This question came up as a review question. Any help with this would be greatly appreciated.
A comet is observed to have a speed when it is at a distance from the Sun, and its direction of motion makes an angle with the radius vector from the Sun. Show that the major axis of the elliptical orbit of the comet makes an angle
with the initial radius vector of the comet where and are dimensionless ratios.
NOTE: and are the velocity and radius of Earth respectively. Assume the Earth's orbit about the Sun is circular.