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

Question

Asteroids X, Y, and Z have equal mass of 9.0 ka each. They orbit around a planet with M-6.20×1024 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 velocity of Z at i is that at r. The period of Z is... that of X The perlod of Y is that of X The angular velocity of Z at s is... that of X at s. The angular momentum of Z is that of X. The angular velocity of X at c is.... that at s. The angular momentum of Z at r is.... that at s.

Explanation / Answer

By the conservation of angular momentum, MV.R? or MRw.R is constant about focus.
The angular velocity of Z at i is greater than ?that at r.
Time period is proportional to a3/2?. [a is the semi major axis]
? The period of Z is equal to that of X.
? The period of Y is greater than that of X.
The angular velocity of Z at s is equal to ?that of X at s.

The angular momentum of Z is less than ? that of X.

The angular velocity at c is equal to ? that at s.
?The angular momentum of Z at r is equal t?o that at s

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