A spaceship is in a circular orbit of radius r₀ about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship’s speed by 50%. This causes the spaceship to move into an elliptical orbit.

a. What is the spaceship’s new speed, just after the rocket burn is complete, in terms of M, G, and r₀?

b. In terms of r₀, what are the spaceship’s maximum and minimum distances from the planet in its new orbit?