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    Nature of the Universe

    Chapter 1

    Units in Astronomy

    We introduce the basic measuring units used by astronomers. Length, measured in meter (m),and time, measured in year (yr) or second (s), are familiar to us. The angular size, measured indegrees () or arc seconds, which is very important in astronomy, is not commonly used ineveryday life.

    Length Scales

    Size does matter. The sizes of various astronomical objects are usually so big that we don't haveany feeling about them. Here we list the length scales of some typical objects. You can see that,for example, the ratio of the size of our Sun to the size of the Earth is about the ratio of the sizeof a human to the size of a bee.

    Length(m) Object

    > 10 26 Size of the universe

    1026 Distance to quasars ( Here is one of the most famous quasars, 3C273 . Courtesy NOAO/NSF .)

    1024 Size of a typical cluster of galaxies ( One example of galaxy cluster, near 3C324 .Courtesy STScI .)

    1021 Galaxies ( A typical galaxy, M31 . Courtesy NASA .)

    1018 Globular clusters ( A typical globular cluster, M80 . Courtesy STScI .)

    1016 Nebula (clumps of gas and dust) ( The Horsehead Nebula ,(C) Anglo-Australian Observatory and

    Photograph by David Malin .), light year

    1013 The solar system

    109 The Sun

    107 The Earth

    106

    Great Wall102 Buildings

    100 Basic unit of distance, humans

    10 -2 Coins, bees, bugs

    10 -4 Diameters of hairs

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    10 -5 Red blood cells

    10 -6 Bacteria

    10 -7 Viruses

    10-8

    Macromolecules10 -9 Micromolecules

    10 -10 Atoms

    10 -14 Nuclei, protons, neutrons

    T ime Scales

    What is the age of our universe and how does it compare to the average life span of a human being?

    Long time ago T here was

    1.4x10 10 yrs Creation of the universe

    1010 yrs Formation of galaxies

    4.6x10 9 yrs Formation of the solar system

    3x10 9 yrs Appearance of unicellar life

    6x10 8 yrs Cambrian era (fossils of complex, hard-bodied animals)

    0.65-2.5x10 8 yrs Dinosaurs

    3x106

    yrs Early hominids (mammals fossils)3x10 5 yrs Appearance of homosapiens (the first real "human")

    5x10 3 yrs Beginning of written human history

    102 yrs Life span of a typical human

    1 yr Earth orbiting once around the Sun

    1 day Life span of some insects

    1 hour Time span of this lecture

    10 seconds Time to read this sentence

    10 -17 seconds Time for light to travel across an atom

    Angular Measures

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    Objects look bigger when they are closer to us. If the distance between an object and theobserver is halved, the apparent size of the object will be doubled. The apparent size or theangular size of the object is the angle sustained by it.

    A full circle has 360 degrees (). One degree equals 60 arc minutes (') and one arc minute

    equals 60 arc seconds (''). The angular size of the Moon viewed from the Earth is about 0.5.

    1= 60', 1'= 60''

    Usually, if an adult has longer arms, he or she will have bigger hands. Thus, the angle sustained by, for example, the fists when we stretch out our arms is about the same for every person. Thus,we can use our hands to measure roughly the angular sizes of various objects.

    At arm's length, the angular size of our fists is about 10, fingers is about 1 and the tip of thethumb to the tip of the little finger of an extended hand is about 20. Note that the Moon is"smaller" than the finger.

    Nature of the Universe

    Chapter 2

    Motions of Heavenly Bodies

    In this chapter, we will discuss the apparent motion of the heavenly bodies. We will understandwhy the Sun, the Moon and the planets "move," but stars do not.

    Motion of Stars

    Everyone knows that the Sun rises from the east and sets in the west. Less well known is thatalmost everything on the sky, including the Moon, planets and most of the stars, also rises from

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    the east and sets in the west. This is the major movement of objects on the sky and it is due to therotation of the Earth.

    We could imagine that the Earthis at the center of a large sphere,

    called the celestial sphere ; andthe Sun, stars, etc. are locatedon the sphere. Because theEarth is rotating from the westto the east, everything on thecelestial sphere will apparentlymove from the east to the west.This is why the Sun rises fromthe east.

    From the picture, we can see

    that those stars near the northcelestial pole never set. We callthem circumpolar stars . Oneof the circumpolar star, called Polaris , is special because it is very near the north celestial pole.Thus, it appears to be stationary.

    The position of Polaris relative tothe ground depends on the latitudeof the observer. For example, for

    people in Hong Kong, Polaris will

    be about 22.4 above the grounddue north.

    Similarly, some stars never rise.People in the northern hemispherecan never see stars near the southcelestial pole, and people on thesouthern hemisphere can never seePolaris. Poor southerners, there isno bright star near the south celestial pole.

    Here are three simulations of what can be seen in the northern hemisphere. The first one is pointing to the north. (Note that Polaris does move a little bit.) The second and the third show themotions of other stars at south and the east respectively.

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    Motion of the Sun

    Stars do not move on the celestial sphere. They are fixed. Thus, if we throw away the rotation of the Earth, stars are stationary. (Note: The truth is that some stars do move on the celestial sphere.We call this the proper motion of stars. Usually, proper motion of a star is very small and canonly be detected if we observe the star for decades.)

    There is one important exception however. The Sun is also a star, but the Sun does move on thecelestial sphere because the Earth revolves around it. It moves from west to east, and completes afull circle in a year. The path that the Sun traces out on the celestial sphere is called the ecliptic

    and the twelve constellations that the Sun goes through are the zodiac . (Note: Ecliptic does alsogo through the constellation Ophiuchus, but due to historical reason, it is not included in thezodiac.) These are the origin of zodiac in astrology. Contrary to common belief, the Sun does not spend equal time on each ecliptic constellation.

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    Question: What is a day?Answer: Most people will define a day as the time the Sun comes back to the same positionrelative to the ground, for example, from one midday to another. This is exactly how the sundialworks. This defines the solar day . There is another less common definition. We call it a day if other stars come back to the same positions. This is the sidereal day . Due to the revolution of theEarth, a solar day is longer than a sidereal day. Approximately, a year has 365 solar days but 366sidereal days. Do you know why?

    We say "approximately" because a year has 365.2422 solar days. To compensate the extra0.2422 days, some years will have 365 days while some years, called leap years , will have 366days. One extra day is added to the end of February every four years. By doing this, we are

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    adding too much. Hence, this extra day will not be added every hundred years, and it will beadded again every four hundred years. For example, we have February 29 in the years 1988,1992, 1996, 2000, 2400, 2800, etc., but there will be no February 29 in the years 1997, 1998,1999 and 1800, 1900, 2100, 2200, etc. This is called the G regorian calendar . Using Gregoriancalendar, the error accumulated in the next 3000 years will not be more than 1 solar day.

    The apparent motion of the Moon is similar. The time between successive full Moons is thesynodic month , it is 29.5 days long. Note that the Chinese calendar is based on both the motionsof the Moon and the Sun, not just the Moon.

    We have not done with the Sun yet. Since the rotational axis of the Earth is tilted from therevolution axis by 23.5, the Sun, for example, rises at different directions at different timesduring the year.

    Similar to the equator on Earth, we have the celestial equator on the celestial sphere. Theecliptic will intersect the equator with an angle 23.5. The two intersection points are the vernalequinox and autumnal equinox . The two points on the ecliptic which are farthest away from theequator are the summer solstice and winter solstice . Usually, the Sun passes through vernalequinox, summer solstice, autumnal equinox and winter solstice on March 20, June 21,September 23 and December 22 respectively. When the Sun is at the summer solstice, it shinesabove the northern hemisphere. The northern hemisphere will receive more sunlight and becomehotter, hence the summer for the northern hemisphere. Note that in southern hemisphere, it iswinter when the Sun is at summer solstice.

    When the Sun is at the summer solstice, it rises at the northern most point and when it is at thewinter solstice, it rises at the southern most point. That's why we have long daylight and shortshadow in summer while the opposite in winter.

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    T he Basic of Stars SpectroscopySpectroscopy is a branch study in astronomy that focus on astronomical objects spectrum. Fromthe spectrum, we can get informations, such as its temperatures, chemical compositions,

    movement speed, etc. Thats why spectroscopy can be considered as one of the fundamental fieldin astronomy. The spectrum of a star (or any other astronomical object) is acquired by using aninstrument called spectrograph.

    Fig 1. Spectrum

    Fig 2. Spectrograph

    One of the fundamental law in spectroscopy is Kirchoff Law (1859) which stated that:

    1. If a liquid or high pressure gas is ignited, they will emit energy in all wavelength whichwill produce a continuous spectrum .

    2. If a low temperature gas is ignited, it will only emit energy in certain range wavelength

    and produce spectrum which have a dark background and some bright lines. That kind of spectrum is called the emission spectrum. T he wavelength of each bright lines are theprecise indicator of what gas that produce them. So, the same gas will producebright lines in certain exact wavelength.

    3. If a white light (which is a equal mixture of all colors) is passed through a cool lowtemperature gas, the gas will absorb energy at certain wavelength. The result spectrumwill be continuous spectrum as the background with some dark lines in certain exactwavelength. The dark lines called absorption lines and that kind of spectrum is called the

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    absorption spectrum. T he wavelength of each dark lines are the precise indicator of what gas that produce them. So, the same gas will produce dark lines in certainexact wavelength.

    Fig. 3 & 4. Continuous, emission and absorptionspectrum (respectively)

    Balmer Series Switzerland scientist, Balmer, state a series equation to predict the wavelength of the absorptionlines of hydrogen gas. The equation is widely known as Balmer series equation.

    Nature of the Universe

    Chapter 3

    Celestial Sphere and Star Atlas

    We will talk more about the celestial sphere and how to tell the positions of the stars in the sky.We will also introduce the constellations and the star atlas.

    Celestial Sphere

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    When we look at the sky, it is difficult to tell how far the stars are. It seems that all the stars lieon a "flat" surface. A similar situation is watching television, the screen of the televisionrepresents the three dimensional world.

    The sky "surrounds" us from all directions. We placed ourselves at the center of an imaginarysphere, the celestial sphere . Everything on the sky will appear on the celestial sphere.

    As mentioned in the last chapter, the celestial sphere does not follow the rotation of the Earth.Thus, stars are fixed on the celestial sphere.

    We need a coordinate system to tell the positions of the stars on the celestial sphere. It is verysimilar to the longitude and latitude on the Earth surface. The projection of the rotational axis of the Earth marks the north celestial pole and the south celestial pole . The celestial equator is

    just the projection of the Earth's equator.

    The declination , similar to the latitude, runs from +90 or 90N, at the north celestial pole, to -90 or 90S at the south celestial pole.

    The right ascension is different fromthe longitude. Instead of running from -180 to +180 like the longitude, theright ascension runs from 0 hour to 24hours from west to east. Each hour has60 minutes and each minute has 60seconds , just like the clock. (Note:These minute and second are NOT equalto the arc minute and arc second

    introduced earlier. Do you know thedifferences?) The starting point of theright ascension is at the vernal equinox.Recall that vernal equinox is one of thetwo intersection points of the celestialequator and the ecliptic.

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    Remarks:

    1. The celestial north does not equal to the magnetic north to which the compass points. (Infact, the difference between the directions of celestial and magnetic north depends on the

    position of the observer.)

    2. Like a spinning top, the rotational axis of the Earth is not fixed in space. It will move in acircle with a period about 26000 years. We call this the precession . Therefore, the vernalequinox and the pole star will change in time. To be precise, we have to mention the time,for example, year 2000.0, when we talk about the celestial coordinate system. We willnot go into the details.

    ConstellationsThe ancient people used their imaginations to create patterns and stories of the stars. These

    patterns become the constellations . Each culture had its own constellations and stories. Before1930, constellations were regions in the sky with only fuzzy boundaries. In that year, theInternational Astronomical Union put the scheme of constellations on a definite system. The skywas officially divided into 88 constellations with sharp boundaries, and each star is in one andonly one constellation.

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    Some important constellations are, for example, the zodiac. Zodiac are the constellations that theecliptic passes through. (Ophiuchus is not one of the zodiac, see Chapter 2 .) Note that it isaround January when the Sun is in Sagittarius, and in the evening, we will see Taurus andGemini, etc. They are called the winter constellations. Similarly, we will see other constellationsin other seasons.

    Star Atlas

    When we use an ordinary map, we do something like this:

    But when we use a star map, we have to lie down and look up. Thus, the east and the west are"reversed."

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    There are many kinds of star atlas. The following is taken from the Hong Kong Space Museum .This shows the whole sky visible at some particular time. Lines connecting the stars are drawn tomake the constellations more "visible." A bigger dot does not represent a larger star, it representsa brighter star. We will talk about stellar brightness later.

    Courtesy Hong Kong Space Museum .

    Just to let you have an idea of what a serious star atlas looks like, the most detailed star atlas on paper nowadays is similar to the atlas below. This figure covers the area bounded by the redcircle in the above all sky map.

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    Previous chapter . Next chapter .

    Title page .

    Motions of Planets

    To ancient people, planets were "stars" that moved on the celestial sphere. Actually, they move because they also orbit around the Sun. There are eight major planets: Mercury, Venus, Earth,Mars, Jupiter, Saturn, Uranus and Neptune, and many dwarf planets and minor planets.

    Mercury and Venus are inferior planets because their orbits are inside the orbit of the Earth.Thus, when watching from the Earth, they are never too far away from the Sun. They just swingfrom the east of the Sun to the west and back, and we can only see them just before sunrise or

    just after sunset. During the period that we can see them before sunrise, we call them the

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    "morning stars." It lasts for many days. When we can see them after sunset, we call them the"evening stars."

    The others (Mars, Jupiter, Saturn, Uranus and Neptune) are called the superior planets . Due totheir own revolutions, they move from west to east most of the time. We call it the progrademotion . Because the orbital speed of the Earth is larger, it sometimes "catches up" the superior

    planets. Apparently, they will move in the opposite direction, from east to west. We call it theretrograde motion . (Inferior planets also have both prograde and retrograde motions.)

    Normally, the retrograde motion of one superior planet will last from weeks to months. So, youcannot see it in a single night.