Partner(s):
Day/Time:
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Name: Partner(s): Day/Time: |
You may have heard the music of Man but not the music of Earth. You may have heard the music of Earth but not the music of Heaven. |
-- Chuang Tzu |
Although much of astronomy developed by the ancient Greeks proved to be incorrect (e.g., Geocentricism), some of the concepts which they used to understand the motions of the Sun and stars are still useful to us today. One of these is the visualization of the night sky as a celestial sphere which contains the stars and rotates about the Earth. Of course we now understand that it is the Earth that rotates so that the stars appear to move, and that the Sun does not revolve around the Earth but vice-versa. This method, however, is still helpful in understanding the motions of the Sun and stars as viewed from the Earth.
This section of the lab will familiarize you with the equatorial coordinate system which astronomers use to describe the position of objects on the sky. Right ascension, or RA, and declination, or Dec, are analogous to latitude and longitude on the Earth, and are the projection of those lines onto the sky. The lines of RA run from pole to pole, and the lines of Dec run parallel to the equator. Like the Earth, the celestial sphere has a celestial equator and north and south celestial Poles, or NCP and SCP, repectively, which are just the projections of these points on Earth onto the sky. Therefore, the North Celestial Pole is that point in the sky directly above the North Pole on Earth. And declination 40° N passes directly overhead at latitude 40° N.
If the Sun was not in the sky, the entire night sky would be visible over every 24 hour period. The Sun, however only allows you to see about 12 hours of night sky every 24 hours. Since the sky rotates around the Earth once in a day, 360° = 24 hours, or 15° = 1 hour. Thus it is convenient to measure RA in hours rather than in degrees. You can't see the entire celestial sphere in 24 hours, but the entire celestial sphere is visible over a year, as the Earth revolves around the Sun. We thus map 24 hours of RA onto a year beginning with 0 hours RA is defined to be the Vernal equinox. This is roughly March 21, the first day of spring which marks the beginning of the tropical year (Day 0). The hours of RA increase eastward so that objects with a larger RA rise later, both in the 24 hour day and in the year. Declination 0° is the celestial equator, and increases as you move towards the NCP. Declination becomes negative as you move towards the SCP. Ann Arbor is located at 40° N Dec and Rio de Janeiro is at -20° Dec.
The ecliptic is the plane of the Earth's orbit about the Sun, and is the path of the Sun in our sky. If the Earth's axis of rotation were perpendicular to the plane of it's orbit, the equator and the ecliptic would match up. However, the Earth's axis is tilted 23.5°, so the ecliptic is tilted with respect to the equator. In the second section of this lab, we will see how this tilt causes the seasonal changes we experience on Earth.
Begin
Finally, we examine how the motion of stars through the sky depends on the observer's latitude and on the declination of the star. Set the globe for your latitude. Place a dot on the globe to represent a star with Dec = 0°. Rotate the globe until your star is rising. Now place two more dots on the globe, for stars with Dec = -30° and Dec = +30°, so that both are just rising. At this point, you should have three dots representing stars with different declinations that are rising at the same time.
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Declination of Star
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Hours above the Horizon |
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-30
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0
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+30
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In this part of the lab, we are going to explore how the motion of the Sun across the sky differs from season to season. You can simulate the daily motion of the Sun (called the diurnal motion of the Sun (diurnal=daily)) by rotating the globe. This motion is due to the rotation of the Earth. In the same way, the stars appear to rise in the east and set in the west because the Earth is rotating west to east. However, the orbital motion of the Earth, caused by the Earth's revolving around the sun causes the Sun to move eastward along the ecliptic from one day the next, the opposite of it's daily motion. In other words, the Earth orbits the Sun in the direction west to east so that the Sun appears to move eastward along the ecliptic.
To describe the path of the Sun, we will note its position when it rises and when it sets, and its meridian altitude. The meridian is the line which runs due north-south (thus passing through both the poles) and passes directly overhead. The altitude of an object is its height in degrees above the horizon. When the Sun crosses the meridian, it is local noon, and the Sun is at its highest point in the sky. For the purposes of this lab, measure the meridian altitude from due south.
In the following figure for an observer at 40º N latitude, notice that geometry dictates that the altitude of the NCP above the horizon is equal to the observer's latitude, as is the declination of objects passing directly overhead.
In the figure above, the person is standing in Ann Arbor, at a latitude of about 40°. The horizon divides the sky into the half which is visible and the half which is not. Therefore, there are 90° between the zenith (a point directly above the observer) and the horizon. The angle between our position and the equator is the latitude, 40°. This implies that the angle between our position and the NP (or the NCP on the sky) must be 50° since the angle between the equator and the NP must be 90° . That leaves us with 40° for the angle between the NCP and the horizon, since the angle between our position and the horizon must also be 90°. (Note, the angles are correct in this illustration, but the size scale is not).
Table 1: Observer at 42° N. Latitude
| Date | Declination of the Sun |
Rising Position |
Setting Position |
Meridian Altitude |
Length of Daylight |
| Mar 21 | |||||
| June 21 | |||||
| Sept 21 | |||||
| Dec 21 |
Last update: 1/6/06 by SAM