A solar sail allows a spacecraft to use radiation pressure for propulsion, simil

Question

A solar sail allows a spacecraft to use radiation pressure for propulsion, similar to the way wind propels a sailboat. The sails of such spacecraft are made out of enormous reflecting panels. The area of the panels is maximized to catch the largest number of incident photons, thus maximizing the momentum transfer from the incident radiation. If such a spacecraft were to be simply pushed away from a star by the incident photons, the force of the radiation pressure would have to be be greater than the gravitational attraction from the star emitting the photons. The critical parameter is the area density (mass per unit area) of the sail.

To solve the second part of this problem you will need to know the following:

the mass of the sun, Msun=2.0×1030kg,

the intensity of sunlight as a function of the distance, R, from the sun,

Isun(R)=3.2×1025WR2,

and

the gravitational constant G=6.67×10?11m3/(kg?s2).

Part B

Suppose that the mirror described in Part A is initially at rest a distance R away from the sun. What is the critical value of area density for the mirror at which the radiation pressure exactly cancels out the gravitational attraction from the sun?

Express your answer numerically, to two significant figures, in units of kilograms per meter squared.

View Available Hint(s)

1.6e?31.6e^{-3}

1.6e?31.6e^{-3}

Explanation / Answer

B)

Isun = 3.2 x 1025/R2

A = area

radiation pressure = gravitational force

2IA/c = GMsun m/R2

2 (3.2 x 1025) A/((3 x 108)R2) = (6.67 x 10-11) (1.99 x 1030) m/R2

2 (3.2 x 1025) A/((3 x 108)) = (6.67 x 10-11) (1.99 x 1030) m

2 (3.2 x 1025) /((3 x 108)) = (6.67 x 10-11) (1.99 x 1030) (m/A)

m/A = 0.0016

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