H By the time the Satif reaches LEO it has ejected the massi

(H) By the time the Satif reaches LEO, it has ejected the massive empty Falcon-9rocket, which it no longer needs. Now, Sarif needs to escape the solar system and travel to Kapteyn-b. To do this it must unfurl a huge solar sail. Starting with impulse-momentum theory, use the Poynting vector for elecromagnetic radiation to derive the expression for solar radiation pressure in terms of the luminous flux (intensity) of the sun and the speed of light.

Solution

Electromagnetic waves transport linear momentum as well as energy. It follows that, as this momentum is absorbed by some surface, pressure is exerted on the surface. We shall assume in this discussion that the electromagnetic wave strikes the surface at normal incidence and transports a total energy U to the surface in a time t. Maxwell showed that, if the surface absorbs all the incident energy U in this time, the total momentum P_em transported to the surface has a magnitude P_em = <U>/c

The pressure exerted on the surface is defined as force per unit area F/A

Pressure P = F/A = 1/A. dP_em/dt = 1/c. (d<U>/dt)/A

We recognize (dU/dt)/A as the rate at which energy is arriving at the surface per unit area, which is the magnitude of the Poynting vector.

So, P = <S>/c = I/c.