# I Vector addition and Newton's law

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1. Jun 1, 2018

### xaratustra

I know that n-body problem can be complicated, but that's for the dynamics. What about a static case:

e.g. if I have the distances of several bodies A, B and C etc. and their distance to a reference mass m, can I just use the vector addition of the Newton's gravitational force to add up all of the forces from all those bodies to the reference mass and obtain the resulting vector? or is it more complicated than that?

2. Jun 1, 2018

### ehild

If you want the net force on the reference body with mass m, just add all the gravitational forces vectorially. Yes, it is that simple. You need the position of all other bodies with respect to the reference body, as the forces of gravity depend on the difference vectors $\vec r_i-\vec r _0$.
The system is static if the net force at each body is zero (not only at the reference body).

Last edited: Jun 1, 2018
3. Jun 1, 2018

### sophiecentaur

It doesn't need to be harder to comprehend in principle but you end up with what's effectively a set of simultaneous non linear equations and it gets very complicated if you want to work out the paths of those bodies. Working out the resultant force on each body is only the start. Look at the wiki article on the three body problem (and that's only three.)