Asteroids X, Y, and Z have equal mass of 3.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 3.0 kg each. They orbit around a planet with M = 5.20×1024 kg. The orbits are in the plane of the paper and are drawn to scale. The three asteroids orbit in the same clockwise direction.

greater than less than equal to  The angular momentum of Z is .... that of X.
greater than less than equal to  The angular velocity of Z at n is .... that at e.
greater than less than equal to  The angular velocity of X at c is .... that at s.
greater than less than equal to  The angular momentum of X at s is .... that at e.
greater than less than equal to  The angular velocity of Z at e is .... that of X at e.
greater than less than equal to  The period of X is .... that of Y.
greater than less than equal to  The period of Z is .... that of X.

Explanation / Answer

The angular momentum of Z is greater that of X (beacuse the mean radius is larger than X)

The angular velocity of Z at n is equal to that at e (because the radius and speed are same on the same orbit)

The angular velocity of X at c is equal to that at s ( because speed of the particle is high at point c but radius is less where as the speed is less and radius is large at e. both compensate as they move in the same oribt)

The angular velocity of Z at e is less than that of X at e. (angular momentum X is larger than Z)

The period of X is less than that of Y ( because period depends on radius and speed. Larger radius and lesser speed has larger period)

The period of Z is less than that of X.

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