What Is the Angle Between Velocity Vector and Radius-Vector of Part A at 4RE?

[assaftolko]

A body moves in circular motion around the Earth with orbit radius of 3R_E
At a certain time the body detaches to 2 identical parts, each one with a mass of m: A and B. A moves in an angle of 34 deg and B moves straight to the center of the earth.

What is the angle between the velocity vector and the radius-vector of part A when it gets to a distance of 4R_E from the center of the earth?

I think I'm suppose to use angular momentum conservation with respect to the center of the Earth for part A and calculate it's angular momentum just after the detachment and when it's at 4R_E. The problem is that I don't really know how can I justify angular momentum conservation... I think that gravity produces torque and so this is a problem...

 

[gneill]

Gravity produced by a point source will not produce a torque on an orbiting point mass. Assuming that the Earth is taken to be a spherically symmetric distribution of mass, it will produce the same field as a point mass located at its center. Angular momentum is always conserved.

 

[assaftolko]

Gravity produced by a point source will not produce a torque on an orbiting point mass. Assuming that the Earth is taken to be a spherically symmetric distribution of mass, it will produce the same field as a point mass located at its center. Angular momentum is always conserved.

I'm sorry I got confused for a second... r and the gravity force lay on the same line for every moment so of course gravity doesn't produce torque... thanks

 

[gneill]

1. After the detachment - can you still say A is "orbiting" something?
2. Can you reffer me to a source that shows why this is true for the angular momentum?

1. Assuming that the mass of the Earth is much greater than that of A, then Earth's field will dominate the motion of A with respect to the Earth. Whether or not the orbit is closed is another matter (check the velocity of A versus escape velocity at R = 3Re).

2. Angular momentum is ALWAYS conserved. For orbiting objects its a constant of the motion. For a proof, any text on astrodynamics should have a derivation of the equation of motion for the two-body system. One of my favorites is "Fundamentals of Astrodynamics" by Bate, Mueller, and White (very inexpensive yet amazingly good).