Asteroids X, Y, and Z have equal mass of 7.0 kg each. They orbit around a planet
ID: 1457969 • Letter: A
Question
Asteroids X, Y, and Z have equal mass of 7.0 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 Y at a is .... the PE of X at u
The TE of Y is .... the TE of Z
The PE of Z at u is .... the PE of X at u
The TE of Z is .... the TE of X
The KE of X at a is .... that at u
The speed of Y at i is .... that at m
The PE of Y at a is .... that at m
The PE of Y at c is .... the PE of Z at u
Explanation / Answer
We know that the total energy, TE=-m(GM)/2a
a=semi major axis
The PE of Y at a is greater than the PE of X at u
(PE increases with distance [=height] from attractive body.)
The TE of Y is greater than the TE of Z
(TE is constant; Y reaches a greater "height")
The PE of Z at u is equal to the PE of X at u
Since asteroids have same mass
The TE of Z is less than the TE of X
The KE of X at a is equal to that at u
The speed of Y at i is less than that at m
(height is less; speed decreases with height
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