The radiation pressure created by electromagnetic waves might someday be used to

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.