ET9 13.P021.MI Plaskett\'s binary system consists of two stars that revolve in a
ID: 1786322 • Letter: E
Question
ET9 13.P021.MI Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is l = 230 km/s and the orbital period of each is 14.1 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 × 1030 kg.) Note that the expected answer is in 'units' of solar masses. solar masses XCM Need Help?Read ltExplanation / Answer
let r is the radius of orbit.
Time period, T = 2*pi*r/v
==> r = T*v/(2*pi)
= 14.1*24*60*60*230*10^3/(2*pi)
= 4.46*10^10 m
now use,
F = G*M^2/(2*r)^2
M*v^2/r = G*M^2/(4*r^2)
v^2 = G*M/(4*r)
==> M = v^2*4*r/G
= (230*10^3)^2*4* 4.46*10^10/(6.67*10^-11)
= 1.41*10^32 kg <<<<<<<<--------------Answer
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