1. Jan 23, 2016

### ft92

1. The problem statement, all variables and given/known data
t has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil.

Assume that the mass of the ship + sail is 1780.4 kg, that the sail is perfectly reflecting, and that the sail is oriented perpendicular to the Sun's rays. How large must the surface area of the sail be if the radiation force is to be equal in magnitude to the Sun's gravitational attraction?

The rate at which the Sun emits energy is 3.90 × 1026 W. The Sun's mass is 1.99 × 1030 kg. The gravitational constant is 6.67 × 10-11 N m2/kg2.

2. Relevant equations
Preflect= 2Ef cos2ϑ /c

3. The attempt at a solution

Ef= (3.9×1026 W)/A = (3.9 ×1026)/ 4πR2 = 3.1×1025/R2

let surface area be Af :

force on ship= Preflect Af= (2×3.1×1025×cos20)(Af)/ 3×108×R2

F= 2.07×1017 (Af)/R2

Fgravitational at R= GMm/R2 = (6.67×10-11×1.99×1030×1780.4)/R2

let F=Fgrav =(6.67×10-11×1.99×1030×1780.4)/(2.07×1017)= 1.14 ×106m2 do you agree with my result?

2. Jan 23, 2016

### Staff: Mentor

The result looks reasonable. Just over a kilometer square.