Help! Calculating the long-term orbits of arbitrary planets.

[sleepcircle]

The orbital elements provided by universe sandbox seem good for short term things but according to other articles and things i've seen out there I would need more stuff, like the perturbations of different planets, and the precession of the orbits themselves.

i'm sure the information is in universe sandbox, even if it's in a different form, I could probably calculate the necessary numbers from other values like angular velocity and position and stuff, but I am super new to the concept of celestial mechanics and I'm feeling a little lost. I've been working like a dog for the past few days to calculate all kinds of stuff, and I've been doing okay so far! but i didn't expect that long-term predictions with the basic orbital elements would turn out to be increasingly inaccurate. Now it turns out I need all-new numbers, and I'm starting to feel really worn down.

I'm still willing to do all the math, myself, but could someone familiar with the subject please tell me what equations I should be looking for or whatever way there is to extract the information I need from the data universe sandbox provides? I'm really losing it, here!

[sleepcircle]

on further examination it looks possible that computing the end point of a system 16000 years onward based on a series of simple variables is the domain of someone who either does not understand celestial mechanics what-so-ever, or who is a crazy person--even if you DO have the precession of apsides etc.--and computing the perturbations looks like an exercise in rather linear physics computations at a very small interval, which is kind of what universe sandbox already does so yeah. I guess I will just let the simulation run for a while.

Although I would like to take this opportunity to seriously seriously thank dan for everything he did to make it possible for me to not have to spend a night and a half programming in java, and instead just have to 'let the simulation run for a while'. you have saved me a tonne of work, man and thanks a huge lot.


If anyone has any suggestions related to this situation, btw, I'd still love to hear them.

[Xriqxa]

It sounds like you are mostly talking about orbital decay and eventual tidal locking. However, I'm not really sure I'm on the same level as you in terms of science and math. Dang, I hate math!

[vh]

yeah it seems the only way is numerical integration aka simulations

https://en.wikipedia.org/wiki/Three-body_problem#n-body_problem

The three-body problem is a special case of the n-body problem, which describes how n objects will move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Sundman for n = 3 and by Wang for n > 3 (see n-body problem for details). However, the Sundman and Wang series converge so slowly that they are useless for practical purposes;[8] therefore, it is currently necessary to approximate solutions by numerical analysis in the form of numerical integration or, for some cases, classical trigonometric series approximations (see n-body simulation).