A planet orbits in an elliptical path of eccentricity e around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by P and the point where it is farthest is denoted by A. Let $\mathrm{v}_{\mathrm{p}}$ and $\mathrm{v}_{\mathrm{a}}$ be the respective speeds at $\mathrm{P}$ and $\mathrm{A}$. Then-

• Correct answer
  A

  $\frac{\mathrm{v}_{\mathrm{P}}}{\mathrm{v}_{\mathrm{A}}}=\frac{1+\mathrm{e}}{1-\mathrm{e}}$
• B

  $\frac{v_{p}}{v_{A}}=\frac{1+e^{2}}{1-e}$
• C

  $\frac{\mathrm{v}_{\mathrm{P}}}{\mathrm{v}_{\mathrm{A}}}=1$
• D

  $\frac{v_{P}}{v_{A}}=\frac{1+e^{2}}{1-e^{2}}$

Hence, the correct answer is option: 'A'.