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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. :)

IT Bear
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    If you know $x$ to be seconds / degree then $\frac{1}{x}$ will be the corresponding degrees / second. Pay attention to the units, however, even more so since you seem to mix up degrees and radians at various points. You don't want to drive the next Mars Climate Orbiter into ground. – dxiv Sep 30 '16 at 06:43
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    Just take the recipral. 2206.8 seconds = 360 degrees. Ergo satellite travels 360/2206.8 degrees per second. And time elapses 2206.8/360 seconds per degree. – fleablood Sep 30 '16 at 06:47
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    I knew it was simple!! It will take some time for me to plug these in to my program and run more simulations, so feel free to post these as answers. But now I have multiple methods to solve for deg/s, so it will become more apparent if I don't account for body rotation or worse, mix up the units in some way. :) Thank you, thank you! – IT Bear Sep 30 '16 at 07:02
  • Did you mean seconds degree to degrees like showing here https://calculate.plus/en/convert/seconds-degree/to/degrees ? – phlegx Nov 19 '16 at 16:29
  • @phlegx Not seconds as a measurement of angle, seconds as a measurement of time. I'm writing a program to rendezvous a launch vehicle directly with an orbiting space station overhead, so if I have my launch vehicle's time to rdzv and Longitude at rdzv, I just need accurate deg/s of the target. (I know a spacecraft's speed is always changing, that's why I said "imagine perfectly circular orbit". I can make it harder on myself later.) I just use decimal degrees and decimal seconds as flat values, so there's less conversions on the processor that way. :) – IT Bear Nov 26 '16 at 23:02

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