- #1

knowlewj01

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## Homework Statement

Dervie Newton's form of Kepler's third law.

decrribing the orbital motion of two stars in circular orbits with masses M1 and M2, separation a, and period P

ie.

Obtain

F=[tex]\frac{ G M1 M2 }{ a^2 }[/tex]

From

M

_{1}+M

_{2}=[tex]\frac{4 \pi^2 a^3 }{GP^2}[/tex]

## Homework Equations

Centre of mass:

M

_{1}r

_{1}= M

_{2}r

_{2}

a = r

_{1}+ r

_{2}

P = [tex]\frac{2\pi r}{v}[/tex]

## The Attempt at a Solution

[not to good at this LaTeX thing so i'll wing it]

1: switch the (M1 + M2) For P^2

P^2 = (4π^2 a^3)/(G(M1 + M2))

switch the P for the term above:

(4π^2 r^2)/v^2 = (4π^2 a^3)/(G(M1 + M2))

π's cancel:

r^2/v^2 = a^3 / G(M1 + M2)

problem is here that i don't know what the r is, do i have to work out this for r1 and r2 seperatly?

anyone done this before that could point me in the right direction?