# hw 20 - homework 20 HETTIGER CHRISTOF Due Mar 5 2008 4:00...

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homework 20 – HETTIGER, CHRISTOF – Due: Mar 5 2008, 4:00 am 1 Question 1, chap 9, sect 4. part 1 of 1 10 points Given: k = 4 π 2 G M s , where M s is the mass of the Sun. Suppose that the gravitational force law between two massive objects is F g = G m 1 m 2 r 2+ ǫ , where ǫ is a small number. Which of the following would be the rela- tionship between the period T and radius r of a planet in circular orbit? 1. T 2 = k r 3+ ǫ correct 2. T 2 = k r 2+3 ǫ 3. T 2 = k r 3 4. T 2 = k r 3 5. T 2 = k r 3 ǫ 6. T 2 = k r 3+2 ǫ 7. T 2 = k r 3 - 2 ǫ 8. T 2 = k r 3+2 9. T 2 = k r 2 - 3 ǫ 10. T 2 = k r 3 - ǫ Explanation: Kepler’s third law changes from its normal form if gravity is not quite an inverse square law. Let M p be the mass of a planet and M s be the mass of the Sun. r will be the radius of the orbit. M p v 2 r = G M s M p r 2+ ǫ . Since v = 2 π r T 4 π 2 r 2 r T 2 = G M s r 2+ ǫ . Kepler’s third law becomes T 2 = 4 π 2 G M s r 3+ ǫ , where 4 π 2 G M s is a constant.

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