Physics
posted by Luis .
two binary stars moving in a perfect circle orbit
The stars have the same mass, the distance between them is one billion km (1x10^9 km), and the time each takes for one orbit is 10.4 Earth years.
Determine the mass of each star (m1=m2).
(this problem DOESN'T uses the gravity formula with the G constant.
this problem must be solve using circular dynamics ecuations so please help!!!!)

Actually, the solution will involve the G constant. You will have to use it to compute the mass, unless you use Kepler's third law in a different form the involves the sum of the masses of the two objects, in terms of solar mass. "G" is already "built in" to that solution
Equalmass stars revolve in orbits (circular in this case) about a point midway between the stars. The radius of each star's orbit is d/2, where d is the interstellar separation, 10^12 m.
Centripetal force = Gravity force
Let either mass be m.
G*m^2/d^2 = m*V^2/(d/2)= 2m*V^2/d
or G*m/d = 2*V^2
V*Period = 2*pi*d/2 = pi*d
Eliminate V from the first equation, using V from the second equation, and solve for the mass, m
V = pi*d/Period = 9573 m/s
m = 2*d*V^2/G