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# homework2sol - Ke y for AST3018 H MW 2 31 Points Leah Simon...

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Key for AST3018 HMW 2 31 Points Leah Simon October 1, 2009 2.1 (3 pts) Using the equation: v esc = 2 GM r (1) and the values G = 6.67 × 10 11 m 3 /kg/s 2 , M = M Sun = 1.989 × 10 30 kg, and r = Earth’s Orbit = AU = 1.496 × 10 11 M we get v esc = 4.21 × 10 4 m/s. Using the equation: v orbit = GM r (2) We find v orbit = 2.98 × 10 4 m/s. Therefore, v esc /v orbit = 2 . 2.2 (3 pts) Using the equation: F = GMm r 2 = mg (3) we find there is a relationship such that M Earth R Earth 2 = a M obj R obj 2 (4) Where a is a constant relating g object to g Earth . Therefore, using values taken from the book, we find a.) g Moon = 0.17 g Earth b.) g Sun = 27.9 g Earth and c.) g Jupiter = 2.54 g Earth 2.3 (3pts) Use the equation W = mg where W is the weight in Newtons, m is the mass in kg and g is the gravitational acceleration on Earth, a) on Earth W = 75 kg * 9.8 m s -2 = 735 N b) on the Moon, recall from previous question g Moon = 0.17 g Earth so W = 75 kg * 0.17 * 9.8 m s -2 = 121 N

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c) in the space shuttle at an altitude of 400 km, g = GM/R 2 , where M = M Earth , R = R Earth + 400 km = 6.778 x 10 6 m, then g shuttle = 8.677 m s -2 and W = 75 kg * 8.677 m s -2 = 651 N 2.4 (3 pts) This is a large problem, but quite simple to solve with the right equations. First we start
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homework2sol - Ke y for AST3018 H MW 2 31 Points Leah Simon...

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