An edge-on spectroscopic binary is monitored throughout its orbit. The spectroscopy indicates the orbits are close to circular (so you may assume circular in this problem) and that the speeds found for the two stars are v1 and v2. Stars 1 and 2 have masses m1, m2 and semi-major axes a1, a2 (same as radius, since circular orbits), respectively. (a) Choosing an axis such that the center of mass position is at xCoM = 0, show that that mass ratio is the inverse of the semi-major axis ratio, i.e. show that m1/m2 = a2/a1. (b) What is the mass ratio, m1/m2, in terms of the two measured speeds, v1 and v2?

An edge-on spectroscopic binary is monitored throughout its orbit. The spectroscopy indicates the orbits are close to circular (so you may assume circular in this problem) and that the speeds found for the two stars are v1 and v2. Stars 1 and 2 have masses m1, m2 and semi-major axes a1, a2 (same as radius, since circular orbits), respectively. (a) Choosing an axis such that the center of mass position is at xCoM = 0, show that that mass ratio is the inverse of the semi-major axis ratio, i.e. show that m1/m2 = a2/a1. (b) What is the mass ratio, m1/m2, in terms of the two measured speeds, v1 and v2?

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Question

An edge-on spectroscopic binary is monitored throughout its orbit. The spectroscopy indicates the orbits are close to circular (so you may assume circular
in this problem) and that the speeds found for the two stars are v1 and v2.
Stars 1 and 2 have masses m1, m2 and semi-major axes a1, a2 (same as
radius, since circular orbits), respectively.
(a) Choosing an axis such that the center of mass position is at xCoM = 0,
show that that mass ratio is the inverse of the semi-major axis ratio, i.e.
show that m1/m2 = a2/a1.
(b) What is the mass ratio, m1/m2, in terms of the two measured speeds,
v1 and v2?

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