Asteroids X, Y, and Z have equal mass of 9.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 9.0 kg each. They orbit around a planet with M = 7.20 times 10^24 kg. The orbits are in the plane of the paper and are drawn to scale. The three asteroids orbit in the same counterclockwise direction. The angular momentum of Y is .... that of X. The period of X is .... that of Z. The angular velocity of X at r is .... that at n. The angular velocity of Y at n is .... that at i. The angular velocity of Y at n is .... that of X at n. The period of Y is .... that of X. The angular momentum of Y at i is .... that at v.

Explanation / Answer

1.Angular momentum of Y is less than that of X

   L = r X mv = rmv sin theta
if r is greater then L also large if other two quantities are same

2. the period of X is less than that of Z

   T = 2pi *a^3/2 /(sqrt(G*M))

   T is proportional to cube root of semi major axis here X has lee semi major axis so the period of X is less than that of Z

3. The angular velovity of x at r is equal to that at n

4. The angular velovity of Y at n is equal to that at i

5. The angular velovity of Y at n is less than that of X at n

6. The period of Y is less than that of X

7.the angular momentum of Y at i is less than that at v

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