# Another gravity question

1. Oct 17, 2012

### assaftolko

A body moves in circular motion around the earth with orbit radius of 3RE
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 4RE 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 4RE. 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...

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2. Oct 17, 2012

### Staff: Mentor

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.

3. Oct 17, 2012

### assaftolko

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

4. Oct 17, 2012

### Staff: Mentor

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).