ch13-p059

# ch13-p059 - 59 Each star is attracted toward each of the...

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59. Each star is attracted toward each of the other two by a force of magnitude GM 2 / L 2 , along the line that joins the stars. The net force on each star has magnitude 2( GM 2 / L 2 ) cos 30 ° and is directed toward the center of the triangle. This is a centripetal force and keeps the stars on the same circular orbit if their speeds are appropriate. If R is the radius of the orbit, Newton’s second law yields ( GM 2 / L 2 ) cos 30 ° = Mv 2 / R . The stars rotate about their center of mass (marked by a circled dot on the diagram above) at the intersection of the perpendicular bisectors of the triangle sides, and the radius of the orbit is the distance from a star to the center of mass of the three-star system. We take the coordinate system to be as shown in the diagram, with its origin at the left-most star. The
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## This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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