(Solved): (7\%) Problem 5: You are a scientist exploring a mysterious planet. You have performed measurements ...

(7\%) Problem 5: You are a scientist exploring a mysterious planet. You have performed measurements and know the following things: -The planet has radius $d$. -It is orbiting his star in a circular orbit of radius $b$. -It takes time $T$ to complete one orbit around the star. -The free-fall acceleration on the surface of the planet is $a$. $50\%$ Part (b) Derive an expression for the mass $M_S$ of the star in terms of $b,T$, and $G$ the universal gravitational constant. $M_S=$ \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline$?$ & $?$ & $\mathrm{a}$ & ( & ) & 7 & 8 & 9 & \multirow{2}{*}{ HOME } \\ \hline $\mathrm{b}$ & $\mathrm{d}$ & $\mathrm{g}$ & $?$ & $?$ & 4 & 5 & 6 & \\ \hline $\mathrm{G}$ & $\mathrm{h}$ & $\mathrm{i}$ & & $?$ & 1 & 2 & 3 & \\ \hline $\mathrm{m}$ & $\mathrm{n}$ & $\mathrm{P}$ & + & - & 0 &. & \multirow{2}{*}{ END } \\ \hline $\mathrm{T}$ & $\mathrm{y}$ & $\mathrm{z}$ & $\sqrt{}($ & BACKSPACE & DEL & CLEAR \\ \cline { 1 - 4 } & & & & & & & & \end{tabular}