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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

  1. Ainsufficient data to deduce the relationship between t₁ and t₂
  2. Bt₁ > t₂
  3. Ct₁ = t₂
  4. 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

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