16) For a corner reflector to be effective,its surfaces must be precisely perpen

Question

16) For a corner reflector to be effective,its surfaces must be precisely perpendicular. Suppose the surfaces of a corner reflector left on the Moon's surface by the Apollo astronauts formed a 90.001 degree angle with each other. If a laser beam is bounced back to Earth from this reflector, how far (in Kilometers) from its starting point will the reflected beam strike Earth? For simplicity, assume the beam reflects from only two sides of the reflector, and that it strikes the first surface at precisely 45 degrees.

Explanation / Answer

With the error stated the third angle of the corner triangle would be 180 - 45 - 90.00002 = 44.99998o So the angle of incidence on the reflector will be 90 - 44.99998 = 45.00002o So the error will be 0.00002o ...Using the mean Earth-moon radius to b 3.48x10^5km ... we have s = r*? = 3.84x10^5km*(0.00002*(2p rad /360o) = 0.134km

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