Simulating orbital gravity with a prediction of trajectory (Multiple attractors)

Game Mechanics
#1

Hello fellow programmers,
I saw this post about simulating orbital gravity : http://www.java-gaming.org/topics/orbital-mechanics-keplers/35771/msg/339215/view.html#msg339215
I’m trying myself to predict more-than-two-body attractions and I don’t really know which data structure I should use to achieve this result, I wanted to know which method you used at the time.
I also tought of only using scalar (something like a ‘gravity’ tension) in a grid.

Thanks in advance for your answers

tl;dr:I’m trying to predict the trajectory of a body with multiple attractors (a static one and multiple moving ones)

#2

Just run the simulation, why would you need to predict anything?

#3

predicting is simulating. anyway, if you want to try discreet instead of continuous … leapfrog integration is a very good choice. it is orbit stable and reversible.

looks like http://cvarin.github.io/CSci-Survival-Guide/leapfrog.html

#4

Maybe this will be of use: https://youtu.be/OAcXnzRNiCY

OAcXnzRNiCY

#5

Sorry, I mean predicting future positions depending on the present ship velocity and position much like what you would see in Kerbal Space Program:

The player would than see how moving his ship alter his orbit.
The difference being that I would like the ship to get attracted by many bodies (The Earth And Asteroids if they are big and/or close enough).
I know that I won’t be able to make exact predictions but approximate ones should be enough.

Hope I’m more clear now and thanks for the quick replies.

#6

Yeah, so simulate it.

#7

I assume that what you’re looking for is: given the data of a body, figure out what its position will be after N seconds given that it is attracted by these K other bodies. This is actually an unsolved mathematical problem: https://en.wikipedia.org/wiki/N-body_problem

[quote]To this purpose the two-body problem has been completely solved and is discussed below; as is the famous restricted 3-Body Problem.
[/quote]
The only real way of “solving” this with more than 2/3 bodies is to simulate the whole thing. There are no known formulas or algorithms that don’t involve integrating with a certain time step (AKA simulating).