Name: Partner(s): Day/Time: Version: Plan Full

# Coordinate Systems in the Planetarium

## Part 1: Altitude - Azimuth Coordinates

1. Your GSI will set the planetarium to display the stars tonight at 8 PM and point out a star to watch north of the equator. Record the star's name as well as the altitude and azimuth for Position 1 in Table 1. Note that the scale in the planetarium is different from the scale in the real world, so you'll need to measure with your hand then compare that to the degree markings on the meridian scale.
2. Your GSI will simulate the passage of time until the star transits the meridian. Record the altitude and azimuth under Position 2 in Table 1 for the first star.
3. Your GSI will restore the position of the sky back to 8 PM and point out a star south of the equator to watch. Record its name and the altitude and azimuth for Position 1 in Table 1.
4. Your GSI will again simulate the passage of time until the second star transits. Record the altitude and azimuth for Position 2 for this second star.
Table 1: Altitude - Azimuth positions
Star name Position Altitude (deg) Azimuth (deg)

1
2

1
2
1. Does the altitude of most of the stars remain constant or change throughout the night?  Does the azimuth?

2. Estimate the angular distance between the two stars in degrees of arc.

3. What is the altitude of Polaris? Note that it is related to the number of circumpolar stars.

## Part 2: Equatorial Coordinates

Now you will observe the same 2 stars just like you did in Part 1, but this time measure their Right Ascension and Declination.

1. Measure the RA and Dec and record your results in Table 2.You'll have to estimate the Declination like you did the altitude, but make sure you measure distance from the celestial equator!
Table 2: RA and Dec
Star name Position RA (hours) Dec (degrees)

1
2

1
2
1. Does the RA of most of the stars remain constant or change throughout the night? Does the Dec?

2. Estimate the angular distance between the two stars in degrees of arc.

3. Has the angular distance from the meridian increased or decreased, for the first star?

## Concluding Questions

1. Does the angular distance between the stars depend on which coordinate system you use? On the time at which you observe? Explain.

2. Which system (equatorial or alt-az) would you use, if you wanted a group of people at different locations around the world to observe the same object? Why?

3. Which system (equatorial or alt-az) would be easier to use to point out a star to a friend in your backyard? Why?

4. Circumpolar stars are those that never set. Would you see more, fewer, or the same number of circumpolar stars in Mexico compared to Ann Arbor? Explain.

5. You find a beautiful, long-exposure photo of the sky from Ann Arbor, in which all the stars appear as star trails. Upon looking closely, you notice that the star trails are all individual arcs, each of which forms about 1/6 of a complete circle. Estimate the exposure time for this photo, explaining how you set up the proportionality to solve this.