Assignment:
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 astronomers use to describe the locations of stars (and other celestial objects) on the Celestial 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 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?
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 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?
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?
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 ascension/declination. Look at Lab 4 if you don't remember.)
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 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 Equatorialgrid 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
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 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 =
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 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?
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 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.
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)
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?
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.
8. How good were your predictions? Explain.
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?
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.
8. How good were your predictions? Explain.
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 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?
Attachment:- Tracking the Night Sky.rar