59. Each star is attracted toward each of the other two by a force of magnitude GM2/L2,along the line that joins the stars. The net force on each star has magnitude 2(GM2/L2) 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 Ris the radius of the orbit, Newton’s second law yields (GM2/L2) cos 30°= Mv2/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.