samp18 - . Note that will cancel out, since both and are...

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SAMPLE PROBLEM (Class 18) ANS. The sun’s gravitational attraction is given by the formula, 2 r GMm F g = , where G is the gravitational constant, M is the mass of the sun, m is the mass of the spaceship, and r is their separation. The force due to radiation pressure on a totally reflecting sail of area A is given by, F I c A I c I I P r P p = = 2 2 4 2 , where is the radiation pressure, since the surface is totally reflecting. The intensity can be expressed as where is the total power radiated by the π , sun, and r is the distance from the sun. This is correct because the sun radiates uniformly in all directions. Then, F p can be written as, F P r c A PA r c F GMm r PA r c r F F r p g g p = = = 2 4 2 2 1 2 2 2 2 2 2 . Now, this can be set equal to the expression for to give,
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Unformatted text preview: . Note that will cancel out, since both and are proportional to . If the two forces are made equal at any distance from the sun, they will be equal everywhere. The last equation can be solved for A to give, A cGMm P A = = -2 2 30 10 6 67 10 199 10 1500 390 10 8 11 30 26 . Then, after we look up the numbers, we get, m/s) N m kg kg kg) W 2 2 ( . ( . / )( . )( . A = 9.62 10 5 m If we take the square root of the answer, we find that the area calculated corresponds to a square sail with edges that are 980 m long. Each edge is nearly a kilometer long, or about 0.61 miles....
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