these cases the configuration information is present in the files. The program requires the use of diverse support programs, specially Qbasic (editor of the programming language Basic. Because of speed considerations, the program Powerbasic is recomended). This program has it´s own royalties and cannot be provided with my program. If for some strange reason you don't have them in your computer (check for them in the directory oldmsdos in the CD of Windows 95&98), it should not be too difficult to find them. These programs will never be provided through e-mail, in any case. Otherwise, they are only used in the eclipse practice, and an executable version of the basic code program is provided, so a Basic compiler program is not completely necessary (you can change Powerbasic by any text editor using the file ‘Configuracion’). The executable mentioned it is the version of the program adapted to the Universidad Complutense of Madrid (general users can avoid references to any university by changing the file ´Configuracion´). To adapt to program to other university you only have to modify the executable name, to configurate the file “configuracion”, and to modify two images in the subdirectory “imagenes”. Centers interested in using the program in support to the teaching should contact with the author in the address that is mentioned below. Please do it, because I want to know who is using my program. Also, those who want to expose some comments, suggestions, or error reports, can feel free of doing it in the same address. Tomás Alonso Albi. E-mail: talonsoalbi@wanadoo.es

1. EXAMPLE OF GUIDE OF PRACTICES ON OBSERVATIONAL ASTRONOMY arriba

Next a suggestion of a guide of practices is exposed. In the programmer's opinion, it can take advantage and it supplement the contents of the program quite well. The idea could be that the students make two practices every time, in a total of three or four days, following the order of the program of two in two. Here is the list.

1. Eclipse, saros cycle. abajo

2. Firmament. abajo

3. Discs and coordinates. abajo

4. Solar System I. abajo

5. Ephemerides. abajo

6. Solar System II. abajo

If you are a home user with no special interest about astronomy, it would be interesting for you to read the following pages, not only because that´s my intention, but also because you would get contact with some details involving each part of the program. Perhaps you will have to read slowly and buy some books to understand …

1. Eclipse, saros cycle. arriba OBJECTIVES: To learn how to predict eclipses in an approximate way. To understand the saros cycle. To visualize sequences of eclipses and the visibility of the same ones. BIBLIOGRAPHY: Any text about eclipses will be useful. The work Calendrical Calculations is very advisable to follow the code of the program of eclipses. DEVELOPMENT: i) Description of the program. Once selected the practice of eclipses the program will present the editor of Qbasic with a small program to predict eclipses, in a very simplified way. The program is based on the lunar mean sidereal, anomalistic, nodal, and sinodic periods. Closing the editor (option 'Exit' of the menu 'File'), the program will execute another part which allows to visualize the eclipses. You will see some icons up which allows you to change the date, the location, and to pass to the following eclipse or to the previous one. The icon of the eye allows you to show the eclipse secuence or to display a visibility map of the eclipse. ii) Practice development. It could be necessary to have some diskette to copy files during the practice. The first objective will be to describe the foundations in those that the first proportionated program is based, explaining the different mean periods (synodic, nodal, and anomalistic). Check the approximate rhythm of those cycles in little more than 18 years. Equally, enumerate the conditions imposed to consider that an eclipse takes place and justify them. Notice the condition of the half value of the latitude of the Moon when considering if it will exist or don't eclipse. The value in the eclipses of Sun should be 0.50º (approximately the sum of the lunar radius and the solar radius), but it is bigger due to the effects (in the topocentric position of the Moon) of the observer's possible situations on the terrestrial surface. In the case of a lunar eclipse the value depends on the size of the cone of terrestrial shade. The program distinguishes among penumbral, partial, total, or annular eclipses. On the other hand, the program is written in language Qbasic, and it is visualized directly in the editor of this programming language, called Qbasic.exe. This language is the most advisable to learn how to program, for its speed when making simple programs mathematically. Use this small program (puncturing the mouse on the menu 'Run' and execution option 'Start') to find some eclipses starting from the current date, and use the output graph of the same one to compare the approached temporary distribution of eclipses of Sun and of Moon along two or more complete cycles saros of 18 years. Uses the output file 'Eclipses.txt' to enumerate the number of eclipses of each type present in each cycle saros (calculate the annual average of eclipses of each type), and explain with the help of the nodal cycle why there are usually two or even three serial eclipses separated by 15 days each one. Discusses equally if the eclipses repeat or not with certain similarity. Keep in mind for it that the program is not certain (the reliability is about 98% in present time), and that the cycle saros doesn't repeat exactly in the reality. Would you know how to explain why those three serial of eclipses (3 serial every 15 days) are always two of Sun and one intermission of Moon? Look for the tetrades (four consecutive total

eclipses, separates by six months) of the Sun and the Moon. When they are produced, for example for the Sun, what kind of lunar eclipses are asociated to them (and the same in the inverse case)? Explain this, taking in mind the diference between the synodic and the nodal periods.

Follow a given eclipse during two or more cycles, seeing if it appears after 6585.32 julian days. Explain the circumstances of the new eclipse in relation to the one of the last cycle. How many different saros series are active at the same time? A saros series is a set of eclipses that repeat of a saros cycle (18 years, 8 hours, and 10 or 11 days, depending on the number o fleap years in that 18), and have similar characteristics (ocultation percentaje, lengh, sent of ecliptic crossing, and so on), one respect the last. A saros series begin with a partial eclipse visible from the north pole or the south, and, because the nodal period is not exactly the same as the synodic period, the eclipse moves in latitude to the south or the north, respectively. The eclipse cross the equator, producing total and longer eclipses, and finally the series end with a partial eclipse in the other pole. This is due to the movement of the position of the ascending node of the Moon orbit respect to the fase (-0.48º in each cycle of 18 years), so the ecliptic latitude is slightly different in the repeated eclipse. In the case of solar eclipse series, if the saros series is an even number, the series start with a partial eclipse visible from the south pole, and the eclipses are produced near the descending node. This first eclipse occurs 17.4º to the east of the descending node, and the series end with another partial eclipse 17.4º west of it, more than 1000 years later. The program gives the inex number (Inex is a cycle of 358 lunations, saros has 223), and the number of the eclipse respect to the total number of them is the series, when this is posible. Use the part of visualization of eclipses to determine some eclipses of Sun and Moon that will be visible in Madrid in next years (about 30 months or something less). For it selects in a given eclipse the option of visualizing (observe the altitude of the Moon above the horizon). While the eclipse is visualized use the icons to move the Moon. The secuence is shown in horizontal coordinates, as you would see the eclipse apparently. Down you will see a bar which shows the lunar center position with the time, respect to the Sun or Earth´s shadow cone. Enumerate the visible eclipses and those that are not visible, so much of Sun as of Moon, and represent the map of visibility of some of them (select the complete map, not Spain). In this map they will appear shadowed in grey the areas of visibility of an eclipse of Moon, and in colors the percentage of entirety of an eclipse of Sun. In both cases only the regions where the moon is visible are shadowed. Describe with brevity the map of visibility for all the eclipses that you represent, and justifie the change in way of the curve of illumination among those eclipses that take place near some equinox and near some solstice. Make a more precise description of the eclipse of Sun of 3-10-2005, and of the eclipse of Moon of 28-4-2004, seen from Madrid. If you want to copy some image remember that you should pulse [Alt] + [Impr Pant], leave the program with [Ctrl] + [Esc], and select then the option 'Edit' and 'Paste' in any image editing program (Photo-editor, Paint, Word,...). Later on you can invest the colors to avoid the black background. Additional exercise: On January 14, 484 took place an eclipse of Sun that, according to the chronicles of the time, it turned out to be total from the city of Athens. According to the observers the entirety arrived soon after of the dawn. Uses the program to find this eclipse. Knowing that Athens is at 38.0º of latitude and 23.8º of longitude, does it coincide the hour and the region of entirety with the one given by the astronomers that observed it? Why?

Additional exercise: Calculate the mean lengh of a saros series knowing that the node moves 0.48º each 18 years (suppose that value as a constant), and the limits of displacement are (+/-) 17.4º. Saros

series 120 will end with a solar partial eclipse on 2195, visible from the north pole. Look for the corresponding partial eclipse that produced this series, and explain where was this eclipse visible from. Calculate the lengh of this series and compare it with the mean lengh. Look in the image the last total solar eclipse of this series, between 1925 and 2033. Explain the image.

2. Firmament. arriba OBJECTIVES: To study how it varies the firmament according to the town and observation date. To understand the precession movement and their long term effects, as well as the characteristic movement of stars. To recognize constellations, objects, and reference lines. To use the diverse coordinate systems. BIBLIOGRAPHY: José Luis Comellas, “Guía del Firmamento”, Rialp, 2001 (6th edition). it is not present in the UCM-library, but it is a highly advisable work in order to supplementing this practice, and like guide to learn how to recognize constellations and objects of the firmament, from a basic level from now on. It can be interesting also some more portable book on constellations, as the work 'Stars' of the series 'Blume natural guides'. DEVELOPMENT: i) Description of the program. The program will present the local firmament of Madrid initially for the current instant. A series of icons in the superior part allows to modify the zoom, the observation date, the observation town, the visible objects, the projection type, etc. The first thing is to familiarize with these icons, although soon it will be seen that their use is extremely simple. To identify stars and objects or to center some position directly with the mouse it is simply enough to make 'clic' with the right mouse button and select the option. If what you want is to center a certain well-known position of right ascension and declination, select the find icon and introduce the coordinates respecting anyone of the two following formats: AR:--h--.-m | AR:--h--m--s , or combining a type with another. [¨] it is obtained with [Shift] + [¨´ {] + [Space] DEC:---º--.-' | DEC:---º--'--¨, with prefix '-' in the case of negative declinations Once introduced this the program will ask you you to introduce the visual field in degrees. If you want to introduce the field in other units, be already of time or of arch, you only have to specify it as suffix: '1', '1º', '4m', '60'', '3600¨', '240s', are all valid and equivalent examples. The allowed minimum field is of 15¨, and the maximum of 360º. When specifying a temporary jump (after introducing the date) to encourage with easiness the firmament, you can also use as suffixes the letters 'd', 'h', 'm', 's', for days, hours, minutes, or seconds of time respectively. To introduce a certain geographical region not present in the file of cities, make the same thing that to look for objects, but using 'LON:' and 'LAT:' instead of 'AR:' and 'DEC:', and using the format of degrees, minutes, and seconds in both cases. To introduce declines or negative latitudes introduce the prefix of the sign '-' in the degrees. All these actions will be equally valid in the practices fourth and sixth. The icon with form of terraqueous globe allows to modify the system of coordinated and the projection type. The systems of coordinated possible are the equatorial one, the ecliptic, the galactic, and the horizontal system of coordinates. Under the system of coordinated the projection type is

shown, and can be selected among the stereographic, polar types (so much of north hemisphere as of south hemisphere, regarding coordinates employee's system), spherical, horizontal, and cartesian. The form of habitually representing the local sky that is as initially it is shown in the screen, it corresponds to the system of equatorial coordinates in stereographic projection. This is in this way because the stereographic projection corrects in an apparent way the deformations of the constellations when representing them in the plane of the screen of the computer. While the spherical projection makes the same thing to simulate that we are seeing a sphere from outside of the same one, the stereographic projection tries to simulate the surface of a sphere seen from the interior center of the same one, that is it that in fact happens seemingly when observing the night firmament from the Earth. The program allows to visualize the SAO catalog, with 256 000 stars until beyond the tenth magnitude, but it is not very advisable to make this, at least without having reduced the visual field to less than 30º. To see the SAO you should go up the magnitude limit to a same value or superior at 7.0. it is important to keep in mind that the catalog SAO is not used more than to visualize stars, so that the actions of to identify and to look for don't apply to this catalog, but to the catalog BSC that has for magnitude limit the 6.9. To look for a certain star you can introduce the name of the same one (if it has it), or the appointment corresponding to its constellation, or its number HD, HR, or SAO. For example, you can look for the star Vega, or 'Alp Lyr' (included quotation marks, with three letters for the Greek appointment Alp, Bet, Gam, etc., a space, and other three letters for the abbreviation of the constellation), or BD172167, SAO67174, or HR7001 (in the three cases without spaces). The program also contains a catalog with more than 10 000 deep sky objects, although it is more advisable to use, of being necessary, the catalog of 850 objects, which has more complete and more reliable information. To look for an object of deep sky as M 45, or NGC 7000, you should select to look for and to introduce M45 or NGC7000 (without spaces). The program will show initially in screen all the comets and the first 30 asteroids. To go to the position of any other asteroid, like for example the one designated as 951 Gaspra, it is enough to select to look for and to introduce the name 'Asteroid 951 Gaspra', always with the quotation marks included when letters inserted with spaces are being introduced. Although it is not indispensable to write the word 'Asteroid' to look for first some of the thirty that the program shows directly, suits to always make it, because confusions could be given with certain names as Pallas (that is the name of an asteroid and of a crater of the Moon) or Vega (that is a star and also a crater), in which case the program usually gives priority to the stars and asteroids in front of the craters. If the program is configured to show all the asteroids the confusions they can increase too much, and, anyway, to avoid them you can introduce the name of the object in question with its identification of object type: 'Asteroid', 'Comet', 'Planet', 'Star', 'Object' (of deep sky, is understood), or 'Crater', so that to look for Pallas like asteroid without error possibility, you should introduce therefore 'Asteroid Pallas'. The addresses of the coordinates in the screen are always the same ones, to facilitate the orientation: north-west-south-east, in the sense of the needles of the clock. Finally, the program will show all the comets of the corresponding file that have a more brilliant apparent magnitude than the 15.0, and its lines are shown supposing that these have a real longitude of 10 million kilometers, that which is almost always a too optimistic supposition. The icon of the lunar globe allows you to represent planetary textures. To see them you will have to amplificate some planet.

ii) Practice development.

As first exercise you can study how the sky seems to be in different dates of the year and towns of the world. Choose them to your pleasure (always writing down the geographical coordinates and the date) and describe what you observe, shortly helping yourself for example with the approximate sidereal time (identifying a star in superior culmination). Begin logically with the sky of Madrid in the current night, and recognize the constellations that the program shows with relationship to those that you should have seen in the previous observation session. Equally, you can look for interesting deep sky objects, with a view to a session of later observation. Next, modifie the date until one year around the year -3000, and check which it should be for then the Polar star. Advance the date in 2000 years, until approximately the year 10 000 or 12 000, and describe the journey that makes the terrestrial axis among different constellations, due to precession, around the north ecliptic pole, located on the constellation of Draco. Equally, you can also notice the slight change in the form of some constellations, for effect of the own movement. Optionally you can pick up graphics of the program if you want it, specially and image of the pole in ecliptic coordinates. Pulse on the third icon for the left to modify the system of coordinates to project the sky. Observe all possible coordinate systems, with special attention to ecliptic, galactic, and horizontal, with which you will have to work next numerically. If you have enough time, you can observe how the projections ecliptic and galactic varies with the precession (you can see it while you change the date to see the precession), using the lines of each class of coordinates as reference. For curiosity, you could represent the firmament in galactic coordinates (in cartesian projection preferably) until a magnitude limit of 8.5, using the SAO, to observe the disposition of the galactic plane of the Milky Way and the intense areas of absorption of the stellar light, especially toward the galactic center. This can also be seen representing the Milky Way textures. Use the abbreviated form of below, based on the three angles of Euler to rotate the coordinates in different reference axis, to solve the following exercises that intend: a) Equatorial coordinates of the center of the galaxy: L, L (leaving null the galactic longitude l and latitude b). The subindex o in the coordinates of right ascension and declination of the formulas refers to the equatorial coordinates of the north galactic pole, which are given under in the equinox 2000.0. b) Horizontal and ecliptic coordinates of planet Jupiter in the current instant. Use the current equatorial coordinates of the planet therefore. Calculate for yourself, with the formula of below, the local sidereal time TSL, or use an approximate value with the right ascension of a star in superior culmination. Use = 23º.439281. h = dj - INT(dj) - 0.5, where dj is the julian day number with decimals (to see practice 7), and INT(x) the integer value of x IF (h <0.0) THEN h = h + 1.0 t = (dj - 2451545.0) / 36525.0 ts = 0.2790572732639 + t * (100.002139037801 + t * (1.07759259E-6 - t * 7.17593E-11)), with E-11 = 1/10''. TSL = h * 1.0027379092 + longe / 360.0 + ts , where longe is the geographical longitude in degrees (-3.717 for Madrid) TSL = TSL - SGN(TSL) * INT(ABS(TSL)) , where SGN(x) returns the sign of x (1 if x>0, -1 if x <0, and 0 if x=0), and ABS(x) returns the absolute value of x. IF (TSL <0.0) THEN TSL = TSL + 1.0 TSL = TSL * 2.0 * , in radians

c) True equatorial coordinates of the Polar star in the year 2000.0, starting from their equatorial coordinates and their own movement (expressed for the year 1950.0): Ra = 01h 48m 48.79s, Dec = +

89º 01 ' 43.7¨, ar = 0.1811 s/y, and dec = - 0.0004 ¨/y (suppose constant the proper motion during the 50 years). Keep in mind that the program of practices provides the apparent equatorial coordinates for any star in the projection of the local sky, for what compare these coordinates with the true equatorial ones, and explain the reason of the slight differences that you observe. If you make the calculations well you will see that the Polar has come closer from a considerable way to the celestial north pole in the last 50 years, and it will follow it making during some decades. The result of correcting the coordinates of the Polar one for proper motion and precession should be: RA 02 h 31 m 51.29 s, DEC +89 º 15 ' 51.3 ¨. The final result of the true coordinates after correcting the previous coordinates for nutation should be something like RA 02 h 31 m 46.22 s, DEC +89 º 15 ' 59.2 ¨. d) Optionally you can calculate the position of the mean celestial north pole (2000.0 coordinates for example) in the different dates in those that have represented the firmament, only taking in consideration the precession. sin y = sin sin o+ cos cos ocos ( - o) [1] x = lo + arctan [(sin - sin y sin o)/(cos cos osin( - o))]

sin = sin y sin o+ cos y cos osin(x - lo) [2] = o + arctan[(cos y cos (x - lo))/(sin y cos o- cos y sin osin (x - lo))]

DATA: Equatorial <=> Galactic Equatorial <=> Horizontal Equatorial <=> Ecliptic o = G = 12 h 51.44 m ; b = y (lat) o = TSL ; a = y (altura) o = -/2.0 ; = y (latitude) o = G= + 27 º 7.7 ' ; l = x (lon) o= ; A = x (acimut) o= - + /2.0 ; = x (longitude) lo = lG = + 33.64 º (2000.0) lo = -/2.0 lo = 0.0

Precession (IAU 1976, expressing the coordinates in the equatorial system, and using [1]) o = (-zeta) * signo o= (-theta + /2.0) * signo lo = z + /2.0

t0 = (dj0 - 2451545.0) / 36525.0 , where dj0 is the initial julian day (1950/1/1.5). See the end of this practice to calculate jd. t = (dj - 2451545.0) / 36525.0 , where dj is the final julian day (2000/1/1.5 = 2451545.0 => t = 0.0, t0 0.5 dt = t - t0 sign = 1 IF (dt < 0.0) THEN sign = - 1, in the case of the proposal exercise, sign is woth unity z = ((2306.2181 + (1.39656 - 0.000139 t0) t0) + ((1.09468 + 0.000066 t0) + 0.018203 dt) dt) dt theta = ((2004.3109 + (-0.8533 - 0.000217 t0) t0) + ((-0.42665 - 0.000217 t0) - 0.041833 dt) dt) dt zeta = ((2306.2181 + (1.39656 - 0.000139 t0) t0) + ((0.30188 + 0.000345 t0) + 0.017998 dt) dt) dt cte = 206264.806247096 z = z / cte , in radians theta = theta / cte zeta = zeta / cte

Nutation (using then ecliptic system of coordinates) Aproximate algorithm: t = (dj - 2451545.0) / 36525.0 , lapse from January, 1, 2000, in julian centuries M1 = (124.90 - 1934.134 * t + 0.002063 * t * t) * M2 = (201.11 + 72001.5377 * t + 0.00057 * t * t) * Dlon = (- 0.0047785 * SIN(M1) - 0.0003667 * SIN(M2)) * , in radians Dlat = 0.00256 * COS(M1) *

More precise algorithm (Peter Duffett): t = 1.0 + (dj - 2451545.0) / 36525.0 , lapse from January, 1, 1900, in julian centuries a = 100.0021358 * t b = 360.0 * (a - INT(a)) L2 = (279.6967 + 0.000303 * t * t + b) * 2.0 * a = 1336.855231 * t b = 360.0 * (a - INT(a)) D2 = (270.4342 - 0.001133 * t * t + b) * 2.0 * a = 99.99736056 * t b = 360.0 * (a - INT(a)) M1 = (358.4758 - 0.00015 * t * t + b) ( a = 1325.552359 * t b = 360.0 * (a - INT(a))

M2 = (296.1046 + 0.009192 * t * t + b) ( a = 5.372616667 * t b = 360.0 * (a - INT(a)) N1 = (259.1833 + 0.002078 * t * t - b) ( N2 = 2.0 * N1 Dlon = (-17.2327 - 0.01737 * t) * SIN(N1) Dlon = Dlon + (-1.2729 - 0.00013 * t) * SIN(L2) + 0.2088 * SIN(N2) Dlon = Dlon - 0.2037 * SIN(D2) + (0.1261-0.00031 * t) * SIN(M1) Dlon = Dlon + 0.0675 * SIN(M2) - (0.0497-0.00012 * t) * SIN(L2 + M1) Dlon = Dlon - 0.0342 * SIN(D2-N1) - 0.0261 * SIN(D2 + M2) Dlon = Dlon + 0.0214 * SIN(L2-M1) - 0.0149 * SIN(L2 - D2 + M2) Dlon = Dlon + 0.0124 * SIN(L2-N1) + 0.0114 * SIN(D2 - M2) Dlat = (9.21 + 0.00091 * t) * COS(N1) Dlat = Dlat + (0.5522 - 0.00029 * t) * COS(L2) - 0.0904 * COS(N2) Dlat = Dlat + 0.0884 * COS(D2) + 0.0216 * COS(L2 + M1) Dlat = Dlat + 0.0183 * COS(D2 - N1) + 0.0113 * COS(D2 + M2) Dlat = Dlat - 0.0093 * COS(L2 - M1) - 0.0066 * COS(L2 - N1) Dlon = Dlon / 3600.0 * ( , en radianes Dlat = Dlat / 3600.0 * (

As much in precession as in the other transformations (except nutation), both x and y already refers to the equatorial coordinates corrected or transformed (use [1] always). For if you don't want to use the exposed algorithms for the nutation, the most precise values for the year 2000.0 are Dlon = - 13.923 ¨ (nutation in longitude), Dlat = -5.764 ¨ (nutation in obliquity). These values come from the IAU1980 Theory of Nutation, and can be obtained in one of the sections of the practice Ephemerides. To correct the nutation first you should pass the equatorial coordinates (referred to the mean equinox J2000.0) to ecliptics (with [1]), then to add Dlon to the longitude to obtain x corrected, and the to undo the transform next by means of the group of formulae [2], using the true obliquity ( + Dlat instead of ). Additional exercise: as you know, Galileo discovered the satellites of Jupiter in the year 1610, and he followed them observing during years. At 23:30 o'clock of December of 1612 Galileo was in the vicinities of Florencia observing Jupiter, and in one of their drawings he found a fifth 'star' aligned more or less with the ecliptic and with the equator of Jupiter. Simulate the firmament on that time and identifie this 'star' observed by Galileo. Additional exercise: the Titanic left the English port of Southampton on April 10 1912. After the escalades in Cherbourgo and Queenstown went to New York. As you know, the transatlantic collapsed in the night from the 14 to April 15, after a colision with an iceberg at the 00:50 hour of the ship. The fourth official, Joseph Boxhall, had estimated the position of the Titanic with very good approach given the circumstances, in 41º 46 ' N, 50º 14 ' W, based on stars' observations. The final hour of the sinking should be around the 2:20 hour of the ship of April 15. Supposing that the hour of the ship was adjusted at previous astronomical noon, that is to say, with three hours of advance regarding the Universal Time according to their geographical position, simulate the visible firmament from the Titanic at 22:55 TU of April 14. For then, the Carphatia went to the rescue from the direction of azimuth 315º (0º = 360º is South, 90º is West, and so on), and it was at 80 km of distance, while the Californian, 15 km in direction 225º, ignored the aid signs. According to the surviving witness the night then was incredibly transparent (the ship probably had already been left without light), and in those instants a small discussion existed between captain Smith and boatswain Rowe on the presence of other hypothetical ship to starboard. Supposing that the prow of the ship went in Southwest direction (to avoid the iceberg it did go to the south), would you know to identify which possible object the causing of the discussion it was? The Titanic was found by Robert Ballard in 1985 in the position 41º 44 ' N, 49º 57 ' W, about 24 kms to the E of the last well-known position. For further confusion in this

sense, the prow of the Titanic in the marine bottom is guided in northeast direction, and its orientation is not known during the shipwreck, because it should rotate when it left the prow part.

CALCULATING THE JULIAN DAY. Being 'a' the year, 'm' the month, and 'd' the day in the gregorian calendar, and being 'Int' the function that gives the inmediately lower integer number of the argument (INT(1.1) = INT(1.6) = 1 , INT(-1.1) = INT(-1.6) = - 2), we have the following.

Gregorian day = 365 * (a - 1) + INT((a-1)/4) - INT((a-1)/100) + INT((a-1)/400) + INT((367 m - 362)/12) + d + n ,

where n = 0 if m < 3 n = -1 if m > 2 and the year is a leap one n = -2 in any other case

One year is a leap year if the rest of the division of the year by 4 is zero, and the rest of the division by 400 is not 100, 200, nor 300.

Julian day = gregorian day + 1721424.5 (at 00:00 UT of that gregorian date)

3. Apparent disks and coordinates. arriba OBJECTIVES: To observe the apparent orientation that the planetary disks shows during the day, and monthly and yearly cycles. To observe transits, ocultations, eclipses, and shades of the satellites of Jupiter, Saturn, and Pluto. To learn in a visual way concepts like paralactic angle, position angle, etc. To use heliographic, planetographic, and selenographic coordinates. Reduce an image of the Sun. BIBLIOGRAPHY: There's no useful bibliographical references on the objectives of the practice. Perhaps you can use Practical Ephemeris Calculations, by Oliver Montenbruck. DEVELOPMENT: i) Description of the program. When selecting the practice the program will present an image of the Sun for the current instant, and like it would be observable from Madrid looking in south direction. To the left of the object the position angles and inclination of the axis will appear (in degrees). It will also appear information on horizontal coordinates, angular radii, or librations and age in the case of the Moon. If some object is not observable in the date and considered instant, the corresponding object will appear filled of blue color. A series of icons in the superior part allows to modify aspects of the representation. The icons of the right allow you to advance or to go back the time in a certain interval that is from one day when beginning the practice. The other icons allow to adjust the observation town, the calculation date and temporary interval of jump, the form of representing the Moon or the planets (with craters in the case of the Moon, or with real textures), the scale of vision, or to conclude the practice. The icon of the eye allows you to change object, among the Sun, the Moon, and all the planets. The icon of the binocular allows you to increase or to reduce the scale, that which is useful to observe the satellites of each planet. In some area of the disk a small yellow circumference that represents the center of coordinates of the object could appear. In all the cases you can move the mouse throght any point of the object to know the coordinates on their surface (in the case of Jupiter and Saturn the coordinates refer to System I, which is related with the equatorial belt. System II is refered to tropical belt, and System III is related with the rotation of the magnetic field), and to see the altitude of the Sun above the horizon in any point of the object (you can observe the subsolar point of any object if you set the location to Centre of the Earth). In the case of the Moon you can make 'clic' to identify craters on their surface. You can also identify satellites. The modification of the scale will also allow you to observe the satellites of the planets, being able to study transits instants therefore, ocultations, or eclipse of the satellites of Jupiter and Saturn (and any other satelite), besides the beginning instants and end of the transits of the shades of the satellites on the planet. When changing the town with certain speed, or to modify the time permanently in the same direction, it is advisable to press space bar, action that will be equivalent to make 'clic' with the mouse on the last icon or position that you have pulsed with the same one. In the inferior part two icons that

are equal to the acquaintances will appear: 'cancel' and 'acept'. On the other hand, when you modify the date and hour of calculation you can introduce the value zero on those fields (year, month, day, hour, minute, or time jump) that you don't want to modify.

The icon of the telescope is used to show real images of the object previously taken and reduced with the program. You can see an example in the case of the Sun.

ii) Practice development. The objective of the practice is to visualize the apparent aspect of the disks of the Moon, the Sun, and the planets, along a margin of sufficiently long time as so that it is representative of the day movement, the cycle of the lunar month, and the annual cycle or the period of the planet. For it you will make 'clic' on the icon of modifying the calculation date, to modify the temporary interval and to study each cycle. The jump of one day used by defect is the best to study the lunar month, during about 30 days, only modifying the date and not the hour. The day movement, so much of the Sun as of the Moon, it can be studied with a step of 1 hour (select “1h” as time step). For the annual cycle of the Sun it is enough to use a jump of about 15 days (leaving preferably of the hour of the noon). For the case of a planet you should keep in mind their sidereal orbital period. Optionally also you can study the movement of rotation of the Sun along one month for a date among the years 1874 and 2002, in which case the program will show the main groups of visible sunspots in each moment, facilitating you the pursuit of the rotation of the Sun. Describe the effect of the paralactic angle when obtaining the apparent image of the disks of the Sun and the Moon in the day movement. Equally, modifie (for a fixed given date) the town and observe the influence of the latitude and the height in the paralactic angle. It suits to use cities with a similar longitude to that of Madrid, and different latitudes, as Abidjan and Manchester. Since the towns go in alphabetical order according to the country, advance down from Spain to find them, or use the icon of the key pulsed to introduce the name of the town directly, always with the initial in capital. If you make this last, introduce 'Manchester (UK) ', with the included quotation marks, or introduce London and then select the icon again, with what Manchester would appear exactly under. Describes equally with brevity the lunar month and the annual cycle of the Sun. Next we seek to observe the apparent orientation of the planes of the planets seen from the Earth. This depends logically on the so much position of the Earth like of the planet in question. In our case we will observe the planets Mars, Jupiter and Saturn (voluntarily, if you have more time, it would be interesting to observe Uranus, and Mercury or Venus, and also the eclipses of Pluto and Charon between 1985 and 1990). You will be able to check that Jupiter doesn't change too much its apparent aspect along the years, when having an orbital inclination of only 1.3º regarding the ecliptic, and a rotation axis only inclined 3.12º regarding the perpendicular to the plane of the ecliptic, so that the apparent inclination varies more for the relative position of the Earth than for the own planet. In this case observe the rotation of the galilean satellites around Jupiter, and describe the diverse phenomenons that you observe along several days, as transits, eclipses, and transits of shades. Next choose an appropriate temporary jump and select to show the coordinate axis in order to appreciate in this way the apparent change of the planet better. Describe the change that you observe in each planet during a complete sidereal orbital period or something more, noticing the influence that has the latitude ecliptic of the planet (or the distance of the same one to the ecliptic) and the orbital position of the same one (the period of Mars is of 1.88 years, that of Jupiter 11.86 years, and that of Saturn almost 30

years) on the inclination or position angle of the pole of rotation of the planet. The position angle of the axis has an apparent orientation that depends on the position of the Earth and of the 23.4º of inclination of its axis, besides varying for the day movement according to the paralactic angle, in a similar way to as you already saw in the previous part with the Moon.

The second part of this practice is to reduce and observation of the Sun. Open the file readme.txt in the directory observaciones and follow the instructions contained there. Then, open the archive with the program and clic with the mouse in any concret feature that you know is present in both images. Clic with the mouse in the feature in both cases. Now, use the mouse and the right and left buttons to put the program generated image just on the real photograph. Just clic in the centre of the disc with the left button to enlarge the program generated image, or with the right button to select the desired option. When the adjustment is exactly, clic the right mouse button and select to finish. The program will then rotate the image and will save it. You can then reload the image to see the coordinates of any feature directly. Additional exercise: use the formulae of Euler angles of the previous practice, together with the information provided by the program, to obtain the heliographic, selenographic, and planetographic longitude and latitude of the positions that are given under. These positions refer to the center of the disk. The procedure to make this is simple, because it is to transform the cartesian coordinates of the apparent disk to cartesian on the real disk of the corresponding object, by means of the appropriate rotations. You can check the results with the program. Sun: 13:28 local time of Madrid of February 26 2000. Position x = -0.276 solar radii (to the left), y = -0.071 solar radii (down). Reject the paralactic angle, because this instant refers to the culmination of the Sun. The result should be approximately: longitude 330º, latitude -16º. It's the NOAA 8882 group. Moon: 03:00 local time of December 13 2000. Position x = -0.416 lunar radii, y = +0.695 lunar radii. In this case reject the libration angles. The result should be approximately: longitude -27º, latitude +47º that belongs together with Sinus Iridum, located in the border NE of the Mare Imbrium. Mars: 00:00 local time of July 27 2001. Position x = -0.326 Mars radii, y = 0.343 radii. The result should be approximately: longitude 137º, latitude +18º, corresponding to the position of the Olympus Mons, the biggest well-known volcano in the Solar System. You can check it visualizing the planet with the textures, although to the telescope it was not easily visible for then, when being the planet just in one of the most intense storms of sand that have been observed. Solution: a valid example of algorithm to make the rotations is the following one. Be (dx, dy) the cartesian coordinates on the apparent disk of the object in seconds of arch, such and as the program gives them, one has that the real coordinates on the disk of the object (lon, lat) are then: radio = SQRT (dx * dx + dy * dy) IF radio IS SMALLER THAN r THEN dz = SQRT (r * r - dx * dx - dy * dy) ang = ATAN2 (dy, dx) dx = - radio * cos (ang + p - P) dy = - radio * sin (ang + p - P) tmp = dy * sin (b0) + dz * cos (b0) dy = dy * cos (b0) - dz * sin (b0)

dz = tmp dir = -1.0 IF THE OBJECT IS EXTERNAL TO EARTH (Mars to Pluto) THEN dir = 1.0 lon = L0 + dir * ATAN2 (dx, dz) lat = ASIN (-dy / r) END IF

Where 'r' is the radius of the disk in seconds of arch, 'P' is the position angle of axis, 'p' is the paralactic angle, 'b0' is the position angle of pole, and 'L0' is the longitude of the central meridian. SQRT(x) represents the square root of x, ATAN2(y, x) represents the arctan of y/x (with result in the correct quadrant, be careful with calculators), and ASIN(x) is the arcsin of x.

4. Solar System I. arriba OBJECTIVES: To recognize objects and types of orbits for their apparent trajectories seen from the Earth, so much for external planets as for the interior planets to the Earth. Orientation of the planes of the planets from the Earth. To identify instants of opposition, conjunction, quadratures, and stationary points. Solar analemma, solstices and equinoxes. To understand the apparent movement of the stars along the time. BIBLIOGRAPHY: You can use any text of spherical astronomy, although it is not completely necessary. DEVELOPMENT: i) Description of the program. The program of this practice is identical to the program of the second practice, with two main differences. The first one is that in this practice they are not available the numerous visualization options and modification of visible objects, and the second one is the possibility of representing the trajectory of any star, planet, comet, or asteroid visualized during the temporary margin that you select, using the icon of the eye. Inside this possibility you can use the icon of the key pulsed to introduce the name of the object by hand, to likeness of what happens when changing town. The program allows to show the position of the planets among the years -1000 (1000 B.C.) to the +5000 (5000 A.C.). A definitive theory doesn't exist for Pluto's movement, and less still orbital parameters of asteroids and comets in remote times, so that these bodies will only be represented in screen among the years 1700 at the 2100. When selecting a same or inferior field of vision to a degree they will be shown in the bottom of the screen some reference lines to be able to estimate distances with easiness. The biggest lines are to intervals of a minute of arch. The shortest lines define intervals of half minute of arch inside the biggest, while the points divide to the previous ones in two, for what the minimum separation between points or lines is of a room of minute of arch. ii) Practice development. The first step that you should make is to represent the apparent trajectory of all and each of the external planets to the Earth, selecting the temporary margin that you believe appropriate to be able to see the complete trayectory that travels the planet seemingly (little more than one year in the most external planets). If you want you can use the ecliptic system of coordinates, with which the deformation that introduces the stereographic projection is the same one for the whole ecliptic. For each planet identifie approximately (with the single help of the curve) the instants of opposition respect to the sun, conjunction, stationary points, and the quadratures. You can use graphics of the program, and to compare later on if you want the results with those that the program provides in the section of ephemerides of the practice of the same name. Compare the different trajectories and explain the differences that you observe, keeping in mind the inclination regarding the ecliptic of the orbit of each planet, as well as their mean daily movement. Make the same thing with some asteroid or comet that has a relatively high inclination regarding the ecliptic, as the comet 14 P / Wolf (27º of inclination), or the asteroid 2 Pallas (34º).

Next make this same for the planets Mercury and Venus. To see a complete curl you keep in mind that their periods of adjournment are respectively of 0.24 years and 0.62 years, so that you will have to show the trajectory during 4 years for Mercury (4 * 0.24 = 1 that is the period of the Earth) and 8 years (you can use 3 years for comfort) for Venus, because the curl has approximately this period. The temporary jump in both cases should locate it around 5 days, to avoid long waits. Once observed the trajectory trie to explain it by means of a mental image. By placing the mouse in any position of the trajectory, you can identify de planet, it´s coordinates, and the date when is placed there. Lastly, repeat the process with the Sun, locating the initial hour of calculation at 12:00 TU. For it you should introduce the initial day of calculation in decimals, with the decimal 0.5. Fixed the temporary jump in an integer number of days between one and three. Change the projection to horizontal coordinates. When making this you will see, instead of the trajectory of the Sun on the ecliptic, the so called solar analemma. In this case what is made is not to represent the positions of the Sun along the year, but their horizontal coordinates day by day, varying the value of the sidereal time this way along the year, and not using a fixed value (referred at once current) as it is made in the representation of the local sky in stereographic coordinates, and in the rest of projections. It is for it that you should introduce the decimal 0.5 in the day to see the analemma, because the Sun is only high on the horizon at noon. Keep therefore in mind that the constellations and stars shown in this case can only be seen in the current instant of calculation (to which refers the current position of the Sun shown as a disk), and not to the rest of the analemma. Explain the obtained curve and identifie equinoxes and solstices on it. How would it be from other latitudes? Why doesn't the Sun seem to culminate on Madrid for mean term at 12:00 TU? As an exercise, represent the apparent altitude of Mercury or Venus just in the sunset or in the sunrise, during a few months. Return to local sky in equatorial coordinates and stereographic projection, and look for any star near the meridian, preferably some brilliant one that has own name, as Arcturus or Vega. Select the icon of showing trajectories, and, next, make 'clic' on the icon of the hand to the left to introduce the name of the object for yourself. Introduces the star's name, and select the margin of time and the temporary jump. Uses around 30 years of time for the trajectory (leaving preferably from the current instant), with a jump of about 30 days, and in a longer term, a jump of 90 days and an interval around 1000 years. Describe the resulting graphics and explain them. Voluntarily you can repeat the process for any other star with an ecliptic latitude quite different. Look for some very near star, and with high own proper motion, to represent their long term trajectory and to observe the relative movement. Good candidates would be HR5459 (also called Toliman or Alpha Centauri), and HR8387. Calculate the distance that has traveled (and the one that will travel) in the last ones (and next) 1000 and 5000 years (use a temporary jump of 365.25 days for the 5000 year-old interval, annulling this way the effect of aberration), and compare it with the one that the star would travel supposing hypothetically that it own proper motion is constant in the time, and similar to its current value. The proper motion can be found in the file 'Stars', in ¨/year, in each star's last two numeric columns, fair before its own name (for Toliman it is about -3.64 ¨/año and +0.7 ¨/año, in RA and DEC respectively). Comment equally how have varied other parameters like the apparent magnitude or the parallax. Additional exercise: imagine that for accident you are caught in a deserted island without having idea of your geographical position, time of the year, and without means in principle to escape from her. What would you make to discover all this and to devise an escape plan?

Additional exercise: one of the big mysteries of the history and of the Christian religion it has been to determine when Jesus was born. Our year 1 begins soon after in theory of this event, although the beginning of our calendar was fixed by Dionisio the Scanty, Franciscan monk that lived in the VI century. It is known that it made a 4 year-old error when not considering the reign of four of one of the Roman kings that he took like reference for their calculation, and it is also known that it made an error from an additional year when not considering the 'year cero' of the calendars (that is to say, to pass of the 1 B. C. to the 1 A. C. directly). so that, although it is not anything sure, Jesus should be born among the current years 5 B. C. and 7 B.C. It is also known (although always without certainty), according to the Bible that Jesus should almost be two years old when Herodes ordered to kill all the male children smaller than this age, and that Herodes died soon after from an eclipse of Moon that took place exactly before the Jewish Easter of spring. Investigate with the program all these 'facts' (supposing that they are all certain ones), to find the eclipse of Moon in question and the approximate date of Christ's birth. The gospel of Matheus speaks about 'Star of Belen' that guided the three kings, probably astrologers, until the place of the birth. Was there some celestial event for then that could have been interpret in this way? Uses the available possibilities of the previous practices. The celestial event in question was also observed by Kepler, which proposed a quite convincing astrological explanation of Christ's birth.

5. Ephemerides. arriba OBJECTIVES: To begin in the foundations of the calculation of ephemerides. To calculate planetary ephemerides numerically. BIBLIOGRAPHY: The support of a good book with the explanation of the algorithms would be the ideal thing. So the book Practical Ephemeris Calculations is recommended for this purpose. DEVELOPMENT: i) Description of the program. Once selected the practice the program will show the editor of MS-DOS, with a quite complete program in ephemerides calculation written in Fortran, very family language in Physics. Then, closing the editor again, the previous program will be executed, with which you will be able to calculate positions of planets (and satellites of Jupiter and Saturn), comets, and asteroids. as well as to predict eclipses, with a lightly less precise algorithm that the second program of the first practice. To leave the program it follows the instructions of the same one, pulsing [t] + [Enter] when you are required.

Finally, it will appear another section of the program which allows you to calculate planetary ephemerides. Use the icon of the eye to select the subroutine to use. ii) Practice development. It could be necessary to have some diskette to copy files during the practice. This practice consists on describing qualitatively the necessary steps to calculate the ephemerides of comets and asteroids in the proportionated program. For it looks for the section of ephemerides calculation, and in it, the section of comets and asteroids (the section of planets is different, because it doesn't use in the calculation any orbital parameter, but a series of perturbative terms). Enumerate the necessary steps, the reason of the different corrections or transformations, and why they are made in the order in that are made. The program makes almost all the possible corrections in ephemerides, although the precision of the result is not enough to justify so many calculations. It has only been made so that you can see what to do to correct small effects as the nutation, the diurnal aberration, and even the deflection of the light. Describe in a qualitative way the different subroutines used in both cases (comets and asteroids), and the differences that you see in the calculation process and in the type of coordinates that is sought to obtain in each case, as they refer the mean equinox of the date, to the true equinox of the date, or to a given equinox (as the 2000.0); and either a position of the apparent type, astrometric, or geometric (possibilities that are distinguished for the way of correcting the aberration), because in each case the later process of calculation is different. A possibility if you want it is to make a schematic diagram with the process step by step, ramifying it according to the different possibilities and according to the object type whose position is calculating. To move with more easiness use the option 'Find' with the name of a certain subroutine to find, and remember that with [F3] you can make a search of the following term directly. Look for a subroutine called 'Datos' to identify in the program

the names of the variables with the corresponding orbital elements, although with some logic and the indications of the program, perhaps it won't be necessary (if you know a little spanish!). Finally, the ephemerides program will be executed. Initially the program explains the results and the calculations thoroughly (only in Spanish version). Press [Enter] the necessary times and introduce the name of the observation town: 'Madrid' (capital always in the initial). Introduce ' 0,0,0 ' in the date (to adapt it at current date), choose ephemerides calculation, and introduce in the following data options marked as 'suggested'. Finally, write the equatorial coordinates of the Sun, the Moon, and the planets for the current instant. Optionally: use the information about times of rising, setting, and culmination of planets, comets, and asteroids to propose objects to observe during next days.

Additional Exercise: After this part the program will show a screen which can be used to calculate planetary ephemerides. Set the date January 1, 2000, 00:00 TT. Then you are free to obtain the RA, DEC, and apparent distance of Mars from Madrid in this date. Use the following orbital elements: a = 1.5236831 UA, l = 6.2267398 rad (mean longitude), e = 0.093317606, l perih = -0.41714137 rad, l node = 0.86501898 rad, i = 0.032286611 rad, julian day reference = 2451547.5. Take in mind that you have to input the argument of perihelium and the mean anomaly: arg p = l perih - l nodo, and mean anomaly is M0 = l - l perih. The result should be: RA: 22h 0m 34.6s, DEC = -13º 19' 22¨, r = 1.8468 UA. The error is 2¨, and the distance r is the one computed before correcting for nutation, because this correction changes the distance to 1.8472 UA, and incorrect value. Follow the method described in the practice of the firmament to correct for nutation. Additional exercise: it is possible to use the ephemerides program to calculate positions of planets, with an error of few seconds of arch. For it optionally you can build a program with the proportionated subroutines, and use the files of the directory ' Efem', to obtain the orbital parameters of all the planets except Pluto. In this files the data of inclination, longitude of the ascending node or longitude of the perihelion appears in radians (if you use Fortran, the appropriate reading format is FORMAT (7(2x, EN14.8)), in the following order: semimajor axis, mean longitude, eccentricity, longitude of perihelion, longitude of the ascending node, and inclination. The data that appears in the seventh and last column is the julian date of reference of these three values that you would also have to use in passing by way of time for the perihelion in the resolution of the equation of Kepler (*). This date goes of year in year between 1700 and 2100, and of 5 in 5 years between -3000 and 1700, and 2100 to 5000. Before beginning to operate in the equation of Kepler you should obtain the mean anomaly in the instant of this date (variable 'M0' in the given program) subtracting the longitude from the perihelion to the mean longitude in the time, as well as the argument of the perihelion (variable 'arg') subtracting the longitude from the ascending node to the longitude of the perihelion. The rest is just as it comes in the listing of the program, in the case of ephemerides of the asteroids, and the margin of error of the result will be of about 2¨ scarce, enough better than the results that it provides the same one with the perturbative terms. (*) The equation of Kepler should be solved using the mean anomaly in passing in the time, the mean daily movement, and the time for the perihelion, so that M = M0 + n (t - t0). In the proposed case the mean anomaly in the time (M0) it is easily to obtain as it is mentioned for the case of the planets, and it should be made this way since its orbital parameters are not referred to the perihelion, but to a given instantaneous date, so that t should be taken as this instant ('perihelion time'), because that of the perihelion is ignored in this case. In the case of the comets with elliptic orbits whose parameters are

habitually refered to the perihelion, it should be used logically M0 = 0 and t like the instant of the facilitated perihelion.

There are some other options in this section no commented previously, such us to obtain the orbital elements of any planet in the nearest available time, to calculate the date in other calendars, to calculate local parameters in the current location, and to calculate ephemerides. The last two options are described now.

The local data will show, under the habitual information of the selected town, diverse parameters frequently used in Astronomy, like they are the julian day number, the mean sidereal time, the difference among the terrestial time TT and the universal time, the mean inclination of the ecliptic, the nutation of the terrestrial axis in ecliptic longitude and latitude, and the equation of time and the equation of equinoxes. As it should be known, one can (and in works of precision it is made this way) to add the equation of equinoxes to the local mean sidereal time to obtain the local and apparent sidereal time, or to be added the nutation in obliquity to the mean inclination to obtain the true obliquity of the ecliptic. The equation of equinoxes is similar to the nutation in right ascension, and it is about a second of time, for what it effect is usually rejected. The equation of time is the difference between the true solar time and the mean solar time, value that oscillates due to the eccentricity of the terrestrial orbit in around +/- 15 minutes. Under this information two graphics will be shown. In the first one the apparent heights of the planets and the Sun appear (in yellow) along the current day (the hours they are shown in the horizontal axis), while in the second are shown the rise curves, culmination (lightly thicker), and setting of the planets along the current year. The shown hours are up from the 17:00 hours TU up to 7:00 TU below. The ephemerides part shows the coordinates of the planets together with multitude of additional information, including perihelion instants, oppositions and conjunctions, etc. The superior graph will show the apparent and current vision of the object from the Earth (understands each other vision 'more or less geocentric', without taking in consideration the height or the paralactic angle this time, and with the north up), and the inferior graph will show a curve that separates the area of the Earth from which is visible that object regarding the area that the object cannot be seen at the moment. The small cross that it will appear represents the geographical position of the Earth such that, of being on it, the object in question would be visible in the zenith direction. It should be noticed that all the calculations in this section, the same as in the rest of the program, are topocentric, so that, for example, to calculate the geocentric instants (also considered as official instants) of the diverse phenomenons the observation town should be changed to the Earth center. It is enough with making 'clic' on the icon of the Earth, then 'clic' on the icon of the hand, and then to introduce 'Center'. In this case, the instants of solstices and equinoxes will belong together with the dice in the news. The instants of lunar perigee, lunar apogee, full and new moon, etc., will be then identical to those of other programs as 'Mooncalc'. The margin of error of this program in any case is not superior to a minute of time in the results.

6. Solar System II. arriba OBJECTIVES: To observe the apparent trajectories of the planets seen from anyone of them. To study oppositions, conjunctions, quadratures, and stationary points. To know the history of the space exploration following the trajectories of the different probes. To identify cases of gravitational assist, and the different types of orbital transfers. BIBLIOGRAPHY: Tomás Elices, Introducción a la Dinámica Orbital, INTA, 1989. DEVELOPMENT: i) Description of the program. Once you select the practice (making 'clic' just under the title, not in the image) the program will present the positions of several objects of the Solar System, the same as the constellations. The superior icons allow to modify the scale, to change the date and the speed of animation, to look for objects, etc. The horizontal arrows allow you to advance or to go back in the time. You can move in ecliptic longitude and latitude puncturing with the mouse in the lateral of the image. You can represent lines on the screen, identify objects, or represent the orbits of the objects by selecting the option in the menu that appears with the right button of the mouse. The comets and visualized asteroids are very few (for not muddling the screen with an excessive number of objects), and they are selected in a concrete way for this practice. When beginning the practice they are visualized the orbits of all the possible objects automatically, with the probes in blue, the comets in white (you will only see the Encke, Pons-Winnecke, and the Halley, up to the left when beginning), the planets of red color, and the asteroids in green. As of habit, you can identify objects pressing the two keys of the mouse. It is advisable again to use the possibility to pulse or to leave pressed a key (as the space bar) as equivalent of making 'clic' with the mouse on the icons to advance or to go back in the time, for example, or to move quickly in ecliptic longitude and latitude. This is quicker and more comfortable than to puncture continually with the mouse. In this practice you can see the elliptic or hyperbolic orbits of almost all the space probes launched up to now, as the Mariner, Pioneer, Venera, Mars, Giotto, Vega, Viking, Voyager, Suisei, Magellan, Galileo, Ulysses, Mars Observer, Mars Pathfinder, Mars Odyssey, Mars Express, and Cassini-Huygens. The probes that will be studied in our case are Ulysses (to study the solar wind in the poles of the Sun), Magellan (Venus), Viking (Mars), Giotto and Vega (Halley comet in its last approach in 1986), Voyager 2 (Jupiter, Saturn, Uranus and Neptune), Galileo, and Cassini. ii) Practice development. The first part of the practice consists on observing the apparent trajectories of the planets seen from any other object of the Solar System. To begin, increase the scale to an appropriate value to see all the possible planets (from Mercury to Jupiter), and go down until an ecliptic latitude next to zero. Select the icon of the clock to modify the speed to a value of 3.0 days, and select to look for the planet Earth with the icon of the glass magnifying (remember always to introduce the initial of the object to look for in capital). After making this the program will ask what object you want to maintain centered (besides the Earth), or, what is the same thing, to what object you want to remain 'looking' while you maintain the Earth centered. Select the Sun like object to center, and observe the movement of the

planets, asteroids, space probes, from the Earth. Repeat this with several planets of the Solar System, modifying appropriately in each case as much the scale as the temporary jump (with the icon of the clock, and maintaining their inferior value to 5 days). Describe the trajectories and their differences insofar as possible. Optionally: observe the Solar System centered in the Earth and check, using information that you obtained in previous practices, the instants of opposition, quadrature, stationary point, and conjunction of external planets and interiors. In the case of the interior planets distinguish among the two types of conjunctions.

Now set an ecliptic latitude of 90º, to see the Solar System from the ecliptic pole. Set the scale in order to see the circle of the ecliptic. Set same date and use the possibility of representing lines on the screen to make a proyection of the position of the planets on the ecliptic, as seen from the Earth. By this you can estimate the geocentric ecliptic longitude of the planets (go from gamma point to the object, in a way similar to a clock). Doing this in sucesive dates you can observe the apparent trayectories of the planets on the sky, by proyecting their positions in the Solar System into the ecliptic. This is what really happen when observing the sky from the Earth. Anyway, this is quite tedious to do. Take in mind that you should make a line with the planet and the Earth. How would you estimate the ecliptic latitude using this? Do it with Pluto. Optionally you can check the results with the Sky practice. You will have to make identifications of the planets when representing the sky in the ecliptic system of coordinates The second part consists on studying the space exploration. Preferably, you can eliminate the visualization of the constellations to increase the speed and softness of the animation. Select to look for and introduce the name of a space probe, for example Galileo (introduce 'Sun' when you are asked by the object to center). Starting from then the program will show the probe Galileo in yellow color, easy to see from all the other ones. If it doesn't appear, then you will change the date to an instant previous to the year 2001 and later to the launching date, in November of 1989. Uses the temporary jump to adapt the speed appropriately. Advance forward from the launching date and observe the maneuvers of gravitational assistance of those that the probe was been good to arrive in Jupiter. Make the same thing with some of the following probes: Magellan (1989/5 from now on), Ulysses (1990/10), Viking (1975/8), Giotto and Vega (1985/7 and 1984/12), Voyager2 (1997/8), and Cassini (1997/10). The object of this part is to identify types of orbital transfers in some of the observed probes. The process of orbital transfer consists on giving a certain impulse (or increment of speed at a short time) to the probe to change the orbit type. It should be distinguished the corrections basically among coplanary orbits and among non coplanary orbits, which also include changes in the orientation of the orbital plane. The transfers between coplanary orbits are of two main types: the transfer between two circular orbits (Hohmann ellipse), in which spends from a distance to another starting from an initial impulse and another impulse at the final distance (necessary to take the probe to the speed required for the new circular orbit), and the transfer among orbits of the circulate-elliptic type. Therefore, you should visualize in the screen the trajectories of some of the mentioned probes, identifying and describing with brevity the cases of transfers that you see, as well as the trajectory that follows the probe. Observe that the necessary impulse rarely takes any expense in fuel (with the exception of the first missions like the Voyager or Pioneer, rushed in times in those that it was not thought about fuel saving), because usually ingenious maneuvers of gravitational assistance are used to impulse the probe during the trip, or other maneuvers as those of air-decelerating in the atmosphere of

the planet in order to circularize the orbit of the probe. The maneuver of gravitational assistance is possibly the most used one. Looks for some attractive case, like the so called VEGA trayectory (Venus-Earth Gravity Assist), in which gravitational assistances of the Earth and Venus are used to send the probe beyond the asteroids belt. Check for more complex cases, as the VVEJGA (Venus-Venus-Earth-Jupiter Gravity Assist) for example.

2. ADDITIONAL EXERCISES arriba It is little less than indispensable to complete the practices here presented of observational astronomy with diverse observation sessions. Next three basic practices are suggested that could be interesting, together with a brief comment. The first practice would go logically guided to the recognition of stars and constellations, being used small portable planispheres and learning how to manage them. It would be convenient to make it just before the practice third, so that the student later on can recognize the constellations in the computer, and to be guided with more easiness. Never in the other way. As report of this practice it could be requested to the students a brief description of the constellations and more important stars that can be observed, a brief description (or at least mention) of those non observables, together with something of mythology for example. The second practice, a couple of weeks after the previous one (in new Moon), would be oriented to preferably visual observation of one or two representative examples of each type of deep sky object, as clusters, nebuloses, or galaxies, if the night allows it. Possible examples in autumn are M 42-3, M 35, M 45, NGC 891, while in spring the objects M 44, M 67, NGC 2903 and M 81-2 could be observed. The practice could require a visual description or even approximate drawing of some of this objects on the part of each group. It is not something really important, but it is worthwhile to make this more than other things, at least once. The third practice, already in growing moon or in full Moon, would consist on observing double stars' examples, the planets that are visible in that moment (Jupiter and Saturn could be seen for some years along the winter and the spring), and, of course, the craters of the Moon. To this respect some interesting exercises could be done with easiness, as measuring the excess of a crater in the terminador with the help of an reticuled eyepiece and then to calculate the size of the crater and the height or elevation of the central pick. Another more interesting exercise would be to observe the lunar formation Rupes Recta or 'Right Wall' (find it in the program by enlarging the Moon in the local sky and selecting to look for). Rupes Recta is a flaw easy to find to the Southwest of Arzachel, visible after the growing moon (with the Moon to 9.0 days of age) not far from the center of the Moon (coordinates 22.1º S, 7.8º W, just next to crater Birt). It extends and it enlarges mainly toward the Southwest, and more secondarily toward the north, from a complex geologic area. Although it is required an instrument and an eyepiece of certain power to observe it with comfort, it is not neither a serious challenge to measure the shade that is projected from this flaw, to determine this way the half difference of the same one, and their longitude on the surface.

3. RELATIONSHIP OF FILES OF THE PROGRAM arriba You can update the asteroids and comets by downloading the appropiate files from Internet. This program uses the most extended format, which is the format that belongs to the commercial program SkyMap. You can also add NOAA archives of solar spots, by downloading them at http://science.nasa.gov/ssl/pad/solar/greenwch.htm. Specially in this last case, before adding the file to subdirectory Sol, you should check that the file does not end with a stranger character (as a rectangle for example). If it is the case, you have to eliminate that character to avoid any problems.

It is not recommended to modify or update any other archive in the program, unless you previously make a back up copy of the file.

All the files, except where another thing is indicated, they have been created or adapted by the author. The directory of the program is composed by the following files. TYPE OF FILE DESCRIPTION Database files. Asters Catalog of asteroids (adapted from 'Skymap'). Asterdim Size in kilometers of the asteroids. Cities Catalog of countries, cities, and geographical positions. Ciudades Spanish version of the previous archive. Cometas Catalog of about 100 comets (adapted from 'Skymap'). Configuracion Configuration File. Conlim Lines of limits of constellations (author: A. C. Davenhall (ROE)). Conlin Lines of contour of constellations in any time. Connom Names of constellations. English Text of the program in English. Español Spanish version of the previous archive. Formas Numeric Data to draw extensive nebula (adapted from 'Skymap'). Luna Lunar Craters (coming from the 'U. S. Geological Survey'). Planetas Orbital elements of planets and other bodies. Objets Reduced and reliable catalog of NGC objects (Adapted from 'Home Planet' and 'Guía del Firmamento'). Objets+ Catalog of 10500 deep sky objects (Adapted from 'Saguaro Astronomy Club Database') Redtass7 Tass1.7 Theory about Saturn's satellites. Sao11,12,13,14 SAO catalog, north hemisphere, 0h-6h,6h-12h,12h-18h,18h-24h. Sao21,22,23,24 SAO catalog, south hemisphere, 0h-6h,6h-12h,12h-18h,18h-24h. Simbolos Symbols of the planets and equinox points. Sondas Orbital data of space probes (Adapted from NASA). Stars Catalog of stars until magnitude 7.0. (Adapted from the 'Bright Star Catalogue' and the 'IRS'). Vialac Catalog of Milky Way limits. Files of images of deep sky objects, in the directory "Imagenes". M[x] / NGC[y]... Images in .bmp format. Files of icons for the program, in the directory "iconos".

Abajo.bmp Lupa.bmp Telescopio.bmp Aceptar.bmp Reloj.bmp Cursor1.cur Arriba.bmp Ojo.bmp Cursor2.cur Cancelar.bmp Parar.bmp Derecha.bmp Tecla.bmp Globo.bmp Mano.bmp Idea.bmp Sol.bmp Info.bmp Tierra.bmp Izquierda.bmp Volver.bmp Luna.bmp Zoom.bmp Files of maps for the planetary and Milky Way textures, in the directory "Texturas" (adapted from David Seal, Björn Jónsson, Axel Mellinger, and James Hastings). Ariel Calisto Caronte Anillosat1-2 Io Europa Ganimedes Anilloura1-2 Jupiter Luna Marte Mat1-11 Hiperion Mimas Neptune Mercurio Oberon Pluton Rhea Saturno Tierra Titan Urano Venus Titania Umbriel Fobos Deimos Tetis Dione Vialac1-5 Files of the Planetary ¨Teoría VSOP87¨, in the directory " Efem " (adapted from BDL): the version ¨VSOP87¨ has been used with elliptic elements to obtain the orbital parameters of all the planets, except the Earth and Pluto. Jupiter Orbital Parameters of Jupiter. Mars Orbital Parameters of Mars. Mercury Orbital Parameters of Mercury. Neptune Orbital Parameters of Neptune. Saturn Orbital Parameters of Saturn. Uranus Orbital Parameters of Uranus. Venus Orbital Parameters of Venus. Vsop87.doc Explanatory document of the Planetary Theory (in English). Pluton Position of Pluto. Pluto.doc Explanatory Document of the theory used in the calculation of Pluto's position. Files of the Lunar Theory ELP2000-82B, in the directory "Efem" (they come from the BDL): the main files, 9 of a total of 36 have been chosen. Elp(1-9) Main files of the theory. Elp2000.doc Explanatory document of the lunar theory (in English).

Files of the sunspots, in the directory "Sol" (they come from the observatory of Greenwich). Gxxxx.txt xxxx is the year between 1874 and 2002.

Files in the subdirectory Eclipses.

Eclipses.txt List of images to be used when representing eclipses. Mapamundi.bmp Map of the whole world.

Europa.bmp Image of Europe region. España.bmp Image of Spain region. Norteamerica.bmp Image of North America. Suramerica.bmp Image of South America. Africa.bmp Image of Africa. Asia.bmp Image of Asia region. Oceania.bmp Image of Australia region.

Files in the subdirectory Observaciones.

Indice.txt List of available subdirectories. Readme.txt Instructions for using real images.

Executable files or of source code of the program. UCM - DEPARTAMENTO DE ASTROFISICA.EXE Program of practices. UCM Version. Configuracion.exe Configuration program. Astr.exe Ephemerides program in fortran (DOS). Astro.exe is the spanih version. Astr.f90 Code of the previous program. Astro.f90 is the spanish version. Eclips.bas Basic code of the program of simplified eclipse prediction. Eclipse.bas is the spanish version of this archive.

Documentation of the program: Practices.doc Document readable with Word from the program (this file). Practicas.doc is the spanish version of the same archive.

4. APPENDIX I: CONSTELLATIONS arriba Next all the constellations are enumerated, with their Latin names, abbreviations, and Spanish names. ANDROMEDA AND Andrómeda LACERTA LAC LagartoANTLIA ANT Neumático LEO LEO LeónAPUS APS Ave del Paraíso LEO MINOR LMI León menorAQUARIUS AQR Acuario LEPUS LEP LiebreAQUILA AQL Águila LIBRA LIB BalanzaARA ARA Altar LUPUS LUP LoboARIES ARI Carnero LYNX LYN LinceAURIGA AUR Cochero LYRA LYR LiraBÖOTES BOO Boyero MENSA MEN MesaCAELUM CAE Buríl MICROSCOPIUM MIC MicroscopioCAMELOPARDALIS CAM Jirafa MONOCEROS MON UnicornioCANCER CNC Cáncer MUSCA MUS MoscaCANES VENATICI CVN Perros de Caza NORMA NOR ReglaCANIS MAJOR CMA Can Mayor OCTANS OCT OctanteCANIS MINOR CMI Can Menor OPHIUCHUS OPH OfiucoCAPRICORNUS CAP Capricornio ORION ORI OriónCARINA CAR Carina PAVO PAV Pavo RealCASSIOPEIA CAS Casiopea PEGASUS PEG PegasoCENTAURUS CEN Centauro PERSEUS PER PerseoCEPHEUS CEP Cefeo PHOENIX PHE FénixCETUS CET Ballena PICTOR PIC PintorCHAMAELEON CHA Camaleón PISCES PSC PecesCIRCINUS CIR Compás PISCES AUSTRINUS PSA Peces AustralesCOLUMBA COL Paloma PUPPIS PUP PopaCOMA BERENICES COM Cabellera de Berenice PYXIS PYX BrújulaCORONA AUSTRALIS CRA Corona Austral RETICULUM RET RetículoCORONA BOREALIS CRB Corona Boreal SAGITTA SGE FlechaCORVUS CRV Cuervo SAGITTARIUS SGR SagitarioCRATER CRT Copa SCORPIUS SCO EscorpiónCRUX CRU Cruz del Sur SCULPTOR SCL EscultorCYGNUS CYG Cisne SCUTUM SCT EscudoDELPHINUS DEL Delfin SERPENS SER SerpienteDORADO DOR Dorado SEXTANS SEX SextanteDRACO DRA Dragón TAURUS TAU ToroEQUULEUS EQU Caballo Menor TELESCOPIUM TEL TelescopioERIDANUS ERI Eridano TRIANGULUM AUSTRALE TRA Triángulo AustralFORNAX FOR Horno TRIANGULUM TRI TriánguloGEMINI GEM Gemelos TUCANA TUC TucánGRUS GRU Grulla URSA MAJOR UMA Osa MayorHERCULES HER Hércules URSA MINOR UMI Osa MenorHOROLOGIUM HOR Reloj VELA VEL VelaHYDRA HYA Hidra VIRGO VIR VirgenHYDRUS HYI Hidra Macho VOLANS VOL Pez VoladorINDUS IND Indio VULPECULA VUL Raposa

5. APPENDIX II: CATALOGS OF DEEP SKY OBJECTS arriba Here is a list of professional catalogs of deep sky objects, used by the program in the third practice (file ¨objets+¨). 3C - catalog of radiosources of Cambridge Abell - George Abell (stellar clusters and planetary nebula) AM - Arp-Madore (globular clusters) Antalova - (open clusters) Ap - Apriamasvili (planetary nebula) Arp - Halton Arp (galaxies in interaction) Auner - (open clusters) Av-Hunter - (open clusters) Bark - Barkhatova (open clusters) B - Barnard (dark nebula) Be - (dark nebula) Basel - (open clusters) BD - Bonner Durchmusterung (you shatter) Berk - Berkeley (open clusters)Bernes - (dark nebula) Biur - Biurakan (open clusters) Blanco - (open clusters) Bochum - (open clusters) Ced - Cederblad (diffuse nebula) Cr - Collinder (open clusters) Czernik - (open clusters) Danks - (open clusters) DDO - David Dunlap Observatory (dwarf galaxies) Do - Dolidze (open clusters) DoDz - Dolidze-Dzimselejsvili (open clusters) Dun - Dunlop (globular clusters) Fein - Feinstein (open clusters) Frolov - (open clusters) Graham - (open clusters) Grasdale - (open clusters) Grindlay - (globular clusters) Gum - (diffuse nebula) H - William Herschel (globular clusters) Haffner - (open clusters) Harvard - (open clusters) Hav-Moffat - (open clusters) He - Henize (planetary nebula, open clusters) Hogg - (open clusters) HP - Haute Provence (globular clusters) Hu - Humason (planetary nebula) IC - 1º and 2º Index Catalogs" (amplification of NGC, all less dark nebula) Isk - Iskudarian (open clusters) J - Jonckheere (planetary nebula) K - Kohoutek (planetary nebula) King - (open clusters) Kr - Krasnogorskaja (planetary nebula) Lac - Lacaille (globular clusters) Latysev - (open clusters) Loden - (open clusters) LDN - Lynds (dark nebula) Liller - (globular clusters)

Lynga - (open clusters) M - Messier (all less dark nebula) Maffei - (dwarf galaxies) Mayer - (open clusters) MCG - "Morphological Catalog of Galaxies" (galaxies according to their form) Me - Merrill (planetary nebula) Mrk - Markarian (open clusters and galaxies) Mel - Melotte (open clusters) Muzzio - (open clusters) M1 to M4 - Minkowski (planetary nebula) NGC - "New General Catalog of Nebulae & Clusters of Stars" (all less dark nebula) Pal - Palomar (globular clusters) PC - Peimbert and Costero (planetary nebula) Pismis - (open clusters) PK - Perek & Kohoutek (planetary nebula) RCW - Rodgers, Campbell, & Whiteoak (diffuse nebula) Roslund - (open clusters) Ru - Ruprecht (open clusters) Sa - Sandqvist (dark nebula) Schuster - (open clusters) Sher - (open clusters) Sh - Sharpless (diffuse nebula) SL - Sandqvist & Lindroos (dark nebula) SL - Shapley & Lindsay (clusters in Magellan's Great Cloud) Steph - Stephenson (open clusters) Stock - (open clusters) Ter - Terzan (globular clusters) Tombaugh - (open clusters) Ton - Tonantzintla (globular clusters) Tr - Trumpler (open clusters) UA - Catalog of selected galaxies doesn't present in the UGC catalogUGC - "Uppsala General Catalog" (galaxies) UKS - United Kingdom Schmidt (globular clusters) Upgren - (open clusters) VV - Vorontsov-Velyaminov (galaxies in interaction) vdB - van der Bergh (diffuse nebula, open clusters) vdBH - van der Bergh & Herbst (diffuse nebula) vdB-Ha - van der Bergh-Hagen (open clusters) Vy - Vyssotsky (planetary nebula) Waterloo - (open clusters) Westr - Westerlund (open clusters) Zw - Zwicky (galaxies)

6. APPENDIX III: CLASSIFICATION OF OBJECTS OF DEEP SKY arriba Diverse classifications of deep sky objects used in the file ¨objets+¨. ----Trumpler classification of open clusters---- Concentration I. Defined, very concentrated in the center II. Defined, quite concentrated III. Defined, without concentration IV. Not very defined due to the stellar field Range of magnitudes 1. small 2. Moderate 3. High Wealth p Poor (<50 stars) m Moderately rich (50-100 stars) r Rich (>100 stars) A " n " continuing to the type of Trumpler denotes cloudiness in the cluster

----Degree of concentration of Shapley-Sawyer for globular clusters---- Value from 1 to 12, from more to less concentrated.

----Types of planetary nebula of Vorontsov-Velyaminov---- 1. Stellar 2. Defined disk (a, brilliant center; b, uniform shine; c, structures almost like a ring) 3. Irregular disk (a, distribution of shine very irregular; b, structures almost like a ring) 4. Annular structure5. Irregular form, similar to diffuse nebula 6. Anomalous form, irregular structure Some combine several classifications. ----Types of galaxies of Hubble---- E Elliptic, E0 are round and E7 the more lengthened or flattened subgrups; 'd' is dwarf, 'c' is supergigant, 'D' has diffuse halo S Spiral, 'a' has closed arms, 'b' has quite open arms, and 'c' has the very open arms (and so on, 'd' ... 'm')SB Spiral with central bar or barredIrr Irregular

7. DEVELOPMENT PROCESS. NEW MODIFICATIONS arriba The project of this program of practices arose for two reasons. The first and main was that I wanted to make some kind of program not excessively complex that could finish in little time (I believed or sought that!), and that it also allowed me to dominate a programming language like Fortran that, without being a marvel, it is better than those languagues I came using up to now, nothing else and anything less than the PowerBasic. Everything with the doubtful possibility of making something quite better in the future (doubtful for the effort that would suppose). The second reason was to create a sufficiently useful program that it could be good for itself for something, and, in this sense, I found a program of practices of observational astronomy the ideal thing, because that I know, no decent program exist exclusively with this type of pretenses, and less still in Spanish. This way I was transforming, developing, and purifying to the maximum diverse algorithms during some weeks, and making tests to see until where I could arrive, because my computer is a Pentium 133 Mhz (that doesn't give to make many marvels) and the language Fortran is sometimes tedious and exasperating with compilation times. After the design corresponding of each practice, and applying the relative experience and the limited knowledge of an effort programmer, fond of the Astronomy and student of Physics, I began the programming process in summer of 2001. The final result is even better of what waited, although the price has been quite expensive, because I would not dare neither to calculate approximately how many thousands of hours I have needed to make this. I hope not to feel the necessity of making something similar again in the future, at least without some help. The idea was clear after speaking with the teacher of this subject in the UCM, Dr. Elisa de Castro, with a preliminary version of what the program would be. I should thank their comments and suggestions to adapt the program the best thing possible to the contents of this subject in the UCM. It supposed to abandon the idea of some practices that I had thought, but that they won't leave very completely, besides the modification of the practice of eclipses. The ephemerides part that had included here was placed by itself as practice fifth, and with optional character. The first practice of calendars was included as practice sixth, and the practice of the heliocentric vision of planets and space probes as practice seventh, both with optional character also. The limitations of time and the priorities of contents forced me to eliminate completely practices that included the three-dimensional vision of the Solar System, besides a very ambitious practice of gravitation that I didn't end up programming. The program finished it therefore with a lot of work and relative speed among the months July of 2001 and April of 2003, due to the use partly of algorithms that it had already developed in other previous programs. The program was developed using Fortran Powerstation 4.0, inside the package Microsoft Developer Studio. I preferred to maintain the original design, sometimes for simplicity and others from necessity, of some sections of the such program as I made them in language Basic and Fortran in old programs. This program of practices finally constituted my project of academic work of fifth course in the orientation of Astrophysics of the Licentiate in Physical Sciences of the Complutense University of Madrid (UCM), titled Simulation of Physical Observations of the Solar System. After a lot to think it, and after several opinion changes, I decided finally that the program should be in the public domain, so anyone can use it. Anyway I didn't hope to become millionaire, because I suppose that there won't be many

Spanish or international universities interested in this program. I should say that it has cost me to make this decision, pleasant for the user and (although you don't believe it) also for me, but I should also leave clear that this program is not go directed to the public in general, but exclusively to schools and universities. NEW MODIFICATIONS

- Versión 1.0 (June, 2003): First version of the program. You can find it in the following web site (UCM, Department of Astrophysics): http://www.ucm.es/info/Astrof/docencia/trab_a_d/Pract_Astro_Obs/Practicas.html

- Version 1.1 (December, 2003): First revision. A lot of bugs corrected.

- Version 1.2 (January, 2004): Second revision, with the following modifications:

Program compiled with Compaq Visual Fortran Professional. Two main advantages: the execution speed is almost four times superior, and the memory problems of the other version have disappeared.

Asteroids, comets, NOAA solar spots (year 2003, update of some others), and NASA probes (Mars Pathfinder, Mars Odyssey, Mars Express, and Cassini-Huygens) archives updated.

Correction of several errors, such as moon texture and eclipse in the sky practice, comets with cuasi-parabolic orbit, the format of the archives of cities and deep-sky objects, and others.

Now you can see different mouse icons, and you can use pop-up messages and menus, so the program is now really very easy to use.

8. REFERENCES arriba Next reference is made to the main files, books, or Internet web sites that have been indispensable in some form to carry out this program. The deserved recognition to all them, mainly to provide in some cases information and valuable programs without spirit of lucre through Internet. Due to the use of algorithms made by the author during years, some references probably will be missing. 1.-Computer program Asterion, Tomás Alonso. 1997-2001. Using part of the below bibliography I made this program of MS-DOS that continues being more precise and complete that this one and that almost any other one that can end up making. Almost five years programming result. 2.-Astronomy with Personal your Computer, Dr. Peter J. Duffett-Smith, 2nd Edition (1992), Cambridge University Press (USA). Programs of eclipses and Moon, all of great quality. Algorithms can be obtained throght Internet. 3.-Astronomical Algorithms, Jean Meeus, Willmann-Bell inc (1992), Virginia (USA). Diverse algorithms, used by programs that I caught on Internet, are based on this work. 4.-Astronomía Enciclopaedia (section astroinformatic). Ediciones Orbis Fabbri (1992), Barcelona (Spain). Several subroutines for the calculation of positions of satellites, comets and asteroids, especially in what refers to physical parameters of observation. The inexpert reader in astroinformatic can begin with this, as I did, although it suits to notice that this work contains numerous typographic errors. 5.-'ftp://ftp.bdl.fr ', Planetary Theory VSOP87 (A&A 202, 309 (1988)), Pluto Tables (A&A Supplement Series, 109, 191 (1995)) & Lunar Semi-Analytical Solution ELP2000-82B (A&A 190, 342 (1988)), M. Chapront, J. Chapront, G. Francou, & P. Bretagnon. Bureau Des Longitudes (Office of Longitudes of Paris). These three theories provide, without place to doubts, the most precise positions of the Moon and the planets to those that a fan can consent, with maximum errors of 1¨ in several millennia. In this program I have used orbital elements among the years -1000 to the 5000, for reasons by speed, but the error rarely overcomes the 5¨. 6.-Alain Vienne, Luc Duriez, TASS1.6: Ephemerides of the major Saturnian satellites, (A&A 297, 588 (1995)). J. Laskar, R. Jacobson, GUST86 - An analytical ephemeris of the Uranian satellites (A&A 188, 212 (1987)). M. Chapront-Touze, Orbits for the Martian satellites from Esapho and Esade Theories (A&A 240, 1, 159 (1990)) 7.-Summary of 1980 IAU Theory of Nutation (Final Report of the IAU Working Group on Nutation), P. K. Seidelmann et all, in Transactions of the IAU XVIII Vol. TO, Reports on Astronomy, P. A. Wayman, ed.; D. Reidel Pub. Co., 1982. 8.-Numerical Expressions for precession formulae and mean elements for the Moon and the planets, J. L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touze ', G. Francou, and J. Laskar. Astronomy and Astrophysics 282, 663-683 (1994). 9.-Recommended values for the direction of the north pole of rotation and the prime meridian of the Sun, planets and satellites, Davies et all, 2000. Information available in the web of the BDL, which also allows to derive the values of the librations of the Moon acceptably.

10.-'ftp://cdsarc.u-strasbg.fr/cats/I '. In this site I obtained the corrected catalog SAOJ2000 (1997), with 260000 stars until magnitude 9.5. I Also obtained the preliminary version of the 'Bright Star Catalog. 5th Edition', with all the information on stars until the sixth magnitude that later on I completed until the seventh magnitude by means of the 'International Reference Star Catalogue' (IRS) and the SAO. I didn't plan to include the SAO in this program, more than anything because it was not necessary, but the temptation could with me. Anyway it's slowness recently useful. 11.-Calendrical Calculations, N. Dershowitz & E. M. Reingold, 1st Edition (1997). Cambridge University Press. Really splendid book to know the secrets of the calendars and the laws that govern them; interesting and well documented, clear notation, and algorithms easy to develop.

12.-Introducción a la Dinámica Orbital, Tomás Elices, INTA (1989). Probably the best and more complete work of the present gender in the library of the UCM, and also in Spanish. Of thanking the quantity of graphics and the easiness to follow the contents. 13.-Guía del Firmamento, José Luis Comellas, 5ª Edition (1996), Rialph, Madrid (Spain). Amplification of the catalog of deep sky objects, with complete information of 850 objects. This book is highly advisable for all those that are interested in beginning in the Astronomy. There is a new edition of the 2001. 14.-'http://www.nasa.gov' (web of the Space Agency of USA). Here I obtained (besides multitude of information and images) the file of space probes (in the Jet Propulsion Laboratory, 1997) that includes their orbital elements. I modified the file to be able to to represent them in the Solar System. 15.-'http://science.nasa.gov/ssl/pad/solar/greenwch.htm'. The whole record of observations of the sunspots of the NOAA is in this web of the observatory of Greenwich. 16.-'http://www.saguaroastro.org' (web of 'Saguaro Astronomy Club', 1998). Database of some 10000 objects of deep sky and other so many double stars. That one of the double perhaps will be added in a future version. The appendixes have also been adapted from the information that appears in this web. 17.-'http://www.skymap.com', Internet site of the commercial computer program SkyMap (2002). In this web I obtained the files of orbital elements of more than 15000 asteroids, and of aproximately a hundred of comets. I have not used them whole to be unnecessary, anyway nobody will complain that 3000 asteroids (until the magnitude limit of approximately 15 or bigger) are few. Both should be updated periodically. 18.-'http://www.maa.mhn.de/Cat/Index.html', complete catalog of limits of constellations, the most complete available, prepared by A. C. Davenhall (1990) in the Royal Observatory of Edinburgh. 19.-'http://maps.jpl.nasa.gov', maps of planetary surfaces of Björn Jónsson and David Seal. I have only used those maps with complete information of the surface of each planet. In some cases, as unfortunately in many satellites or in Mercury, it doesn't still exist a complete topographical map. Pluto, Charon, Mercury, Earth (for eclipses), and Uranus rings images come from James Hastings, in his web site 'http://gw.marketingden.com/planets/planets.html'.

20.-Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants, J. H. Lieske, T. Lederle, W. Fricke, and B. Living, Astronomy and Astrophysics 58, 1-16 (1977). 21.-Contributions to the Earth's obliquity rate, precession, and nutation, James G. Williams, Astron. J. 108, 711-724 (1994). Correction of the classic expression of the precession of Lieske. 22.-Some algorithms from Steve L. Moshier (JPL), to calculate approximate positions of satellites of Mars and Uranus in adjustment for square minima, and other things. Later I improved this using 20th reference. 23.-Mil aspectos de la Tierra y del Espacio, Instituto Gallach (1950). Photographic archives of several observatories, with excellent pictures fom the begining of the last century (many probably taken by Milton Humason and Edwin Hubble in Mount Wilson in the twenties). I Obtained also the orbital period of the satellites of Uranus and Neptune. It doesn't exist a book so well cultured and supplemented in charts and information of all type. 24.-'http://wwwflag.wr.usgs.gov/USGSFlag/Space/nomen/moon/moonTOC.html', complete catalog of craters of the Moon of the U. S. Geological Survey. 25.-'http://www.gsfc.nasa.gov', catalog of eclipses of Fred Spenak, from the Goddard Space Flight Center. 26.-'http://ssd.jpl.nasa.gov/horizons.html', orbital elements of probes, and positions of planetary satellites. With them one can aproximate the orbits of Triton and Charon to circles.

27.-'http://faculty.rmwc.edu/tmichalik/mlkyway.htm', Milky way textures by Axel Mellinger.

28.-'http://user.online.be/felixverbelen/catzeute.htm', 'http://www.phys.uu.nl/homepage.htm', and some other web sites, used as reference and as information font to prepare the eclipse practice.

29.-Practical Ephemeris Calculations, by Oliver Montenbruck. Springer-Verlag, 1989. Thanks to him I resolved my problems about the diverse longitude systems in Saturn.

30.-Programming libraries MSFLIB, PORTLIB, USER32 and programming modules 'bitmap.f90', 'descriptor.f90', and 'cursor.f90'. (c) 1995 Microsoft Corporation. Congratulations by the way to Microsoft for the great program Fortran Powerstation 4.0. This version is compiled with Visual Fortran Professional.

9. ADDITIONAL REFERENCES arriba The following references have been used to improve the precision in diverse algorithms, and information of them has also been obtained. 1.-Program 'planetary surfaces', developed previously to the program of practices by the author to check the viability of representing planetary textures. In spite of the slow that it works, I believe that it is a good incorporation to the program, following my ideology that the more visual and realistic, better. Also, I have never seen a program that makes this kind of things, even with the proyections of the satellites of Saturn, Uranus, and Pluto. 2.-Photographic archive of the author. The most recent pictures that I took of some objects, some pictures taken by students at UCM-OAN Observatory, as well as select part of photographic files of some observatories (with very interesting and valuable pictures from the begining of the last century), have also been included in diverse sections of the program. In a hypothetical future revision perhaps cheer up to put many more. 3.-'http://www.starlight.demon.co.uk/mooncalc'. Mooncalc Program, by Dr. Monzur Ahmed. With it I proved diverse algorithms related with the Moon. 4.-'ftp://ftp.bdl.fr'. Several programs (Planeph and Satel13e.exe) of the Office of Longitudes of Paris, related with the positions of the planets and their satellites, used especially as checkup and to improve the positions of the satellites of Uranus. Also, I used it to check the instants of transits of satellites and their shades in Jupiter. 5.-'http://www.Homeplanet.com'. HomePlanet Program, by John Walker. From this program I obtained some information about deep sky objects.

10. LEGAL WARNING arriba This program is protected by the law. This implies that the program is not freeware, and can only be distributed without any modification. Equally, it is forbidden their use outside of the terms settled down by the author, which reduce the use only to home users, or teachers and students in a teaching classroom of practices of astronomy (with the author's previous authorization). In a same way, it is absolutely forbidden all modification of anyone of the files of the program, except configuration archives (files cities, configuracion, and eclipses.txt). The use of information or graphics from the program for any propose should be specified with clarity, mentioning the program and its author. The programmer doesn't assume any responsibility about the precision or validity of the algorithms used. Equally, neither it assumes responsibility about any problem that could arise as consequence of the use of the program, although that the source code of the same one has been desined with as care as possible. For a good operation of the program it is recommended to use a computer with processor Pentium 300 MHz, 64 MBytes of RAM, 70 MBytes of free space in the hard disk, and operating system Windows 2000. Due to the administration of virtual memory of Windows it can be necessary to have more hard disk space free, mainly if it is executed this and other programs at the same time in computers not very powerfull, in which case it could arise some problems. When this program is used in those circumstances it is advisable not to maintain executed neither in memory any other program at the same time. Any comment, suggestion, or error report will be thanked by the author with the objective of to improve and to enlarge possible future revisions of the program.

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PRACTICES ON OBSERVATIONAL ASTRONOMY (UCM 1.0 Version)Copyright (c) Tomás Alonso Albi, 2001-2003. All rights reserved.

Contact with the author in the following e-mail addressE-mail: talonsoalbi@wanadoo.es

Revised by last time on Thrusday, January 1, 2004.33000 code lines (1.1 MBytes). 80 Mbytes in size.