Query on an object moving in a 2D plane

Athgar

An object is at a known point in a 2D plane, travelling at a known speed in a known direction

In the plane are other objects with known mass and location

With this information, how do you work out where the object will be located one second later?

Doc Al

What forces act on the object?

Athgar

Gravitational attraction from the other bodies in the plane

Doc Al

Unless it's a simple configuration of masses, you'll probably have to use numerical methods to solve for the acceleration and position as a function of time.

Athgar

I'll have to show my ignorance, what is meant by a simple configuration of masses?

Doc Al

By that I just meant a configuration simple enough to solve analytically, without the need for numerical methods.

Athgar

That would typically not be the case

How would I go about solving for the acceleration and position as a function of time?