Question

Consider a spacecraft in an elliptical orbit around the Sun with a semi-major axis of 0.5 AU and an orbital eccentricity of 0.5.

A. What is the speed of the spacecraft at the perihelion of its orbit?

B. Suppose that at perihelion, it instantaneously deploys a massless solar sail directed such that the surface of this solar sail is exactly normal to a line from the Sun to the spacecraft. Assume that the sail is large enough that the radiation pressure from the solar photons exactly balances the Sun's gravitational force on the spacecraft. Suppose that subsequent to this, the solar sail's surface is always normal to the Sun-spacecraft line. Describe what will happen to the spacecraft. Be as quantitative as possible. (Neglect the effect of the solar wind, and Poynting-Robertson effect and consider only the effects from radiation pressure and gravity from the Sun).

C. What is the area of the solar sail that is required so that the forces associated with radiation pressure and gravity cancel? You may assume the sail itself has negligible mass. Assume the mass of the spacecraft is 5000kg, and the radiation pressure coefficient, Q=2.

D. Suppose that its new orbit takes it directly by Pluto. How long will it take the spacecraft to reach Pluto? (Assume Pluto is at a distance of 40 AU from the Sun).

Answer 1