Watch, When, and WhereWatch, When, and Where

Or Universal Time, Julian Date, Or Universal Time, Julian Date, and Celestial Coordinates.and Celestial Coordinates.

OverviewOverviewWhat are the things you need to What are the things you need to know in order to give a location of know in order to give a location of

the origin of a cosmic ray?the origin of a cosmic ray?

Universal TimeUniversal Time Julian DateJulian Date Local CoordinatesLocal Coordinates

Watch:Watch:UNIVERSAL TIMEUNIVERSAL TIME

Universal TimeUniversal Time The times of various events, particularly astronomical and weather The times of various events, particularly astronomical and weather

phenomena, are often given in "Universal Time" (abbreviated phenomena, are often given in "Universal Time" (abbreviated UTUT) which ) which is sometimes referred to, now colloquially, as "Greenwich Mean Time" is sometimes referred to, now colloquially, as "Greenwich Mean Time" (abbreviated (abbreviated GMTGMT).).

When a precision of one second or better is needed, however, it is When a precision of one second or better is needed, however, it is necessary to be more specific about the exact meaning of UT. For that necessary to be more specific about the exact meaning of UT. For that purpose different designations of Universal Time have been adopted. In purpose different designations of Universal Time have been adopted. In astronomical and navigational usage, UT often refers to a specific time astronomical and navigational usage, UT often refers to a specific time called UT1, which is a measure of the rotation angle of the Earth as called UT1, which is a measure of the rotation angle of the Earth as observed astronomically.observed astronomically.

However, in the most common civil usage, UT refers to a time scale However, in the most common civil usage, UT refers to a time scale called "Coordinated Universal Time" (abbreviated called "Coordinated Universal Time" (abbreviated UTCUTC), which is the ), which is the basis for the worldwide system of civil time. This time scale is kept by basis for the worldwide system of civil time. This time scale is kept by time laboratories around the world, including the U.S. Naval Observatory, time laboratories around the world, including the U.S. Naval Observatory, and is determined using highly precise atomic clocks.and is determined using highly precise atomic clocks.

UTC and Local TimeUTC and Local Time UTC is the time distributed by standard radio stations that UTC is the time distributed by standard radio stations that

broadcast time, such as WWV and WWVH. It can also be broadcast time, such as WWV and WWVH. It can also be obtained readily from the Global Positioning System (GPS) obtained readily from the Global Positioning System (GPS) satellites.satellites.

Countries lying on meridians east or west of the Greenwich Countries lying on meridians east or west of the Greenwich meridian do not use GMT as their local civil time. It would meridian do not use GMT as their local civil time. It would obviously be impractical to do so as the local noon, the time obviously be impractical to do so as the local noon, the time at which the sun reaches its maximum altitude, gets earlier or at which the sun reaches its maximum altitude, gets earlier or later with respect to the local noon on the Greenwich later with respect to the local noon on the Greenwich meridian.meridian.

To avoid confusion, the world is divided into time zones, each To avoid confusion, the world is divided into time zones, each zone corresponding to a whole number of hours before or zone corresponding to a whole number of hours before or after UT. This time is known as your local time.after UT. This time is known as your local time.

Conversion to UTCConversion to UTCIt is often convenient in making astronomical calculations to It is often convenient in making astronomical calculations to use UT and local time may be converted into UT in the use UT and local time may be converted into UT in the following manner.following manner.

Local Time = Universal Time - 6 hr (central standard time)Local Time = Universal Time - 6 hr (central standard time) - 5 hr (central daylight time)- 5 hr (central daylight time)

Local Time = Universal Time - 7 hr (mountain standard time)Local Time = Universal Time - 7 hr (mountain standard time) - 6 hr (mountain daylight time)- 6 hr (mountain daylight time)

When: When: JULIAN DATEJULIAN DATE

The Julian timelineThe Julian timeline Julian dates (abbreviated JD) are simply a continuous count of Julian dates (abbreviated JD) are simply a continuous count of

days and fractions since noon Universal Time on January 1, 4713 days and fractions since noon Universal Time on January 1, 4713 BCE (on the Julian calendar). Almost 2.5 million days have BCE (on the Julian calendar). Almost 2.5 million days have transpired since this date. Julian dates are widely used as time transpired since this date. Julian dates are widely used as time variables within astronomical software.variables within astronomical software.

Calendar dates — year, month, and day — are more problematic. Various Calendar dates — year, month, and day — are more problematic. Various calendar systems have been in use at different times and places around calendar systems have been in use at different times and places around the world. Primarily there are two calendars: the Gregorian calendar, now the world. Primarily there are two calendars: the Gregorian calendar, now used universally for civil purposes, and the Julian calendar, its predecessor used universally for civil purposes, and the Julian calendar, its predecessor in the western world.in the western world.

Sometimes the modified Julian date, MJD, is quoted. This is equal to the Sometimes the modified Julian date, MJD, is quoted. This is equal to the JD - 2 400 00.5; MJD zero therefore began at 0h on November 17th JD - 2 400 00.5; MJD zero therefore began at 0h on November 17th 1858.1858.

Conversion to Julian DaysConversion to Julian DaysThe Julian date of any day in the Julian calendar may be found by the The Julian date of any day in the Julian calendar may be found by the method below.method below.

√ Set y= year, m = month and d = daySet y= year, m = month and d = day√ If m = 1 or 2 subtract 1 from y and add 12 to mIf m = 1 or 2 subtract 1 from y and add 12 to m√ Calculate A= integer part of y/100; B = 2 - A+ integer part of Calculate A= integer part of y/100; B = 2 - A+ integer part of (A/4)(A/4)√ Calculate C = integer part of 365.25 • yCalculate C = integer part of 365.25 • y√ Calculate D = integer part of 30.6001 x (m + 1)Calculate D = integer part of 30.6001 x (m + 1)√ Find JD = B + C + D + d +1720994.5Find JD = B + C + D + d +1720994.5

Example: Calculate the Julian date for February 17.25, 1985.Example: Calculate the Julian date for February 17.25, 1985.y=1984, m=14, d=17.25, A=19, B=-13, C= 724656, D = 459y=1984, m=14, d=17.25, A=19, B=-13, C= 724656, D = 459JD = 2446113.75JD = 2446113.75

Where:Where:ASTRONOMICAL ASTRONOMICAL COORDINATESCOORDINATES

Types of CoordinatesTypes of Coordinates

Topocentric System Topocentric System (Altitude and Azimuth)(Altitude and Azimuth)

Equatorial System Equatorial System (Right Ascension and Declination)(Right Ascension and Declination)

Galactic System Galactic System (Galactic Latitude and Longitude)(Galactic Latitude and Longitude)

Viewing the SkyViewing the Sky

Actual Distance and ViewActual Distance and View

Topocentric (Horizon) SystemTopocentric (Horizon) System

Azimuth (A)Azimuth (A) This is the direction of a This is the direction of a

celestial object, celestial object, measured clockwise measured clockwise around the observer's around the observer's horizon from north. So horizon from north. So an object due north has an object due north has an azimuth of 0°, one an azimuth of 0°, one due east 90°, south due east 90°, south 180° and west 270°. 180° and west 270°. Azimuth and altitude Azimuth and altitude are usually used are usually used together to give the together to give the direction of an object in direction of an object in the topocentric the topocentric coordinate system. coordinate system.

Topocentric SystemTopocentric System

Altitude (h)Altitude (h) The angle of a The angle of a

celestial object celestial object measured upwards measured upwards from the observer's from the observer's horizon. Thus, an horizon. Thus, an object on the horizon object on the horizon has an altitude of 0° has an altitude of 0° and one directly and one directly overhead has an overhead has an altitude of 90°. altitude of 90°. Negative values for Negative values for the altitude mean that the altitude mean that the object is below the object is below the horizon.the horizon.

Equatorial (Celestial) Equatorial (Celestial) CoordinatesCoordinates

The term "Celestial Sphere" The term "Celestial Sphere" describes the appearance of the describes the appearance of the nighttime sky. The stars revolve nighttime sky. The stars revolve in in diurnal rotationdiurnal rotation without without changing their positions relative changing their positions relative to one another. Because our to one another. Because our eyes are not sensitive to the eyes are not sensitive to the varying "distance of the stars" varying "distance of the stars" away from us, the stars appear away from us, the stars appear to lie all at the same large to lie all at the same large distance away. This leads to the distance away. This leads to the concept of the sky and stars as a concept of the sky and stars as a sphere concentric with the earth sphere concentric with the earth and rotating around it. This and rotating around it. This apparent rotating sphere apparent rotating sphere carrying the stars on its surface carrying the stars on its surface is known as the Celestial Sphere.is known as the Celestial Sphere.

Equatorial CoordinatesEquatorial Coordinates

Right Ascension (Right Ascension ()) In the sky with right ascension In the sky with right ascension

(celestial longitude) we need (celestial longitude) we need some point to play a similar role some point to play a similar role to that of Greenwich, England to that of Greenwich, England for terrestrial longitude. for terrestrial longitude. Astronomers have chosen the Astronomers have chosen the Vernal EquinoxVernal Equinox to define the to define the starting point for the starting point for the measurement of right measurement of right ascension. The Vernal Equinox ascension. The Vernal Equinox is the point where the sun is the point where the sun appears to cross the Celestial appears to cross the Celestial Equator at the beginning of Equator at the beginning of spring.spring.

Equatorial CoordinatesEquatorial CoordinatesDeclination (Declination ())

Declination works on the surface Declination works on the surface of the Celestial Sphere much like of the Celestial Sphere much like latitude does on the surface of the latitude does on the surface of the earth, that is, declination earth, that is, declination measures the angular distance of measures the angular distance of a celestial object north or south of a celestial object north or south of the Celestial Equator. Lines of the Celestial Equator. Lines of declination are analogous to declination are analogous to parallels of latitude on the earth. parallels of latitude on the earth. An object lying on the Celestial An object lying on the Celestial Equator has a declination of 0°. Equator has a declination of 0°. The declination increases as you The declination increases as you move away from the Celestial move away from the Celestial Equator to the Celestial Poles. At Equator to the Celestial Poles. At the North Celestial Pole therefore, the North Celestial Pole therefore, the declination is + 90°.the declination is + 90°.

Galactic CoordinatesGalactic Coordinates Here the fundamental line is Here the fundamental line is

the galactic circle, a great circle the galactic circle, a great circle represented by the course of represented by the course of the “Milky Way”. The galactic the “Milky Way”. The galactic circle or equator, intersects the circle or equator, intersects the celestial equator at an angle of celestial equator at an angle of about 63 degrees. about 63 degrees. Galactic Galactic longitude (longitude (l)l), is measured from , is measured from the center of the galaxy, the center of the galaxy, eastward along the galactic eastward along the galactic equator. equator. Galactic latitude (Galactic latitude (b)b), , is measure on the great circle is measure on the great circle through the object and the through the object and the galactic pole, and counted galactic pole, and counted north (+) or south (-) with north (+) or south (-) with respect to the galactic equator.respect to the galactic equator.

Referencing - Horizon ViewReferencing - Horizon View

This is an image of This is an image of

the night skythe night sky looking directly looking directly south from Lincoln. south from Lincoln. In the middle of the In the middle of the image is the object image is the object M-4, a globular M-4, a globular cluster in Scorpius. cluster in Scorpius. This is how the This is how the observer would see observer would see the cluster relative the cluster relative to the horizon at to the horizon at 10:15 PM on July 5, 10:15 PM on July 5, 2001.2001.

What would be its What would be its azimuth and azimuth and altitude?altitude?

M-4

SSWSE

Az 180 ° Alt 30°

Referencing - Horizon and Equatorial ViewReferencing - Horizon and Equatorial View

This view shows This view shows the same image the same image as before but as before but with the with the addition of the addition of the equatorial grid equatorial grid overlayed on overlayed on the horizon the horizon view. view.

What is M-4’s What is M-4’s Right Ascension Right Ascension and and Declination?Declination?

M-4

16 h 30 m-23°

Referencing - Equatorial and Galactic ViewReferencing - Equatorial and Galactic View

This view shows This view shows the horizon the horizon removed and removed and the equatorial the equatorial aligned with the aligned with the celestial celestial equator. The equator. The galactic system galactic system has been has been inserted over inserted over the equatorial the equatorial system.system.

What is M-4’s What is M-4’s Galactic Galactic longitude and longitude and latitude?latitude?

M-4

350°+20°

Referencing - Galactic ViewReferencing - Galactic View

This view This view shows only the shows only the galactic galactic system. Notice system. Notice how the center how the center of the galaxy of the galaxy runs along the runs along the galactic galactic equator line.equator line.

M-4

Referencing - Galactic SkyReferencing - Galactic Sky

This view shows This view shows the galactic system the galactic system projected for the projected for the entire sky. The entire sky. The galactic poles are galactic poles are at the top and at the top and bottom of the bottom of the image.image.

Referencing - Equatorial SkyReferencing - Equatorial Sky

This view shows This view shows the the galaxy the the galaxy projected onto the projected onto the equatorial system. equatorial system. The celestial poles The celestial poles are at the top and are at the top and bottom.bottom.

Referencing - Horizon SkyReferencing - Horizon Sky

This view shows This view shows the the galaxy the the galaxy projected onto the projected onto the horizon system.horizon system.

Equatorial to Galactic Coordinate ConversionEquatorial to Galactic Coordinate ConversionIn previous pictures you should have noticed that all of the In previous pictures you should have noticed that all of the coordinate systems are based on spheres. Conversion from one coordinate systems are based on spheres. Conversion from one system to another is based on the use of spherical trigonometry.system to another is based on the use of spherical trigonometry.

The set of equations below forms The set of equations below forms the basis of spherical trigonometry, the basis of spherical trigonometry, which governs, amongst other which governs, amongst other things, the change in coordinates things, the change in coordinates consequent upon a rotation of the consequent upon a rotation of the axes. The equations are useful axes. The equations are useful when the angles are less than when the angles are less than 180º, and the sides of the figures 180º, and the sides of the figures are formed from arcs of great are formed from arcs of great circles.circles.

cos cos aa = cos = cos bb cos cos cc + sin + sin bb sin sin cc cos A cos A sin sin aa /sin A = sin /sin A = sin bb / sin B = sin / sin B = sin cc / sin C / sin C sin sin aa cos B = cos cos B = cos bb sin sin cc - sin - sin bb cos cos cc cos A cos A

Equatorial to Galactic Coordinate ConversionEquatorial to Galactic Coordinate Conversion

In order to list a cosmic rays origin in galactic coordinate In order to list a cosmic rays origin in galactic coordinate you must know its equatorial coordinates. The you must know its equatorial coordinates. The conversion formulas are:conversion formulas are:

bb = sin = sin-1-1{cos {cos cos (27.4) cos ( cos (27.4) cos ( - 192.25) + sin - 192.25) + sin sin (27.4)} sin (27.4)}

ll = tan = tan-1-1{(sin {(sin - sin - sin bb sin (27.4))/ cos sin (27.4))/ cos sin ( sin ( - 192.25) cos (27.4)} + 33 - 192.25) cos (27.4)} + 33

The numbers come from the following facts about our The numbers come from the following facts about our Galaxy: north galactic pole coordinates Galaxy: north galactic pole coordinates = 192º 15’, = 192º 15’, = 27º 24’; ascending node of galactic plane on celestial = 27º 24’; ascending node of galactic plane on celestial equator equator ll = 33º. These are 1950.0 coordinates. = 33º. These are 1950.0 coordinates.

Equatorial to Galactic Coordinate ConversionEquatorial to Galactic Coordinate Conversion

Example: What are the galactic coordinates of a star Example: What are the galactic coordinates of a star whose right ascension and declination are a = 10 h 21m whose right ascension and declination are a = 10 h 21m 00s and d = 10º 03’ 11”?00s and d = 10º 03’ 11”?

bb = sin = sin-1-1{cos {cos cos (27.4) cos ( cos (27.4) cos ( - 192.25) + sin - 192.25) + sin sin (27.4)} sin (27.4)}

ll = tan = tan-1-1{(sin {(sin - sin - sin bb sin (27.4))/ cos sin (27.4))/ cos sin ( sin ( - 192.25) cos (27.4)} + 33 - 192.25) cos (27.4)} + 33

bb = 51.122268º or 51º 07’ 20” = 51.122268º or 51º 07’ 20” l l = 232.247874 or 232º 14’ 53”= 232.247874 or 232º 14’ 53”

Additional ConversionsAdditional Conversions

Horizon

Equatorial

GalacticEcliptic

Universal Time

Good Source and More…..Good Source and More…..

Practical AstronomyWith Your Calculator

ByPeter Duffett-Smith