Gravitational Forces

[bstepp99]

Hi, this is my first post and I would really appreciate some help I have for an astronomy homework assignment. The 1st problem involves what would be the net gravitational force exerted on a center asteroid (B) of arbitrary mass 10 placed between two other asteroids, with the left (A) asteroid having an arbirtrary mass of 5 and an arbitrary distance of 3, and the right asteroid © having an arbitrary mass of 10 and an arbitrary distance of 3.

 

I thought that the net gravitational force on (B) would be the gravitational force between (B) and (A) combined with the gravitational force between (B) and ©, but I'm not entirely confident in that idea, and would like assurance for or against it.

 

The diagram for this can be found here:

 

http://img241.imageshack.us/img241/7687/image29st.jpg

 

The 2nd problem is a little simpler, involving identical asteroids with a small distance between them and both having a spheroid shape, and an astronaut being in four points on them. I'm suppose to rank the positions in order from greatest to least in regards to the net gravitational force that would be exerted on the astronaut in the system.

 

I'm not sure if he would feel any difference because the gravitational forces between two objects in a system should be the same on each object, regardless of mass. I would like to know if his location in the system would make any difference. The diagram of this can be found here:

 

http://img71.imageshack.us/my.php?image=image12kp.jpg

 

I'm really sorry for the somewhat confusing and long post, but thanks for anyone who replies, and I deeply appreciate it.

[Ivan]

Hm looks simple but it could be tricky...As for the first question you should be looking mesaurment of gravitational field that exist in the center of asteroid B. You`ll be able to do that by using superpositotion model. Calculaton of force should be easy afterwards if you have knowlage of gravitational force vectors. However you have to asume that the problem is static and to insure that you are determining vector of force in particular moment (for istance t=0) cause if they are moving and have some values of speed then calculs of force in fuction of time becomes a lot harder.