Question

The following figure shows the elliptical path of a planet about the Sun. The two shaded parts, $S1$ and $S2$, have equal areas. If $t_1$ and $t_2$ be the time taken by the planet to go from $A$ to $B$ and from $C$ to $D$ respectively, then:

• A. $t_1>t_2$
• B. $t_1<t_2$
• C. $t_1=t_2$
• D. $t_1$ and $t_2$ cannot be compared.

Answer 1

The correct option is C $t_1=t_2$

According to Kepler’s law, the line joining a planet and the Sun sweeps equal areas in equal intervals of time during the rotation of the planet around it.
Here, the regions $S1$ and $S2$ have the same area. Thus, the time taken for the planet to go from $C$ to $D$ is equal to the time taken for the planet to go from $A$ to $B$. Hence, $t_1=t_2$