Question

The figure represents an elliptical orbit of a planet around sun. The planet takes time $T_1$ to travel from $\text{A}$ to $\text{B}$ and it takes time $T_2$ to travel from $\text{C}$ to $\text{D}$ . If the area $\text{CSD}$ is double that of area $\text{ASB}$, then

• A. data insufficient
• B. $T_1=0.5T_2$
• C. $T_1=T_2$
• D. $T_1=2T_2$

Answer 1

The correct option is B $T_1=0.5T_2$

According to Kepler’s second law of planetary motion,

$\text{Areal velocity for path AB =Areal velocity of path CD}$

Hence,

$\frac{\text{Area ASB}}{T_1}=\frac{\text{Area CSD}}{T_2}...\left(1\right)$

According to problem,

$\text{Area CSD =}2\times \text{Area ASB}$

Substituting this in equation $\left(1\right)$, we get

$\frac{\text{Area ASB}}{T_1}=\frac{2\times \text{Area ASB}}{T_2}$

$\Rightarrow \frac{1}{T_1}=\frac{2}{T_2}$

$\therefore T_1=0.5T_2$

Hence, option (c) is correct answer.

Why this question: To make students familiar with the implications of Kepler’s second law.