by quickfur » Wed May 14, 2014 5:05 pm
I remember somebody posted a link here some time ago to an applet that lets you choose various orbital system parameters, such as the mass of the star, which inverse law gravity obeys (1/r, 1/r^2, 1/r^3, etc.), and you can place points representing planets on the chart and set their initial momentum.
Playing around with it gave a good intuition on why anything other higher than 1/r^2 is basically impossible to make a stable orbit out of. I think 1/r actually does give stable orbits as well, in the form of petal-shaped curves (the orbital path traces out flower petals), and 1/r^2 of course gives the familiar elliptical orbits. I could hardly get a single revolution around the star with 1/r^3, don't even talk about long-term stability! Almost every attempt crashes into the star after less than 1 revolution, or flies off into outer space around the same time. Even the theoretically possible spiralling path (where the orbital distance changes by a constant amount per revolution) is almost next to impossible to get, and those aren't stable paths either (and definitely not habitable for life, since every year the distance to the sun will change, so you will either fry after n years, or freeze to death). Perfect circular orbits require such extreme precision (not to mention extreme sensitivity to the smallest perturbations) that in practice it simply doesn't exist.