Lecture 2: The Motion of the Stars and the Sun

The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings.

-- WIlliam Shakespeare, Julius Caesar

2.1 The Stars

(Discovering the Universe, 5th ed., §1-0, §1-1)

• The human eye can see about 6000 stars without aid.
  
  The picture below covers a field of view of about 70° x 46°, roughly 5% of the entire sky.

• The stars are grouped into constellations.
  
  Most of these are the same ones described by the ancient Greeks and Babylonians, although the southern hemisphere has many that were "created" by European explorers a few centuries ago.
  
  The ancients thought of the constellations as representing mythical figures such as Orion the Hunter and Taurus the Bull.

• Nowadays we often think of constellations as "stick figures", consisting of lines connecting the major stars.

• These figures leave out many stars and other objects, including those that require telescopes to be seen.
  
  So, astronomers now think of a constellation as one of 88 regions that divide up the sky and completely cover it.
  
  Any object can now be said to lie in one constellation or another.

• Many stars have names from Arabic or Greek, e.g. Betelgeuse means "armpit" in Arabic.
  
  The stars are also given names such as "Alpha Orionis", using letters from the Greek alphabet followed by the constellation name.
  
  After that, numbers are typically used, e.g. "37 Orionis".
  
  This ordering is typically (but not always) according to brightness.
  
  Extra: an extensive listing of common Star Names and their meanings.
  
  Extra: purchased star names are not recognized by any scientific organization. See the statement on Buying Stars and Star Names by the International Astronomical Union for more information on how astronomical names are actually selected.

2.2 The Celestial Sphere

(Discovering the Universe, 5th ed., §1-3)

• An important characteristic of the stars is that they have relatively fixed positions with respect to each other, i.e. the constellations do not change with time.
  
  
  • The stars do actually move, but this motion is only noticeable to the unaided eye after a long time, tens of thousands of years or more.
    
    
  • Nearby stars also exhibit parallax, but this is only visible in a telescope.
     
    
    
• Although the stars have many different distances from the Earth, this is not distinguishable with the naked eye (again, it requires a telescope).
   
  
  
• It is therefore useful to think of the stars as being "painted" on the interior surface of a large sphere centered on the Earth, called the celestial sphere.
   
   
  
• As you are no doubt aware, the Earth rotates once a day.
  
  We cannot detect this motion, however, so it appears to us as if the stars (and Sun and Moon and planets) are rotating around us: they rise in the east and set in the west, once a day.
  
  This is called diurnal motion.
   
  
  
• We can imagine diurnal motion as being due to the "rotation" of the celestial sphere around the Earth.
  
  

Picture Information

• This motion can be seen in the time-lapse photograph at the right, centered on the north pole of the celestial sphere.
  

2.3 Latitude and Longitude

(Discovering the Universe, 5th ed., §1-4)

• It is useful to be able to precisely specify positions on the celestial sphere.
  
  So, a set of coordinates is used that is similar to latitude and longitude on the Earth.
  
  The system of latitude and longitude was first suggested by Hipparchus, a Greek astronomer in the 2nd C. B.C.
   
  
  
• Recall that the Earth's rotation axis is a line that passes through the geographic poles (the North and South Poles), and the center of the Earth.
  
  The Earth rotates around this axis, leaving the poles fixed.
   
  
  
• The equator is a circle on the Earth's surface that is perpendicular to the axis and equidistant from the poles.
  
  It is a great circle because it is centered on the Earth's center, making it as large as possible.
  
  The northern hemisphere is the half of the Earth north of the equator, and the southern hemisphere is the half south of the equator
   
  
  
• Any circle parallel to the equator is called a circle of latitude.
  
  The angle (with vertex at the center of the Earth) between a given circle of latitude and the equator describes that circle and any point on it.
  
  So, the North Pole is at 90° north latitude, the equator itself is 0° latitude, and Johannesburg, South Africa is roughly 30° south latitude.
   
  
  
• Any semicircle passing through the poles is called a meridian of longitude.
  
  One of these is designated as the prime meridian, namely the one passing through the Royal Observatory in Greenwich, England (just outside London).
  
  The angle (with vertex at the center of the Earth) between a given meridian and the prime meridian describes that meridian and any point on it.
  
  So, Johannesburg is at 30° east longitude.
  
  Note that 180° west longitude is the same meridian as 180° east longitude.

2.4 Celestial Coordinates

(Discovering the Universe, 5th ed., §1-2)

• We describe the celestial sphere using a similar geographical notation:
  
  
  • The North Celestial Pole is the point on the celestial sphere directly above the Earth's North Pole.
    
    Similarly, the South Celestial Pole is directly above the Earth's South Pole.
    
    
  • The star Polaris, in the constellation Ursa Minor, is located very close to the North Celestial Pole.
    
    Polaris is therefore also called the North Star.
    
    Question: can you identify Polaris in the photo of the polar sky above?
    
  • The celestial equator is directly above the Earth's equator.
     
    
    
• Positions on the celestial sphere can also be measured relative to these markings, although different names are used besides latitude and longitude.
   
  
  
• Declination corresponds to latitude, and is measured in the same way, but relative to the celestial equator (0° dec).
  
  The north celestial pole is at 90° north declination (+90° dec). The south celestial pole is at 90° south declination (-90° dec).
  
  Circles of constant declination are all parallel to the celestial equator.
   
  
  
• For any position on the surface of the Earth, the point on the celestial sphere that is directly overhead is called the zenith.
  
  Since the Earth and the celestial sphere are concentric, simple geometry shows that the zenith will always have a declination equal to the latitude of the observer (such as for Atlanta in the picture).
   
  
  
• A star's position along a circle of constant declination is described by a second number called right ascension.
  
  Right ascension corresponds to longitude, but different units are used.
  
  Instead of 360°, a circle is broken into 24 hours of right ascension.
  
  So, 360° = 24 h R.A., 15° = 1 h R.A., and 1° = 4 min R.A.
  
  Note that hours of right ascension is a unit of angle, not time, although there is an obvious connection due to the daily rotation of the celestial sphere.
   
  
  
• Right ascension is measured from the celestial meridian, chosen to be 0 h R.A. (which is also the same as 24 h R.A.)
  
  The celestial meridian is a semicircle connecting the celestial poles and passing through a particular point on the celestial equator called the vernal equinox (defined below).
  
  Question: to what position on Earth is the vernal equinox analogous?
  
  Right ascension increases from west to east (note that we are looking at the exterior of the celestial sphere in the above picture).
   
  
  
• With the two numbers of declination and right ascension, the position of any object in the sky can be precisely described.
  
  Question: what is the approximate position of the galaxy shown?
  

2.5 The Motion of the Sun

(Discovering the Universe, 5th ed., §1-6)

• Although the stars are fixed relative to each other, the Sun moves relative to the stars.
  
  Once a year, the Sun traces out a circle on the celestial sphere called the ecliptic.
  
  The ecliptic is tilted at an angle of 23.5° with respect to the celestial equator.
  
  (The Moon and planets also move near the ecliptic.)
   
  
  
• The Sun crosses the celestial equator at exactly two points, called equinoxes, from the Latin for "equal nights" (for reasons we'll see later).
   
  
  
• The equinox where the Sun ascends from the southern to the northern hemisphere is called the spring or vernal equinox because the Sun is there on March 21.
  
  The vernal equinox is chosen to be 0 h R.A.
   
  
  
• The Sun again crosses the celestial equator halfway around, at 12 h R.A.
  
  This position is called the autumnal equinox because the Sun is there on September 23.
   
  
  
• The positions where the Sun reaches its highest and lowest points are called solstices, from the Latin for "the Sun stops" as it changes direction.
   
  
  
• The Sun is highest in the sky (in the northern hemisphere) when it is at 6 h R.A.
  
  This position is called the summer solstice because the Sun is there on June 21.
  
  The Sun then has a declination of +23.5°.
   
  
  
• The Sun is lowest in the sky (in the northern hemisphere) when it is at 18 h R.A.
  
  This position is called the winter solstice because the Sun is there on December 21.
  
  The Sun then has a declination of -23.5°.

2.6 The Local Horizon

(Discovering the Universe, 5th ed., §1-6)

• To an observer on the Earth, only one half of the celestial sphere can be observed at a time.
  
  As a result, in Atlanta the sky appears roughly as shown at the right.
   
  
  
• The local horizon, often just called the horizon, is the circle that divides the Earth and the sky from each other.
  
  The compass directions north, south, east, and west are marked along the horizon.
  
  North will be underneath the north celestial pole.
  
  When we face north, east is on our right and west is on our left.
   
  
  
• Another coordinate system that is commonly used to locate objects in the sky is the altazimuth system, which is based on the local horizon.
  
  The altitude of an object is the angle between it and the horizon.
  
  The horizon has an altitude of 0° and the zenith has an altitude of 90°.
  
  The azimuth of an object is the angle between it and north, measured clockwise along the horizon.
  
  North has an azimuth of 0°, east has an azimuth of 90°, south has an azimuth of 180°, and west has an azimuth of 270°.
   
  
  
• The local meridian, often just called the meridian, is a semicircle that passes through the celestial poles and the zenith.
  
  Question: the local meridian is a projection onto the celestial sphere of what previously described item on the Earth?
   
  
  
• Note that the horizon, zenith, and meridian are fixed relative to the observer; hence the stars and sun will move past them with time.
  
  Question: what happens to these items when the observer moves to a different location on the Earth?
   
  
  
• Simple geometry shows that the angle between the zenith and the celestial equator (i.e. the zenith's declination) must also be the angle between the north celestial pole and the north horizon.
  
  Since the zenith's declination is equal to one's latitude, Columbus was always able to determine his latitude when he crossed the Atlantic Ocean by measuring the altitude of Polaris.
   
  
  
• During the summer, the Sun is located near the summer solstice, north of the celestial equator.
  
  In Atlanta, it therefore appears high in the sky at transit, 33.7° - 23.5° = 10.2° away from the zenith.
   
  
  
• During the winter the Sun is near the winter solstice, south of the celestial equator.
  
  In Atlanta, it therefore appears low in the sky at transit, 33.7° + 23.5° = 57.2° away from the zenith.
   
  
  
• At a latitude of 23.5° N, the tropic of Cancer, the Sun just reaches the zenith on the summer solstice.
  
  At 23.5° S, the tropic of Capricorn, it just reaches the zenith on the winter solstice.
  
  
  
  Between these latitudes (the tropics), the Sun crosses the zenith twice during the year.
  
  Tropic is from the Greek for "turning", again describing the Sun's motion at the solstice.
  
  Cancer and Capricorn are the constellations where the Sun is located at the solstices (or rather where it was located in 500 B.C...).
   
  
  
• The closer the Sun is to the zenith, the more concentrated its light is on the Earth's surface, so the more energy it transfers.
  
  This is why summer is warmer and winter is colder, and why the tropics are warm year round.
  

2.7 Day and Night

(Discovering the Universe, 5th ed., §1-4)

• We define the synodic day as the time for the Sun to transit twice.
  
  The synodic day is defined to be exactly 24 hours long, i.e. it is the "day" you are familiar with.
   
  
  
• When the Sun is at transit we say it is 12 noon.
  
  Since this can only happen at one longitude at a time, it used to be that every town had its own "time zone".
  
  This was a nightmare for the railroads to keep track of, so in the 19th century they convinced Congress to implement time zones, breaking up the country into four broad areas that shared the same clock time.
  
  This meant that, for most places, noon no longer occurred when the Sun was at transit, but it simplified scheduling, especially when broadcast radio and TV came along.
  
  Atlanta is on the western edge of the Eastern Time Zone, so the Sun doesn't transit until 12:40 P.M. EST (1:40 P.M. EDT).
   
  
  
• As the Sun rises and approaches the meridian, it is "before the meridian" or ante meridian (A.M.).
  
  As the Sun sets toward the horizon, it is "after the meridian" or post meridian (P.M.).
   
  
  
• Because the Sun is so bright, we can only see the stars at night.
  
  These are the stars on the opposite side of the celestial sphere from the location of the Sun.
  
  But which stars we see depends on the time of the year, because the Sun moves along the ecliptic!
  
  The Sun moves about one degree, or about 4 minutes of RA, along the ecliptic every day (360°/365 d).
  
  This solar motion means that a particular star will rise (or transit, or set) about 4 min earlier on each subsequent night.
  
  The sidereal day is defined as the time for a star to cross the meridian twice.
  
  The sidereal day is equal to 23 h 56 min 4 s.

Star charts are produced on a Macintosh with the Voyager II program, and are ©1988-93 Carina Software, 830 Williams St., San Leandro, CA 94577, (510) 352-7328. Used under license.

Thanks to Martin Weinelt and his Online Map Creation web page, which generated most of the images of the Earth used in this document.

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