The radiation pressure created by electromagnetic waves might someday be used to
ID: 1402667 • Letter: T
Question
The radiation pressure created by electromagnetic waves might someday be used to power spacecraft through the use of a "solar sail".
1) Assuming total reflection, what would be the pressure on a solar sail located at the same distance from the Sun as the Earth (where I = 1350 W/m2)? P = ?
2) Suppose the sail material has a mass of 2×103 kg/m2 . What would be the acceleration of the sail due to solar radiation pressure? a = ?
3) A realistic solar sail would have a payload. How big a sail would you need to accelerate a 150-kg payload at 1×103 m/s2? A = ?
Explanation / Answer
since,I = 1350 W/m² at earth.
A = area of sails .
For a completely reflective sail , where: c = 3 ×10^8 m/sec
Pressure = 2I c = 2(1350) (3 ×10^8) = 9 ×10^(- 6) N/m²
now P = m* a
9 ×10^(- 6) = 2×103 * a
a = 4.5 x 10^-3 m/s^2
here m' = 0.002 kg/m^2 * A + 150
Force = pressure * area
m' * 1 x 10^-3 = 9 ×10^(- 6) N/m² * A
(0.002 kg/m^2 * A + 150) * 1 x 10^-3 = 9 ×10^(- 6) N/m² * A
0.002 kg/m^2 * A* 1 x 10^-3 - 9 ×10^(- 6) N/m² * A = - 150 * 1 x 10^-3
A(0.002 kg/m^2 * 0.001 - 9 ×10^(- 6) N/m²)= - 150 * 1 x 10^-3
A = 150 * 0.001 / (7 x 10^-6 ) = 21428.57 m^2