Satellite surrounded by four asteroids question

[tjhero123]

Homework Statement

A 100 kg satellite is surrounded by four asteroids. Asteroid A has a mass of 8.5x10^5 kg and is 800 km North of the satellite. Asteroid D has a mass of 9.0x10^4 kg and is 500 km West of the satellite. Asteroid B is 1200 km south of the satellite and asteroid C is 1500 km East of the satellite. The satellite is in equillibrium.
A) What are the masses of asteroids B and C?
B) What is the gravitational force between asteroids B and C?
C) Describe how the satellite would move if asteroid A was suddenly removed.

Homework Equations

Pythagorean theorem
F=(Gm1m2)/(r^2)
G=6.67384x 10^-11 m^3 kg^-1 s^-2

The Attempt at a Solution

Honestly I have no idea. My inital idea was to create right triangles between A and D to find the distance between them and use Newtons universal gravitation equation to calculate the force due to gravity in that area. Then i thought i could use that value for the other asteroids and make right triangles with them to do the same thing except solving for masses instead. But I am not sure if that would be correct. I assume this is the process used to find the answer to B though. But i need the masses first. Am i on the right track by using right triangles? For C, I was thinking that maybe the satellite would move towards the center of the triangle formed by asteroids B,C , and D and become an incenter of that traingle or something. Any help would be nice. thanks in advance :)

 

[pgardn]

It easier than you are making it.

Two asteroids along the x axis, east and west, must exert the same force on the satellite.
Same for the north south, y axis, if you wish.

 

[tjhero123]

since the satellite is at equillibrium, that means there is no acceleration or unbalanced forced in the system. Am i right in that the only forces in action are the one that each asteroid has on the satellitle and the four oppositly directed forces the satellite has on the asteroids? I don't see how i can use this to find the masses or even the forces. What am i missing??

 

[pgardn]

since the satellite is at equillibrium, that means there is no acceleration or unbalanced forced in the system. Am i right in that the only forces in action are the one that each asteroid has on the satellitle and the four oppositly directed forces the satellite has on the asteroids? I don't see how i can use this to find the masses or even the forces. What am i missing??

Set the forces of the asteroids (on the satellite), directly across from each other, equal to each other using your universal gravitation equation. The mass of the satellite should drop out(G as well) and you should have one unknown, the mass of one of the two asteroids.

All we care about is the satellite. The asteroids might have unbalanced forces acting on them, but all we care about is the immediate situation presented in the problem.

 

[tjhero123]

So you would get an equation identical to (9.0x10^4)/(500^2)=(mass of asteroid C)/(1500^2). And you solve to get 8.1x10^5 kg? and then i would do the same with the Y axis asteroids? And for B, once I know their masses, is there where I would use a right triangle to find their distance and solve using universal gravitation equation? Also for C if A is removed, will the Satellit accelerate North due to the force of asteroid B? Thank you for all the help by the way.

 

[pgardn]

So you would get an equation identical to (9.0x10^4)/(500^2)=(mass of asteroid C)/(1500^2). And you solve to get 8.1x10^5 kg? and then i would do the same with the Y axis asteroids? And for B, once I know their masses, is there where I would use a right triangle to find their distance and solve using universal gravitation equation? Also for C if A is removed, will the Satellit accelerate North due to the force of asteroid B? Thank you for all the help by the way.

Yes.

Part b just asks for the force between a pair of masses. You could do this for any pair as long as you know both masses and the distance between their centers using the gravitation equation and solving for force. It's a 3rd law thing. Be careful with your units, G is usually expressed with the use of meters, not km.

For c you can draw the relative magnitude and direction of all the forces acting on the asteroid and get a relative net force, thus a description of the satellites accel. and motion given the immediate setup of masses. Here is where you can finally use your triangle stuff if they want an exact direction of the initial motion.