Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation
The elliptical path of a planet around the sun is illustrated in the figure. The two shaded regions have equal areas. If t₁ and t₂ represent the time taken by the planet to travel from a to b and from c to d respectively,
Options
- Ainsufficient data to deduce the relationship between t₁ and t₂
- Bt₁ > t₂
- Ct₁ = t₂
- Dt₁ < t₂
Correct answer
C. t₁ = t₂
Step-by-step solution
According to Kepler's second law of planetary motion, the areal velocity of a planet revolving around the sun is constant. This means that the line joining the planet to the sun sweeps out equal areas in equal intervals of time. Let A₁ and A₂ be the areas of the two shaded regions. It is given that A₁ = A₂ . Since the areal velocity A t is constant, the time taken to sweep equal areas must be equal. Therefore, the time t₁ taken to travel from a to b is equal to the time t₂ taken to travel from c to d . Thus, t₁ = t