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Two-body problem



 
 
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Old March 10th 14, 01:09 PM posted to sci.physics,sci.astro
Yousuf Khan[_2_]
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Default Two-body problem

I was asked this by somebody doing a homework question, and I realized
that I don't know how to solve for the mass of the smaller body. Here's
the question:

"You observe a main sequence type B5 star that moves as if it is in a
binary system, but no companion is visible. If the period of the system
is 8.4 years and the semi-major axis is 8 AU, what is the mass of the
system? What is the mass of the companion?"

Using Kepler's 3rd Law, I was able to deduce that the star is about 7.25
solar masses, which conforms well to known masses of Class B5 stars (eg.
Rho Aurigae, http://is.gd/w85MlS). Here's the formula I used:

G · m · t² = 4 · π² · r³

Now, how do you solve for the mass of the companion? I assume it is a
planet, being much smaller than the star.

Yousuf Khan
 




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