Asteroids X, Y, and Z have equal mass of 8.0 kg each. They orbit around a planet

Question

Asteroids X, Y, and Z have equal mass of 8.0 kg each. They orbit around a planet with M=6.20E+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 Y at u is ... the PE of X at a The PE of Y at i is ... the PE of Z at i The speed of Y at u is ... that at i The PE of X at a is ... the PE of Z at i The PE of X at s is ... that at u The TE of Y is ... the TE of X The TE of Z is ... the TE of X The KE of Z at r is ... that at i

Explanation / Answer

The PE of Y at u is greater than PE of X at a (because u is farther out than a)

The PE of Y at i is the same as PE of Z at i (since the asteroids have the same mass)

The speed of Y at u is less than that at I (height is less; speed decreases with height)

Rest also have the same reasoning as above unless stated otherwise

The PE of X at a is greater than the PE of Z at i

The PE of X at s is less than at u

The TE of Y is greater than TE of X

The TE of Z is nearly equal to the TE of X (their semi major axes are approximately equal)

The KE of Z at r is equal to that at i (at same distance)

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