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 threestar system. We take the
coordinate system to be as shown in the diagram, with its origin at the leftmost 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.
 Spring '08
 Any
 Physics, Force

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