# Homework Help: Three-body problem

1. Nov 30, 2011

### MrRandom66

1. The problem statement, all variables and given/known data

Three asteroids of masses M1 = 1.00 ×10^6 kg, M2 = 2.00 ×10^7 kg and M3 = 3.00 ×10^7 kg can be found at the positions r1 = (0, 0) m, r2 = (1 ×10^3, 0) m and r3 = (0, 6 ×10^2) m respectively. Calculate the resultant gravitational force on the asteroid of mass M1.

2. Relevant equations

F= (G m1 m2 m3 / r^2) r (this second r with a caret ^ and in bold type, thus being a unit vector)

3. The attempt at a solution

I'm usually pretty good at equations, but what has confused me is how to use the vectors in the equation. As i'm pretty sure the answer will require a vector which has a direction and magnitude, i'm not really sure where to begin with this one.

2. Nov 30, 2011

### RTW69

Plot the asteroids on a coordinate system. Find the magnitude and direction of the gravitational forces from asteroids 2 and 3 on asteroid 1. Add the two vectors together to get resultant vector. Calculate magnitude and direction of resultant vector.

3. Dec 1, 2011

### MrRandom66

Three Body Problem

deleted

Last edited: Dec 1, 2011
4. Dec 1, 2011

### Staff: Mentor

Re: Three Body Problem

No.

First calculate the force that M2 exerts on M1. That will involve find the distance between them, but that's easily gotten from the coordinates without any calculation. Find the magnitude and direction of that force.

Do the same for the force that M3 exerts on M1.

Then add those two vectors to find the total force on M1.

5. Dec 1, 2011

### MrRandom66

Re: Three Body Problem

So, use the equation here? G m1 m2 / r^2 = force 1
G m1 m3 / r^2 = force 2

then force 1 + force 2?

6. Dec 1, 2011

### Staff: Mentor

Re: Three Body Problem

Yes. Where r is the distance between the masses.
Yes, but you must add them as vectors. Direction matters.

7. Dec 1, 2011

### MrRandom66

Re: Three Body Problem

the distance between the masses only depends on m1 and m2, and then m1 and m3 right?

And by adding the vectors, is this where i use pythagarus' therom?

8. Dec 1, 2011

### Staff: Mentor

Re: Three Body Problem

Right.
Yes.

9. Dec 1, 2011

### MrRandom66

deleted to clarify

Last edited: Dec 1, 2011
10. Dec 1, 2011

### MrRandom66

ok, redone my calcs, to get 5.7 x 10^-3

11. Dec 1, 2011

### MrRandom66

Completed it, thanks guys!

Last edited: Dec 1, 2011