The pink/orange lines showing the transfer of the two (real) spacecraft Earth to Mars would I guess be something like in your game. For that you need to remember that the gravitational force of $a$ on $b$ is $$\vec$ and go back to 2.Īs an "incredibly rhetorical" question, heh, can you see any ellipse-ness in the planets orbits? Your ultimate game result would, I imagine, look something like that webapp. The easiest approach is to do a numerical integration of the equation of motion of your system.
Feeling a little guilty that I seem to have forgotten virtually all math I learned in college just over a decade ago, and I kind of want to reverse some of that decay. So far I've been looking at Kepler's 3rd Law equations but I'm not sure if that's a good place to start. But if I could just be pointed in the right direction for what to learn or refresh my memory on, I'd like to try and figure this out myself. If someone posts a formula I can just plug in I won't complain. Where would this planet be, in X/Y coordinates, at time=x?) Here's some sample parameter data below in case it helps provide a better example. (Since this is a 3D simulation, eventually I'd also like to work inclination in, but I'm trying to start off simple for now, so inclinations will all be zero.)
Right now I'm thinking perihelion, mass, and time elapsed. So if this becomes easier using some other method of defining the orbit, I'm open to it. I'm flexible on WHICH parameters need to be provided. So if I decide to set time = 1e10, I need to be able to calculate the x and y positions of each planet in their orbit at that precise time. I'd like the planets to move around their orbits at the correct speed given the parameters supplied. At the start of the simulation, time=0 seconds, all planets would be lined up in a row (planning on just placing them on the same axis at their perihelion distance from the star). I'll have a configuration file with some basic starting parameters for each planet. I just want something that a lightweight simulation or a game might do. no need for multi-body calculations, just a star and a planet will do. Unfortunately this has made me realize exactly how much math I've forgotten since college.Ĭomplete accuracy isn't important, and I'm not looking to do anything sophisticated. I'm trying to simulate a virtual/imaginary "solar system" in software-just a hobby project for now.
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