Interlocking Orbits

This week has focused on figuring out whether having planets move around the sun can be fun.

Moving planets complicate the trajectory plots in a couple of different ways. The simplest is that I need to move the planets while calculating the trajectories. The harder problems are that:

• Close to a planet, the trajectory ought to be plotted relative to that planet's local reference frame.
• When traveling long distances, the trajectory doesn't help rendezvous with moving planets since it doesn't indicate where they will be in the future.

Moving planets also complicate the construction of the solar system, because each planet needs a path that won't collide with any of the others. They may need to be spread out more from each other. To experiment, I adapted my orrery program to generate random solar systems instead of reading data about the real one.



This one really needs to be seen in motion to appreciate it. Here's a Windows executable.

This program is just generating random orbit parameters and then using brute-force searching to see if the new orbit collides with any of the existing ones. I could undoubtedly do better but it proves the basic concepts. I do some simple checks: if one orbit's minimum distance exceeds the other's maximum distance, they can't possibly collide. Otherwise, I figure their common period (m * n / gcd(m, n)) and then integrate along that period in small steps, checking the distance between the planets at each step.

The random orbits are all generated such that their periods are all integral multiples of a common base (the innermost planets' period). There are ten discrete possible periods in the current solar system, which helps me ensure that they will interlock. I'm currently using a bit of a binomial distribution on planet size and orbit eccentricity, so you'll see few eccentric orbits and few large planets.

The current problem of interest is what gameplay purpose planetary motion ought to serve. Does territorial control mean anything in a solar system? If the planets were stationary I could imagine having planetary defenses that would form a “wall” of sorts along the boundary of a controlled region. With the planets swirling around it's not nearly as clear how that would work.

There are points in time where it is definitely cheaper to go from one planet to another; this is why Mars missions are launched approximately every two years, for instance. I don't know if having a delay element like this in a game would be fun at all, though.