This may be super simple, but I am lost and clueless.
Here is my real world example:
I am trying to calculate the Degrees per Second a satellite orbits around a parent body. To simplify this immensely, imagine the satellite is in a perfectly circular orbit, body is in a 2D universe, not 3D (body is a circle, not a sphere, no axial tilt, satellite is perfectly equatorial) and the parent body is not rotating. I can deal with body rotation later if I get this right.
This satellite orbits the parent body in exactly 2206.8 seconds. I'm doing this in a simulator, so the simulator gives me the exact orbital period without me having to calculate it.
So, since the satellite takes 2206.8 seconds to travel 360 degrees around the body, if I divide seconds by 360, I get Seconds per Degree. Am I correct so far?
If I have this value, how do I now convert it do Degrees per Second? (Is it possible?)
Before you say there are better ways to do this, I have gotten a different equation from someone else:
v / r = rad/s
where
v = velocity (2038 m/s, for example)
r = radius (body radius + altitude, so 600,000m + 165,000m for example)
Which gives me radians per second, which I can then convert to deg/s.
I will also use a sanity check method, where I measure the satellite's longitude, wait exactly 1 second, then measure its longitude again. Sample2 - Sample1 = deg/s, correct? If I wait exactly 5 seconds, then I can do (Sample2 - Sample1) / 5, and have an average deg/s over 5 seconds.
Am I on the right track here? My accuracy is still way off and deg/s is the single most important value for all the rest of my calculations. I feel like there must be more than one method to solve for it, and I don't like v/r because there are many different ways to measure velocity: orbital, surface, ground speed, air speed. Too many variables.
I never took calculus or any advanced math in high school and I'm kicking myself for it now. I barely passed algebra because I thought I didn't like math at the time and my head was filled with other things. So please, explain as you would to a child. :)