Deduce that a satellite orbiting a planet of mass $\mathrm{M}$ in a circular orbit of the radius $\mathrm{R}$ has a period of revolution given by

$\mathrm{T}=\sqrt{\frac{4{\mathrm{\pi }}^2{\mathrm{r}}^3}{\mathrm{GM}}}$.

Two stars of equal masses $\mathrm{M}$ orbit a common mass as shown in the diagram. The radius of orbit of each star is $\mathrm{R}$. Assume that each star has a mass equal to $1.5 \mathrm{solar} \mathrm{mass}$  ( solar mass=$2.0\times {10}^{30}\mathrm{kg}$ ) and the initial separation of the star is $2\times {10}^{9 }\mathrm{m}$.

State the magnitude of the force on each star in terms of $\mathrm{M},\mathrm{R} \mathrm{and} \mathrm{G}$.

Two stars of equal mass $\mathrm{M}$ orbit a common mass as shown in the diagram. The radius of orbit of each star is $\mathrm{R}$.

Deduce that the period of revolution of each star is given by $T^2=\frac{16{\pi }^2{r}^3}{GM}$

Two stars of equal mass $\mathrm{M}$ orbit a common mass as shown in the diagram. The radius of orbit of each star is $\mathrm{R}$. Assume that each star has a mass equal to $1.5 \mathrm{solar} \mathrm{mass}$  (solar mass=$2.0\times {10}^{30}\mathrm{kg}$ ) and the initial separation of the star is $2\times {10}^{9 }\mathrm{m}$.

Deduce that the period of revolution of each star is given by $T^2=\frac{16{\pi }^2{r}^3}{GM}$

Evaluate the period numerically