The figure represents the space shuttle S, which is (a) in a circular orbit about the earth and (b) in an elliptical orbit where P is its perigee position. The exploded views on the right represent the cabin space with its x-axis oriented in the direction of the orbit. The astronauts conduct an experiment by applying a known force F in the x-direction to a small mass m. Explain why F = m does or does not hold in each case, where x is measured within the spacecraft. Assume that the shuttle is between perigee and apogee in the elliptical orbit so that the orbital speed is changing with time. Note that the θ t- and x-axes are tangent to the path, and the -axis is normal to the radial r-direction.
