# What is the correct way of integrating in astronomy simulations? [closed]

I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean plane, that have properties such as position, velocity, mass, radius and the resultant force.

I want to update the universe in small time steps, usually a few milliseconds, but I'm not sure how to correctly calculate the changes in position.

The force is simple: fr = sum(G * body.m * bodyi.m / dist(body, bodyi)^2).

But how do I go on from there?

I could do this:

a = Fr/body.m
v += a*dt
position += v*dt


But that would, of course, be false. Maybe if I added 0.5 as a factor in position calculation?

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The FAQ says 'Some kinds of questions should not be asked here: [...] Computational questions'. See the scientific computation beta site. But search first as I think this has already been addressed. There are also several such questions on Stack Overflow. –  dmckee Oct 27 '12 at 19:50
And don't fret the silly automatic down vote: it will time out in a few days. –  dmckee Oct 27 '12 at 19:50
I reposted it on the computation site. Also, if you see those similar questions on SO, please throw me a link. –  akled Oct 27 '12 at 20:02
I don't have any particular questions in mind, but searches like "planet gravity" turn up some possibilities that look promising. –  dmckee Oct 27 '12 at 20:26
@dmckee automatic downvote, WTF ...?! Who has implemented such a needless and mean thing into SE? I quite often disagree about how things work or are implemented by the "overlords" into the SE sites against the will or needs of the respective communities, but such a thing is really over the top now ...! So I +1 the question to revert it –  Dilaton Oct 27 '12 at 22:18