A satellite of mass m = 3.94e + 3 kg is in circular orbit around the Earth, and the radius of this orbit is ro = 1.04e + 4 km. Take th mass of the Earth to be ME = 6 × 1024 kg. The satellite is subject to a small frictional force of magnitude f = 0.0269 N due to the outer atmosphere of the Earth. Because of this force, the satellite will slowly spiral back towards Earth. What is the change in radius Ar of the satellite after one revolution (assuming the starting radius is ro as given above)? Hint: Assume that the change in radius is slow enough that at any instant of the orbit the satellite can be considered to be undergoing circular motion. Also, since this change in radius will be small, in the sense that A«1, you may (and should) use a Taylor expansion to find a close (i.e., first-order) approximation to the exact answer. Note: You should take Newton's constant to be G 6.674 x 1011 Nkg-2m?

A satellite of mass m = 3.94e + 3 kg is in circular orbit around the Earth, and the radius of this orbit is ro = 1.04e + 4 km. Take th mass of the Earth to be ME = 6 × 1024 kg. The satellite is subject to a small frictional force of magnitude f = 0.0269 N due to the outer atmosphere of the Earth. Because of this force, the satellite will slowly spiral back towards Earth. What is the change in radius Ar of the satellite after one revolution (assuming the starting radius is ro as given above)? Hint: Assume that the change in radius is slow enough that at any instant of the orbit the satellite can be considered to be undergoing circular motion. Also, since this change in radius will be small, in the sense that A«1, you may (and should) use a Taylor expansion to find a close (i.e., first-order) approximation to the exact answer. Note: You should take Newton's constant to be G 6.674 x 1011 Nkg-2m?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 38PQ

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