NASA is doing research on the concept of a solar sailing cra

NASA is doing research on the concept of a solar sailing craft. if the total output of the sun is 3.9x 10^26 W, how large of a sail is needed to propel a 10,000kg spacecraft against the pull of the sun?

Solution

Photon momentum P = E/c
Since F = d(momentum)/dt,

F = power/c
Power intensity I = P/(4r^2) w/m²
Fsail = I*area/c = P*area/(4r²c)
We want Fgrav = Gm(s)M/r^2 = Fsail = P*area/(4r^2c)
Then area = (4c)*Gm(s)m(vehicle)/P

A=(4*3*10⁸)*(6.67*10^-11 *10000)/(3.9*10²⁶)

A=12.8km²