Suppose a spaceship runs out of fuel near a star. The crew erects a square, white sail 7.06 km on a side, and adjusts it so it faces the star so the photons hit the sail head-on. At their current distance the intensity of the starlight at the ship's location is 6380 W/m2. Assume:

- the sail is totally reflective: the photons strike the surface and bounce off at the same speed.

- the central frequency of the photons from the star is the same as the photons from part a.

- the central frequency of the photons from the star is also the average frequency.

i. Find the magnitude of the force exerted by the photons on the sail:

F = N

ii. Find the temperature of the star's surface:

T = K

iii. If the star is evolving so its surface temperature is rising at 683 K per century, the rate at which the central frequency is changing is:

df/dt = Hz/century