STANDARD Physics Kepler's Laws MCQ Question

The relationship between the two time periods is $t_1 = 2t_2$.

Step-by-Step Explanation

Kepler's Second Law (Law of Equal Areas)A line connecting a planet to the Sun sweeps out equal areas in equal periods of time.

This means the ratio of the area swept to the time taken is always constant:$\frac{\text{Area}}{\text{Time}}=\text{Constant}$Set up the RatiosLet the smaller area $SAB$ be equal to $A$.

The problem states that area $SCD$ is twice area $SAB$. So, $\text{Area } SCD = 2A$.Apply the Formula$\frac{\text{Area\ }SCD}{t_{1}}=\frac{\text{Area\ }SAB}{t_{2}}$Substitute the values into the equation:$\frac{2A}{t_{1}}=\frac{A}{t_{2}}$Simplify the EquationCancel out $A$ from both sides:$\frac{2}{t_{1}}=\frac{1}{t_{2}}$Cross-multiply to solve:$t_{1}=2t_{2}$