Three-Body Problem: Calculate Force on Asteroid M1

[MrRandom66]

Homework Statement

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.

Homework Equations

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

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.

 

[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.

 

[MrRandom66]

Three Body Problem

deleted

 

[Doc Al]

Am I right in believing I have to calculate the distance from M1 to M2, and from M1 to M3, add togethter the vectors, to find a new one.

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.

 

[MrRandom66]

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.

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

then force 1 + force 2?

 

[Doc Al]

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

Yes. Where r is the distance between the masses.

then force 1 + force 2?

Yes, but you must add them as vectors. Direction matters.

 

[MrRandom66]

Yes. Where r is the distance between the masses.

Yes, but you must add them as vectors. Direction matters.

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?

 

[Doc Al]

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

Right.

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

Yes.

 

[MrRandom66]

deleted to clarify

 

[MrRandom66]

So, I have G m1 m2 / r^ 2 = 1.3 x 10^-3

G m1 m2 / r^ 2 = 5.6 x 10^-3

(1.3 x 10^-3)^2 + (5.6 x 10^-3)^2 = 2.00000169

this doesn't seem correct.

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

 

[MrRandom66]

Completed it, thanks guys!