The document describes a lab activity on tracking the night sky using different coordinate systems. It introduces the right ascension/declination (RA/Dec) coordinate system used by astronomers to describe celestial objects. Students learn about and practice using the RA/Dec system on a star wheel and in the Stellarium software to determine coordinates of stars and observe how the night sky appears at different locations, including San Francisco, the North Pole, and the equator. Key findings include that Polaris' declination does not change but its altitude does based on location, and that the visibility of different stars depends on one's latitude.

1. Lab 6: Tracking the Night Sky II
Part I: A coordinate system tied to the Celestial Sphere
The altitude/azimuth system that we have been using thus far is
ideal for describing
the locations of celestial objects in the sky at a given day and
time. But it has some
drawbacks. In particular, as we have just seen, since the Earth
spins, the altitude and
azimuth of a star keeps changing!
It’s useful to also have a system in which every star has a
unique set of coordinates.
Here we will introduce the Right Ascension/Declination
(R.A./Dec.) system that as-
tronomers use to describe the locations of stars (and other
celestial objects) on the Ce-
lestial Sphere. The coordinates in this system are analogous to
the latitude/longitude
system used to describe the locations of cities and geographical
features on the Earth.
But it will take some getting used to, because the names of the
coordinates are different.
For one of the coordinates, the units are different as well!
Coordinate on Earth Coordinate on Celestial Sphere
Latitude → Declination (Dec.)
Longitude → Right Ascension (RA)
Watch the following short video to help you visualize the

2. coordinate system better:
https://youtu.be/WvXTUcYVXzI
Coordinates on the Star Wheel
The RA/Dec coordinate system is used on your Star Wheel
(which, after all, is just
a flattened version of the Celestial Sphere!). Take a close look
and you’ll see that the
celestial equator is shown as a thin, solid line (large circle)
running from east to west; it’s
visible on both sides of the Star Wheel. Along the celestial
equator, you will see R.A.
values indicated (e.g., 17h, 18h, etc).
1. Does the value of Right Ascension increase from west to east
or from east to west?
Check both sides of your Star Wheel!
2. What is the total range of R.A. values along the Celestial
Equator?
(c) 2020 SFSU. DO NOT DISTRIBUTE 1
https://youtu.be/WvXTUcYVXzI
3. In view of this, what unit do you think R.A. is measured in,
i.e., what does the “h”
represent?
4. Can you think of a reason why this is a natural unit in which
to measure R.A.? Explain.
5. Now notice the eight radial lines emanating from the NCP on

3. your Star Wheel. These
are the solid lines coming straight from the center circle
outward. These are lines of
constant R.A. They cross the Celestial Equator at certain points,
what are the values of
the R.A. along these lines? Don’t forget to include the unit.
1. 2. 3. 4. 5. 6. 7. 8.
6. Along each radial line you will see a series of tick marks. On
four of the radial lines,
the tick marks are labeled with numbers. What do these numbers
represent, and what
are the units?
7. Turn the Star Wheel over so you can see the southern half of
Celestial Sphere (or part
of it anyway). Look at the markings along the radial lines below
the Celestial Equator.
What range of Declination values do you see?
(c) 2020 SFSU. DO NOT DISTRIBUTE 2
Use the R.A. and Dec. coordinate system on your Star Wheel to
answer the following
questions:
8. What are the coordinates of the star Rigel in Orion? RA =
Dec =
9. What are the coordinates of the star Vega? RA = Dec =
10. In what direction do stars that are on the Celestial Equator
rise?

4. 11. In what direction do stars that have Declination = 30◦ set?
12. What is the declination of the NCP?
13. In San Francisco, at a latitude of 38◦, what is the altitude of
the NCP? (Hint:
Don’t forget that altitude and azimuth are a different coordinate
system than right ascen-
sion/declination. Look at Lab 4 if you don’t remember.)
(c) 2020 SFSU. DO NOT DISTRIBUTE 3
Part II: Coordinates in Stellarium
In Lab 5, we learned about about how the sky appears to move.
The new coordinate
system that we’ve been discussing in this lab, Right Ascension
and Declination, is one
that astronomers use more frequently than the previously
discussed Altitude and Azimuth
coordinate system. Astronomers use the RA/Dec. coordinate
system more because the
Alt./Az. system depends on where you are on Earth, the RA/Dec
system works does not
and works for any astronomer alls across the globe.
Let’s look a bit more into Right Ascension and Declination in
Stellarium (https:
//stellarium-web.org/). Use the directions in Lab 5 to set up
Stellarium again.
Once Stellarium is setup, we’re going to change one thing. Turn
off the “Azimuthal

5. Grid” and turn on the “Equatorial Grid”. As you do this watch
how the lines change
on the screen. The Azimuthal grid are your Alt./Az. coordinates
while the Equatorial
grid are your RA/Dec coordinates.
Let’s find the Celestial Equator in Stellarium. To do this, look
toward the South.
For each of the horizontal lines across the sky there are
declination values labeled on the
edge of your screen. The yellow arrows on the image below
shows where to find them.
These are declination values. The horizontal line that has a
declination of zero degrees
is the Celestial Equator. The Celestial Equator has a declination
of 0◦. Each line
parallel to the celestial equator is a line of declination and will
have a different value of
declination.
(c) 2020 SFSU. DO NOT DISTRIBUTE 4
https://stellarium-web.org/
https://stellarium-web.org/
1. Find the Celestial Equator using the above directions and
image to help you. You
should see that line cross the horizon at two locations. What are
those two cardinal
directions?
Notice the vertical lines that cross the Celestial Equator. These
are lines of Right
Ascension and each one has a different value. If you follow the
lines to the top of your

6. screen (can be hard to see) you should see what the value of
each line is. The image
below points out each value of RA with a pink arrow and each
value of Dec. with a yellow
arrow.
Now use the RA/Dec system projected in Stellarium to estimate
coordinates for the
following objects. Try to actually find each star and not use the
search function. If you
can’t remember what constellation the star is in, look on your
Star Wheel and then try
to find the constellation in Stellarium. Use your Star Wheel to
confirm you guess in
Stellarium. Remember to use hours and minutes for R.A., and to
indicate if Dec. is
positive or negative!
2. What are the coordinates of the star Altair in the summer
triangle? RA = Dec =
3. What are the coordinates of the star Anteres? RA = Dec =
(c) 2020 SFSU. DO NOT DISTRIBUTE 5
4. Now simulate time moving forward by changing the time
(bottom right corner) to
02:00. Check the coordinates above again. Did the RA/Dec
values change?
The View from San Francisco
We learned in the last two labs how to determine our latitude on
Earth from the

7. altitude of Polaris. Let’s put it to the test and learn about the
sky a little more in
different locations on Earth. Let’s start here in San Francisco.
1. What is your latitude here in San Francisco?
2. What is the declination of Polaris?
3. What is the altitude of Polaris? (Don’t forget we’re still using
the RA/Dec coordinate
grid! To change between the RA/Dec grid and the Alt./Az. grid
you need to use the
icons at the bottom of the screen.)
Make a prediction: From San Francisco, do you think we get to
see the entire
Celestial Sphere as time goes by? Why or why not?
(c) 2020 SFSU. DO NOT DISTRIBUTE 6
4. Now use the up hour time arrow to make time move forward
and watch carefully as
you simulate a day or two (as shown in the image below). OR
hold down the up minute
arrow to pass time a bit slower.
Describe and/or sketch the overall pattern of motion of stars in
the North and South
directions. Spend a bit of time watching time go by in every
direction.
5. Which stars on the celestial sphere, if any, are rising and
setting (all, most, half,
some or none)? Give a few example constellations and state

8. whether they are in the
southern or northern celestial hemisphere.
6. Which stars on the celestial sphere, if any, are always above
the horizon (all, most,
half, some or none)? Give a few example constellations and
state whether they are in
the southern or northern celestial hemisphere.
7. Which stars on the celestial sphere, if any, are never above
the horizon (all, most,
half, some or none)? Give a few example constellations and
state whether they are in
the southern or northern celestial hemisphere.
8. How good were your predictions? Explain.
(c) 2020 SFSU. DO NOT DISTRIBUTE 7
The View from the North Pole
Let’s change your location in Stellarium to the North Pole
(bottom left) by
typing in “North Pole” into the Earth location search bar. Make
sure the atmosphere
icon is off, otherwise you won’t see any stars. Once there, look
for Polaris. Maybe use
your drawings in Lab 4 to help you.
1. What is your latitude here at the North Pole?
2. What is the declination of Polaris? (Don’t forget to change
back to the Equatorial
grid for this question)

9. 3. What is the altitude of Polaris? (Switch to the Azimuthal grid
for this question)
Make a prediction: Standing on the North Pole, do you think
you’ll be able to see
the entire Celestial Sphere as time goes by? Why or why not?
(c) 2020 SFSU. DO NOT DISTRIBUTE 8
4. Now use the up hour time arrow to make time move forward
and watch carefully as
you simulate a day or two. Describe and/or sketch the overall
pattern of motion of stars
in the North and South directions.
5. Which stars on the celestial sphere, if any, are rising and
setting (all, most, half,
some or none)? Give a few example constellations and state
whether they are in the
southern or northern celestial hemisphere.
6. Which stars on the celestial sphere, if any, are always above
the horizon (all, most,
half, some or none)? Give a few example constellations and
state whether they are in
the southern or northern celestial hemisphere.
7. Which stars on the celestial sphere, if any, never rise at all
(all, most, half, some or
none)? Give a few example constellations and state whether
they are in the southern or
northern celestial hemisphere.

10. 8. How good were your predictions? Explain.
(c) 2020 SFSU. DO NOT DISTRIBUTE 9
The View from the Equator
Let’s change your location in Stellarium to the city of Quito in
Ecuador.
This is the capital of Ecuador and is one of the largest cities to
straddle the Equator.
Once there, look for Polaris. Maybe use your drawings in Lab 4
to help you.
1. What is your latitude here at the Equator?
2. What is the declination of Polaris? (Don’t forget to change
back to the Equatorial
grid for this question)
3. What is the altitude of Polaris? (Don’t forget to change back
to the Azimuthal grid
for this question)
Make a prediction: Standing on the Equator, do you think you’ll
be able to see the
entire Celestial Sphere as time goes by? Why or why not?
(c) 2020 SFSU. DO NOT DISTRIBUTE 10
4. Now use the up hour time arrow to make time move forward
and watch carefully as
you simulate a day or two. Describe and/or sketch the overall

11. pattern of motion of stars
in the North and South directions.
5. Which stars on the celestial sphere, if any, are rising and
setting (all, most, half,
some or none)? Give a few example constellations and state
whether they are in the
southern or northern celestial hemisphere.
6. Which stars on the celestial sphere, if any, are always above
the horizon (all, most,
half, some or none)? Give a few example constellations and
state whether they are in
the southern or northern celestial hemisphere.
7. Which stars on the celestial sphere, if any, never rise at all
(all, most, half, some or
none)? Give a few example constellations and state whether
they are in the southern or
northern celestial hemisphere.
8. How good were your predictions? Explain.
(c) 2020 SFSU. DO NOT DISTRIBUTE 11
Summary Questions
1. What did you notice about the declination of Polaris in all of
the different locations?
2. What did you notice about the altitude of Polaris in all of the
different locations?
3. Were your observations of the rotation of the sky facing

12. North and South in Lab 5
confirmed while observing the rotation of the sky in Stellarium?
4. What is a benefit to the RA/Dec coordinate system (why do
astronomers like this
coordinate system)?
5. What is a benefit to the Alt/Az coordinate system?
(c) 2020 SFSU. DO NOT DISTRIBUTE 12