Asteroids X, Y, and Z have equal mass of 6.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 6.0 kg each. They orbit around a planet with M=3.20E+24 kg. The orbits are in the plane of the paper and are drawn to scale.

In the statements below, TE is the total mechanical energy, KE is the kinetic energy, and PE is the potential energy.

The PE of Z at s is .... the PE of X at r
The PE of Z at m is .... the PE of Y at r
The PE of Y at c is .... that at m
The TE of Y is .... the TE of X
The KE of X at r is .... that at s
The TE of Y is .... the TE of Z
The PE of Z at s is .... the PE of X at s
The speed of Z at m is .... that at i

Greater than / Less than / equal to

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Explanation / Answer

The PE of Z at s is equal the PE of X at r - because the height is same.

The PE of Z at m is greater the PE of Y at r - because its semi major axis is greater

The PE of Y at c is less than that at m

The TE of Y is less than the TE of X - because its semi major axis is smaller

The KE of X at r is equal that at s - because both are at the same revolution

The TE of Y is (greater than) the TE of Z - because it's semi major axis is larger.

The PE of Z at s is greater the PE of X at s -

The speed of Z at m is .... that at i

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