First you should load Cas-A. This is a good beginner study. Choose a really bright spot on the image somewhere away from the center. Similar to the one circled in red.
How can we find out how far away that spot is from the earth? Pretty easily actually.
1) Suppose a fast moving knot is observed to be moving (again, via the Doppler effect) at 5000 km/sec. , how far does it travel in 10 years?
L= 5000km/sec x 3 x 10 8 seconds = 1.5 x 10 12 km.
2) During that time, suppose the knot is observed to move 3 arc-seconds. What is the distance to object? What is an arc-second?
L= theta(arc-seconds) x distance to object / 206,265
so distance= 206,265 x L / theta
or d= 206265 x 1.5 x 10 12 km / 3 = about 1 x 10^17 km or 3 kpc.
Light travels about 9.46 x10^12 km in a year so you do the math. How many light years is Cas-A from earth? Answer is below.
3) Suppose this knot is now 100 arc-seconds from the center of the remnant. When did the Supernova explode?
If it has been traveling at a constant velocity, and it moves 3 arc-sec in ten years, it moved 100 arc-sec in about t= 100 arc-sec / 3 arc-sec per 10 years = 330 years ago or around 1670 AD.
(or, 3 arc-seconds per 10 years is 30 arc-seconds per 100 years or 100 arc-seconds per 330 years). Drawing a simple picture will help visualize this idea...
So what did you learn? Assuming you know the velocity of an object in the sky (via the doppler effect or using a coordinate system of objects relative to each other) you can find out how far an object is from the earth and its velocity.
You can do this for any of the Case Studies on the Chandra Website.
Could you use the knowledge you've learned to prove that the earth spins once every 24 hours? Perhaps using the moon would help with your calculations.