Answer:
T=0.7 [y]
Step-by-step explanation:
The period equation in a circular motion can be written as:
(1)
where:
- v is the tangential velocity
- T is the period of revolution
is the distance between the first star and the center of mass. - r is the distance between two stars
We can find v using the gravitational force equation between two stars:
(2)
- G is the gravitational constant
- M is the mass of the stars
Now, the force here is just a centripetal force, so

Combining this relation with (2) we have v:
(3)
Let's put (3) into (1):


Before finding the period, let's recall some information:
(distance between earth and sun)
(solar mass)
(gravitational constant)
Finally the period in years will be:
![T=\sqrt{(2\pi^(2) r^(3))/(GM)}=2.24\cdot 10^(7) [s]](https://img.qammunity.org/2020/formulas/physics/high-school/pgatsgrlt74z935hvynpnhork7ch10c7qu.png)
![T=0.7 [y]](https://img.qammunity.org/2020/formulas/physics/high-school/fx45ky8ksm0fqr72iuwddtu09mnc75azdk.png)
Have a nice day!