The relationship $r_{c}\left|\overrightarrow{v_{c}}\right|=r_{f}\left|\overrightarrow{v_{f}}\right|$ for an elliptical orbit follows from the fact that the satellite's velocity is perpendicular to its position vector at the two extreme points and also from
A) Conservation of angular momentum.
B) Conservation of energy.
C) Conservation of momentum.
D) Newton's second law.
E) Some other properties of ellipses.
F) (The given relationship is false!)

Question

Quizplus · Accepted Answer

The relationship $r_{c}\left|\overrightarrow{v_{c}}\right|=r_{f}\left|\overrightarrow{v_{f}}\right|$ for an elliptical orbit is a consequence of the conservation of angular momentum. This principle states that the angular momentum of a system remains constant if no external torque acts on it. In the context of a satellite in an elliptical orbit around a planet, the satellite's angular momentum at the closest approach (periapsis) and the farthest point (apoapsis) must be the same because the central gravitational force provides no external torque.

The Relationship rc∣vc→∣=rf∣vf→∣r_{c}\left|\overrightarrow{v_{c}}\right|=r_{f}\left|\overrightarrow{v_{f}}\right|rc​​vc​​​=rf​​vf​​​ For an Elliptical Orbit Follows from the Fact That the Fact

The Relationship $r_{c}\left|\overrightarrow{v_{c}}\right|=r_{f}\left|\overrightarrow{v_{f}}\right|$ For an Elliptical Orbit Follows from the Fact That the Fact