Asteroids X, Y, and Z have equal mass of 4.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 4.0 kg each. They orbit around a planet with M = 3.20×1024 kg. The orbits are in the plane of the paper and are drawn to scale.

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

Explanation / Answer

The period of X is less that of Z.

The angular velocity of Z at c is less than that at n. due to conservation of angular momentum because c is at large distance as compare to n. angular momentum=m*v*r so here r is more for c so velocity will be less

The angular momentum of Y at e is equal to that at s because angular momentum will remain conserved

The angular momentum of Z is equal to that of X because both are having same mass and in angular momentum m*v*r mass is same and the term v*r will also remain same so momentum same

The angular velocity of X at n is equal to that at e because both are at same distance

The period of X is less than that of Y

The angular velocity of Z at n is greater than that of X at n

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