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# The Celestial Sphere

 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

## Overview

• Become familiar with celestial coordinates and vocabulary.
• Demonstrate the seasonal variations of the Sun.
• Observe the differences in the sky's appearance due to changes in observing locations.

## Introduction

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.

## The Equatorial Coordinate System and the Ecliptic

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.

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. 0 hours RA is defined to be the Vernal equinox, roughly March 21, which is also the beginning of the tropical year (Day 0). The hours of RA increase eastward so that objects with a larger RA rise later. Declination 0° is the celestial equator, and increases as you move towards the NCP. Declination becomes negative as you move towards the SCP.

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.

1. On the globe, locate:
a) the north and south celestial poles
b) the celestial equator
c) the ecliptic
d) the equinoxes
e) the solstices
f) the horizon
2. a) What is the declination of the North Celestial Pole?

b) What are the coordinates (RA & Dec) of the summer solstice?

c) What are the coordinates (RA & Dec) of the vernal equinox?

3. Which star is located at the coordinates 5h 55m and +7°24' Dec?

4. Which constellation is near the coordinates 17h RA and -40° Dec?

5. In what constellation is the Sun located on the following days?
a) July 5

b) January 20

c) November 10

## Location and Motion of the Sun

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) 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).

1. First, you must set the globe to represent the sky at your location. Do this by placing the NCP at an altitude equal to the latitude in Ann Arbor (about 42°).
2. Place the Sun at its position on March 21.
a) Record the declination of the Sun in Table 1.
b) As you rotate the globe, note the direction (marked on the globe) in which the Sun rises and sets, and its meridian altitude. Also record these values in Table 1.
c) Rotate the globe until the Sun rises again and mark the rising position with your finger. Rotate the globe until the Sun sets and mark the setting position. Imagine a line connecting these two points along the surface of the globe, and count the number of hours of right ascension between the rising and setting positions. This is the length of daylight - the number of hours the Sun is above the horizon. Record the length of daylight in Table 1.
3. Record the above information for June 21, Sept 21, and Dec. 21 also.
4. Repeat the above steps for an observer at the equator, and at 70° north latitude. Record your observations in Table 2 and Table 3.
5. Describe in words what the motion of the Sun is like as the year progresses at the North Pole, i.e. imagine how the Sun moves on March 21, and then on each of the other dates. Check your guess with the globe.

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

Table 2: Observer at 0° Latitude

 Date Declination of the Sun Rising Position Setting Position Meridian Altitude Length of Daylight Mar 21 June 21 Sept 21 Dec 21

Table 3: Observer at 70° N. Latitude

 Date Declination of the Sun Rising Position Setting Position Meridian Altitude Length of Daylight Mar 21 June 21 Sept 21 Dec 21

## Diurnal Motion of the Stars

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.

1. Rotate the globe to simulate the paths of the stars across the sky. Do the stars cross the meridian or set at the same time? If this is different from what you expected, why?

2. Find the number of hours each star is above the horizon, and record the results in Table 4. What is the relationship between the declination of a star and the number of hours it is visible?

 Declination of Star Hours above the Horizon -30 0 +30
3. Are there any stars that you can never see at your location? If so, describe where they are using coordinates. Where would you have to go to see some of these stars?

4. Repeat the above steps for an observer at the equator. Find the number of hours each star is above the horizon, and record the results in Table 5. How do the paths of the stars in the sky as seen at the equator differ from the paths of the stars as seen at our latitude?

 Declination of Star Hours above the Horizon -30 0 +30
5. Are there any stars that cannot be seen from the equator? Why?

6. Repeat the above steps for an observer at the north pole. Can the three stars be placed so that they rise at the same time? Rotate the globe, and describe the paths of your stars. How long is each above the horizon?

7. Are there any stars that can never be seen at the North Pole, and why?

Last update: 1/6/06 by SAM

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