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 M_{Sun} x M_{planet}) / (r x r) = (M_{planet} x V x V) / r
where:
G = Newton's Constant of Gravity
M_{Sun} = The Mass of the Sun
M_{planet} = 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:
M_{Sun} = (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
