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The Question

(Submitted May 27, 1997)

What are the different methods to weigh a star? Is it possible to use the Doppler shift?

The Answer

Yes, you are correct, the most accurate method of "weighing" a star is by use of the Doppler shift. Let me explain.

To find the mass of the Sun we take advantage of the planets orbiting it. Each planet requires a centripetal force to keep it from flying away; this force is supplied by the Sun's gravity. Setting these two forces equal to each other we can write an equation (also in introductory physics books):

Force of Gravity = Centripetal Force

(G x MSun x Mplanet) / (r x r) = (Mplanet x V x V) / r

where:
G = Newton's Constant of Gravity
MSun = The Mass of the Sun
Mplanet = The Mass of the Planet (like the Earth)
V = The Velocity the planet that is orbiting
r = The distance from the planet to the Sun (1 A.U. for the Earth)

simplifying the equation we see the the mass of the planet cancels out (using algebra) so:

MSun = (V x V x r) / G

Now, we will apply this same idea to other stars. However there is one big catch -- we cannot see planets orbiting other stars. So what do we do? We look at binary star systems. In a binary star system, there are two stars orbiting each other.

We measure the velocity of each star (V) using the Doppler shift that you referred to, and the distance between each star the their common center of mass (r) (which we find by taking pictures of the stars through a telescope). So we can find the total mass of the stars using the same equation as above.

I hope this explains your question.

Thank you very much for asking.

Sincerely,

Jonathan Keohane
for Ask an Astrophysicist

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