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A spacecraft is powered through a solar sail, which reflects sunlight. The area of the sail is 1 km^2, oriented perpendicular to the direction to the Sun. The spacecraft is at 1 AU from the Sun. The sunlight falling on the sail has a power of 1380W/m^2.

(a) Calculate the momentum in this sunlight, and from this derive the pressure exerted on the solar sail by the sunlight;

(b) What is the maximum mass of the sail for which the force from light exceeds the gravitational force from the Sun?

For (a), which forumulae should be used here? I didn't find anything useful online and have no idea of a systematic textbook that I can read.

For a single photon, the momentum p=E/c which depend on frequency or wavelength. But here only enegry flux and surface area are given.

For (b), I presume I should equate the gravitational force and the light pressure to solve for the mass. Or do I have to consider the escape speed of the solar system?

PS: This question is at the level of first year uni physics.

Thank you.

lkjhgtf
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The force exerted by radiation on a surface has a magnitude of $$ F = \frac{1+R}{c}\int \vec{N}\cdot d\vec{A},$$ where $\vec{N}$ is the time-averaged Poynting vector (power per unit area) of the incoming radiation in Wm$^{-2}$, with a direction given by the direction of the electromagnetic waves (or photons). This is integrated over the area $A$ of the solar sail, but the scalar product takes account of the angle of the sail to the radiation. The term $R$ is the reflectivity of the sail, where $R=1$ doubles the force applied to the sail, because the momentum change of the light is doubled.

An important point though, is that this is only the magnitude of the force. The direction of the force will be opposite to the net momentum change of the radiation.

ProfRob
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