Arturo O. answered • 04/17/18
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Both stars move in a circle of radius r under a centripetal force mv2/r. You know v, and you can get r from
v = 2πr/T,
where T is the given orbital period.
r = vT/(2π)
Plug in v in m/s and T in seconds to get r in meters. The centripetal force must equal the gravitational attraction from the other star at a distance 2r.
mv2/r = Gm2/(2r)2
v2/r = Gm / (4r2)
v2 = Gm/(4r)
m = 4rv2/G
Plug in v in m/s, r in meters, and G in Nm2/kg2, and get m in kg.
Arturo O.
The stars are not orbiting a center mass. They are orbiting AROUND the center of mass. That is not the same thing. The gravitational attraction between 2 masses m1 and m2 separated by a distance d is
F = Gm1m2/d2
In this problem,
m1 = m2 = m
d = 2r (they are at opposite sides of the circle)
Then
F = Gm2/(2r)2
But this same F is what keeps them both in the circular path, so for both masses,
Gm2/(2r)2 = mv2/r
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04/18/18
Gnarls B.
04/17/18