Question

A comet is moving in an elliptical orbit around the Sun. When it is closest to the Sun, its distance from the Sun is R and its speed is V. Its time period is 3 years. When the other comet is farthest from the Sun, its distance is 3R and the time period for this comet will be
(A) $9\sqrt{3}\mathrm{Years}$ (B) $9\sqrt{2}\mathrm{Years}$ (C) $3\sqrt{9}\mathrm{Years}$ (D) $6\sqrt{3}\mathrm{Years}$

Answer 1

Dear Student ,
Here in this case from the given data we can write that ,
$$\begin{gathered} \frac{{T_1}^2}{{T_2}^2}=\frac{{R_1}^3}{{R_2}^3} \\ \Rightarrow \frac{{\displaystyle 9}}{{\displaystyle {T_2}^2}}=\frac{{\displaystyle R^3}}{{\displaystyle 27R^3}} \\ \Rightarrow T_2=\sqrt{27\times 9}=9\sqrt{3}years \end{gathered}$$
Regards