I’m going to be running an RPG set in space, and I need to come up with a simplified way to determine the distance between two planets in the system. Been a while since I did any trig, so I’m trying to create a handy chart that I can consult. Here’s what I have so far:
Since it is a small star, the orbital distances are comparatively smaller than that of Earth.
Planet 1 is at a distance of 21 million miles, planet 2 at a distance of 29 million miles. (I realize that metric is sexier for science but all the unit measurements in GURPS are imperial.)
Planet 1 orbits in 58.8 Earth days, planet 2 orbits in 97.41. I looked at that and said, hey! The ratio is about 60:100. Or to look at it like a clock, every Earth day that passes, planet 1 moves 1 minute, and planet 2 moves 36 seconds.
Now I just need a way to calculate their distance from the number of “minutes” apart they are. I grok that the number of “minutes” * 6 = degrees, and that degrees * pi/180 = radians.
I also grok that at 0 minutes/0 degrees (their closest separation), the distance is distance2 - distance1, and that at 30 minutes/180 degrees (their farthest separation, as the spacecrow flies), the distance is distance2 + distance1. At 15 minutes/90 degrees apart, the Pythagorean theorem will suffice (since the orbital distances form the legs of a right triangle and I can solve for the hypotenuse).
It’s all them other distances between that get me. How do I figure 'em?