HW17 - Prof. I. Biaggio Solutions HW 17 Physics 90, Fall...

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Prof. I. Biaggio Solutions HW 17 Physics 90, Fall 2006 1-5 Solutions Homework 17 24 From the orbital period of the moon and its distance we can find the centripetal acceleration that is responsible to keep it on its orbit. This centripetal acceleration must be given by the force of gravity, which then gives us the mass of the earth. The mass for a circular orbit is easily found by equating centripetal acceleration to the acceleration due to the gravitational force, GM/r 2 . For a general orbit, the same thing holds true but one needs to replace the distance with the average distance. This goes under the name of “Kepler’s third law”. Picture the Problem Kepler’s 3 rd law is normally written to relate the period of the moon to the mass of the earth and the mean earth-moon distance. ( a ) Using Kepler’s 3 rd law, relate the period of the moon to its mean orbital radius: 3 m E 2 2 m 4 r GM T ! = Solve for M E : 3 m 2 m 2 E 4 r GT M = Substitute numerical values and evaluate M E : ( ) ( ) kg 10 02 . 6 h s 3600 d h 24 d 3 . 27 /kg m N 10 6.6726 m 10 3.84 4 24 2 2 2 11 3 8 2 E ! = " # \$ % ! ! ( ! ! = ) ! M *26 The acceleration of any object while it falls depends only from the gravitational force that is acting on it. So we just need to calculate the gravitational field and we have the acceleration. The only possible complication (but a trivial one) is that we are given the position of the object in terms of its distance from the surface of the earth, so we must add the radius of the earth to find the distance from the center of the earth. As one last little trick, we can find the solution to this problem by comparing with the acceleration at the surface of the earth. Picture the Problem We can relate the acceleration of an object at any elevation to its acceleration at the surface of the earth through the law of gravity and Newton’s 2 nd law of motion. Letting

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This note was uploaded on 04/02/2008 for the course PHY 90 taught by Professor Unknown during the Spring '08 term at Lehigh University .

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HW17 - Prof. I. Biaggio Solutions HW 17 Physics 90, Fall...

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