Question

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$, respectively. If $T_{A}$ and $T_{B}$ are the time period of star $A$ and star $B$, respectively, then:

• A. $\frac{T_{A}}{T_{B}}=\left(\frac{r_{A}}{r_{B}}\right)^{\frac{3}{2}}$
• B. $T_{A}=T_{B}$
• C. $T_{A} T_{B}\left(\right.$ if $\left.m_{A}>m_{B}\right)$
• D. $T_{A}>T_{B}\left(\right.$ if $\left.r_{A}>r_{B}\right)$

Answer 1

Answer: (B)

$T_{A}=T_{B}$ (since $\omega_{A}=\omega_{B})$