Question

Asteroids X, Y, and Z have equal mass of 6.0 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.

Options are (greater than, less than, equal to)

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

Answer 1

Total energy of asteroid of mass m, orbiting a plant of mass M is an elliptical orbit of semi major axis a is T E = -G H m/2 a Since energy is observed T E = K E + P E since angular momentum Vertical-bar L Vertical-bar = m v r sin theta where v is speed of asteroid at a distance r from planet and theta is the angle between r and v For a circular orbit of radius R potential energy is same every where P E = -G H m/R Kinetic energy is same every where K E = m v^2/2 = G H m/2 R (1) conserving the angular momentum of X at C and at S . m r_c r_c sin theta_c = m v_s r_s sin theta_s