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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman
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Binary Star—Equal Masses. Two identical stars with mass M

Chapter 13, Problem 71P

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QUESTION:

Binary Star—Equal Masses. Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. (a) Find the gravitational force of one star on the other. (b) Find the orbital speed of each star and the period of the orbit. (c) How much energy would be required to separate the two stars to infinity?

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QUESTION:

Binary Star—Equal Masses. Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. (a) Find the gravitational force of one star on the other. (b) Find the orbital speed of each star and the period of the orbit. (c) How much energy would be required to separate the two stars to infinity?

ANSWER:

Solution 71P The gravitational force of attraction between two bodies with masses M and M and separated 1 2 by a distance R is given by F =GM M1 2 …..(1) R2 Since the two stars are always on the opposite sides of the circle of radius R, hence the distance between them is = 2R Each star has a mass of M. (a) Substituting these values in equation (1), we get 2 F = GM 2 (2R) GM 2 F = 4R2 Th

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