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A solar sail spacecraft consists of a boat of mass m fitted with a large flat canvas of area A. The boat is accelerated by the radiation force from sunlight. Find the acceleration of the boat at a distance r from the Sun (power of the Sun = P; assume the sunlight strikes the canvas perpendicularly and the canvas reflects 100% of the incident light).
- PA/(4*pi*r²*c*m)
- PA*c/(4*pi*r²*m)
- PA/(2*pi*r²*c*m)
- PA*c/(2*pi*r²*c*m)
Correct answer: PA/(2*pi*r²*c*m)
Solution
The solar intensity at distance r is I = P/(4*pi*r²). For a perfect reflector, radiation pressure = 2I/c. Force on canvas = 2IA/c = 2PA/(4*pi*r²*c) = PA/(2*pi*r²*c). Acceleration a = F/m = PA/(2*pi*r²*c*m).
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