Circular Motion and Gravitation of a star

AI Thread Summary
The discussion centers on a homework problem involving two equal-mass stars in circular motion, maintaining a constant distance of 8.0 x 10^10 m apart and rotating every 12.6 years. The key question is why the stars do not collide due to gravitational attraction and what their mass must be. The initial calculation for mass yielded 2.4 x 10^26 kg, which was incorrect compared to the book's answer of 9.6 x 10^26 kg. The error was identified as a misunderstanding of the distance used in the gravitational force equation, where the full distance between the centers of mass was needed instead of half. The discussion concludes with the realization of this mistake and a correction to the mass calculation.
Carpe Mori
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Homework Statement


Two equal-mass stars maintain a constant distance apart of 8.0 x10^10 m and rotate about a point midway between them at a rate of one revolution every 12.6 yr
(a) why don't the two stars crash into one another due to the gravitational force between them
(b) what must be the mass of the stars

Homework Equations



F = G*m1*m2/r^2
F(r) = ma(r)
a(r) = v^2/r
v = 2*pi*r/T

The Attempt at a Solution


part b i said m1 = m2 = m
F = ma(r)
F(12) = m*(2*pi*r/T)^2 / r
F(12) = G*m^2 / r^2

substitution and solving for m gave me

m = ((2*pi*r)^2 * r )/ (G*T^2)

substituting i got 2.4 *10^26 kg

answer in book is like 9.6*10^26 kg

can someone point out my error(s) to account for this discrepancy?
 
Physics news on Phys.org
anyone?
 
oh snaps i figured it out

if anyone cares...

my mistake was that in the equation for graviational attractive force (F = G*m1*m2/r^2) the r is actual distance between the two center of masses and my mistake was that i thought it was half of that distance (the radius)

so yeah...cheers?
 

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