Vector addition and Newton's law

  • #1
38
0

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
ehild
Homework Helper
15,427
1,824
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:
  • #3
sophiecentaur
Science Advisor
Gold Member
24,284
4,308
? or is it more complicated than that?
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.)
 

Related Threads on Vector addition and Newton's law

Replies
4
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
633
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
685
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
4
Views
813
Replies
4
Views
450
Top