Question

The sun has a mass of 1.99 x 10³⁰ kg and a radiation power of 3.90 x 10²⁶ Watts. A spaceship might be propelled in our solar system by the radiation pressure from the sun, using a large sail made of foil (sailing on the solar wind). If the ship has a mass of 1,000 kg and if the sail is a perfectly reflecting square with sides of length L, what is the smallest value of L (in meters) that will allow the ship to escape the sun's gravitational attraction? (The gravitational constant G = 6.67  x 10^-11 Nm²/kg².)

Answer 1

To find the minimum sail size we set the magnitude radiation force equal to the magnitude of the gravitational force as follows

where I have used I = P_sun/(4πr²) with r is the distance to the sun. Solving for L yields,