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Physics · GRAVITATION

हिन्दी

A planet orbits the Sun in an elliptical path. The distance of the planet at perihelion is \( r_P \) and at aphelion is \( r_A \). If the linear speed of the planet at perihelion is \( v_P \), what is its linear speed \( v_A \) at aphelion?

  1. \( v_A = v_P (\frac{r_A}{r_P}) \)
  2. \( v_A = v_P (\frac{r_P}{r_A}) \)
  3. \( v_A = v_P \sqrt{\frac{r_P}{r_A}} \)
  4. \( v_A = v_P (\frac{r_P}{r_A})^2 \)

Correct answer · Option 2

\( v_A = v_P (\frac{r_P}{r_A}) \)

Explanation

By conservation of angular momentum about the Sun, \( L = m r_P v_P = m r_A v_A \), which yields \( v_A = v_P (\frac{r_P}{r_A}) \).
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