A possible spacecraft design uses a solar sail made of aluminized plastic. As su

Question

A possible spacecraft design uses a solar sail made of aluminized plastic. As sunlight reflects off the sail, radiation pressure drives the spacecraft outward away from the sun. If the sail material has a density of 625.0 kg/m3, what is the maximum thickness of the sail for which the force due to radiation pressure exceeds the gravitational force on the sail?


If the collector's area is 1.2106 m2. its thickness is 1 µm, and the craft carries a 78.0 kg payload, what is its acceleration at the radius of the Earth's orbit?

please i need very well detailed answer

Explanation / Answer

force of radiation pressure = area of sail*2I/c where I is intensity of sun I = Power of sun / 4pi r^2 Grav force on sail = G *mass of sun* mass of sail / r^2 So, putting this together: G M m / r^2 = A * 2 P / c 4 pi r^2 cancel r^2 both sides G M (density of sail*Area of sail* thickness) = 2 A P / 4 c pi cancel A both sides... "d" is thickness: G M d = 2 P / 4 c pi (note: P is power output of sun, M is mass of sun) so d = P / 2 pi c G M = 3.86x10^26 / 2pi 3x10^8 * 6.67x10^-11 * 1.99x10^30 = 0.00154 meters or 1.54 millimeters

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