A spacecraft is powered by a solar sail which has a total cross-seclMal area A o

Question

A spacecraft is powered by a solar sail which has a total cross-seclMal area A of 9.05x10^5 m^2, and a total mass of 6.15x10^3kg. Assuming the solar sail m pointed.so that its axis is parallel with the radius-vector from the Sun, and that it is perfectly reflective, what acceleration will the spacecraft experience if it is at tht distance from the Sun as planet Mars, 1.89 times Karth's distance from the Sun? Assume the luminosity of the Sun L_Sum =3.839xl0^26 W, and the radius of V.arth s orbit R_Eo- 1.50xl0^11M.

Explanation / Answer

In astronomy, luminosity is the total amount of energy emitted by a star, galaxy, or other astronomical object per unit time

Hence the total power received by the satelite will be

P = L * area of satelite/ area of the sphere ( the sphere is the one with sun at the center and satelite on surface)

p = 3.839 * 1036 * 9.05 105/ 3.14 * 2.25 *1022*1.89*1.89 = 1.37 * 1019 W

Mass of the satelite is given to be 6150 Kg.

Heence the acceleration will be

We know that the force is given in this case by

Perfect reflectance: F = 9.08 N per square metre (9.08 Pa)   in the direction normal to surface.

F = ma = 9.08 *10-6 * 9.05 *105 = 8.1 N

a = 1.31 mm/sec2

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