Question

In a certain binary star system, each star has the same mass as our sun.They revolve about their centre of mass.The distance between them is the same as the distance between earth and the sun. What is their period of revolution in years ?

• A. $0.31yr$
• B. $0.71yr$
• C. $0.82yr$
• D. $0.94yr$

Answer 1

The correct option is B $0.71yr$

$\frac{2\pi }{\sqrt{GM}}{r}^{3/2}=1$ yr

$\frac{G\left(M\right)\left(M\right)}{r^2}=\frac{M{v}^2}{\left(r/2\right)}$

$\therefore v=\sqrt{\frac{GM}{2r}}$

$T=\frac{2\pi \left(r/2\right)}{v}$

$=\frac{\pi r}{\frac{\sqrt{GM}}{2r}}$

$=\sqrt{2}\left(\frac{\pi }{\sqrt{GM}}\right)r^{3/2}$

$=\sqrt{2}\left(\frac{1}{2}\right)$yr $\left[as\frac{\pi r^{3/2}}{\sqrt{GM}}=\frac{1}{2}yrs\right]$

$=0.71yr$