For a planet in orbit around a star the perihelion distance is r_p and its speed at perihelion is v_p.The aphelion distance is r_a and its speed at aphelion is v_a.Which of following is true? A)v_a = v_p B)v_a/r_a = v_p/r_p C)v_a r_a = v_pr_p D)v_a/r_a² = v_p/r_p² E)v_a r_a² = v_pr_p²

Question

Quizplus · Accepted Answer

The correct answer is based on the conservation of angular momentum in an elliptical orbit, where the product of the speed and the radial distance at any two points (such as perihelion and aphelion) remains constant. This is expressed as $v_{\text{a}} r_{\text{a}} = v_{\text{p}} r_{\text{p}}$, where $v_{\text{a}}$ and $v_{\text{p}}$ are the speeds at aphelion and perihelion, respectively, and $r_{\text{a}}$ and $r_{\text{p}}$ are the corresponding radial distances.

For a Planet in Orbit Around a Star the Perihelion