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=5.20E+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.

1. The PE of Y at s is .... the PE of X at i

2.The PE of Y at r is .... the PE of Z at i

3.The TE of Z is .... the TE of X

4.The speed of Y at s is .... that at a

5.The PE of X at u is .... that at s

6. The TE of Y is .... the TE of X

7.The PE of Y at r is .... the PE of Z at r

8.The KE of Z at m is .... that at r

Explanation / Answer

1. The PE of Y at s is ..greater.. the PE of X at i (s is farther than i)

2.The PE of Y at r is ..equal.. the PE of Z at i (both at same distance from the planet)

3.The TE of Z is ..greater.. the TE of X (semimajor axis of x is greater than z)

4.The speed of Y at s is .greater... that at a (more the radial distance less the speed)

5.The PE of X at u is ..less.. that at s (more the radial distance less the speed, so kinetic energy will be high and potential energy will be less)

6. The TE of Y is ..greater.. the TE of X (semimajor axis of y is greater than x)

7.The PE of Y at r is ..equal.. the PE of Z at r (both at same distance from planet)

8.The KE of Z at m is ..equal.. that at r (both at same distance from planet)

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