University of Michigan - Department of Astronomy

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The Celestial Sphere:

Motion of the Sun and Stars

The Sun, the stars and the seasons as they pass, some can gaze upon these with no strain of fear.

-- Horace

Overview

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.

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

  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 +724' 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



    d) your birthday



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 (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 40 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.

Figure showing position of NCP and equator relative to the observer

In the figure above, the person is standing in Ann Arbor, at a latitude of about 42. 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, 42. This implies that the angle between our position and the NP (or the NCP on the sky) must be 48 since the angle between the equator and the NP must be 90 . That leaves us with 42 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).

From Ann Arbor, Michigan

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). Make sure it is above the northern horizon!

  1. When is the sun highest at noon in the sky? How high does it get? Where is the sun on the Celestial Sphere (compared to the celestial equator)?



  2. When is the sun lowest at noon in the sky? What is it's altitude at noon? Where is the sun on the Celestial Sphere (compared to the celestial equator)?



  3. Where does the sun rise in the summer? Where does the sun set in the summer?

  4. Where does the sun rise in the winter? Where does the sun set in the winter?

  5. When does the sun rise and set exactly in the east/west? (give a specific day or days)

  6. When is the longest day of the year for observers in Michigan(give a specific day or days)? Explain your answer using what you observed with the Celestial Sphere. Keep in mind that it takes one hour for 1 hr of Right Ascension to cross the meridian.






  7. When is the shortest day of the year for observers in Michigan(give a specific day or days)? Explain your answers using what you observed.





  8. When does the length of day equal the length of night? (give a specific day or days)







    At the North Pole

The north celestial pole is the projection of the Earth’s north pole onto the Celestial Sphere. Knowing this, set your Celestial Sphere to show the sky from the North Pole.

  1. How many degrees above the northern horizon is the North Celestial Pole?

  2. Describe the motion of the sun at the north pole. Be specific about how the "days" are different at the North Pole compared to what we experience here in Michigan.











    Putting it all together
  3. Describe how the altitude of the sun at noon changes as you move farther north from Michigan or farther south towards the equator.









  4. Describe how the length of day on the longest day of the year changes as you move farther north and farther south from Michigan.








  5. Describe how the length of day on the shortest day of the year changes as you move farther north and farther south from Michigan.








  6. What does this mean for the length of the day at the equator? Use the globe if you need to.










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. Return the position of the globe to Ann Arbor's latitude.

  1. 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?








  2. Are there any stars that you can see all of the time (we call stars and constellations that are always above the horizon circumpolar)? If so, describe where they are using coordinates.







  3. What happens to the visibility of stars as you move towards the equator? Are there stars that you couldn't see from Ann Arbor? What happens to the circumpolar stars?







  4. What happens to the visibility of stars as you move towards the north pole? Are there stars that you couldn't see from Ann Arbor? What happens to the circumpolar stars?








Planning an Observation

You are an astronomer preparing for an observing run. You want to study the famous Orion Nebula (M42) located in the constellation of Orion the Hunter. Keep in mind that the best position in the sky to observe an object is when it is high in the sky. When it is low, near the horizon, you are looking through alot more of the atmosphere which makes the image blurry. Locate M42 in Orion on your globe.

  1. Where would be a good place to observe the Orion Nebula from and why?





  2. What time of year should you observe the Orion Nebula and why?





You also want to observe the globular cluster of stars called M13 in the constellation of Hercules. Locate M13 in Hercules on your globe.

  1. Where would be a good place to observe this star cluster (and where wouldn’t be)?





  2. What time of the year should you observe this star cluster and why?









Last modified 9/15/06 by SAM Author: JP

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