A binary star system consists of two stars of masses M1 and M2 revolving in circular orbits of radii R1 and R2 respectively. If the respective time periods are T1 and T2

Question

A binary star system consists of two stars of masses M1 and M2 revolving in circular orbits of radii R1 and R2 respectively. If the respective time periods are T1 and T2 (A) T1>T2 if R1>R2 (B) T1>T2 if M1>M2 (C) T1=T2 (D) (T1/T2)=((R1/R2))3/2

Tardigrade Admin · Accepted Answer

In a binary star system, there are two stars moving under their mutual gravitational force of attraction. Their angular velocities are equal and hence their periodic times are also equal.

[∵ ω = \frac{2 π}{T}]

∴ T_{1} = T_{2}

Q. A binary star system consists of two stars of masses $M_{1} an d M_{2}$ revolving in circular orbits of radii $R_{1} an d R_{2}$ respectively. If the respective time periods are $T_{1} an d T_{2}$

$T_{1} > T_{2} i f R_{1} > R_{2}$

$T_{1} > T_{2} i f M_{1} > M_{2}$

$T_{1} = T_{2}$

$\frac{T _{1}}{T _{2}} = (\frac{R _{1}}{R _{2}})^{3/2}$

In a binary star system, there are two stars moving under their mutual gravitational force of attraction. Their angular velocities are equal and hence their periodic times are also equal.
$[∵ ω = \frac{2 π}{T}]$
$∴ T_{1} = T_{2}$

Q. A binary star system consists of two stars of masses M1​andM2​ revolving in circular orbits of radii R1​andR2​ respectively. If the respective time periods are T1​andT2​

T1​>T2​ifR1​>R2​

T1​>T2​ifM1​>M2​

T1​=T2​

T2​T1​​=(R2​R1​​)3/2