Which of the following equation implies that the motion of a planet lies in a plane?

A) $\mathbf { r } ( t ) \times \mathbf { v } ( t ) = 0$
B) $\frac { d } { d t } ( \mathbf { r } ( t ) \times \mathbf { v } ( t ) ) = 0$
C) $\mathbf { r } ( t ) \bullet \mathbf { v } ( t ) = 0$
D) $\frac { d } { d t } ( \mathbf { r } ( t ) \cdot \mathbf { v } ( t ) ) = 0$
E) $\frac { d } { d t } ( \mathbf { r } ( t ) \bullet \mathbf { v } ( t ) ) = 1$

Question

Which of the following equation implies that the motion of a planet lies in a plane?

A) $\mathbf { r } ( t ) \times \mathbf { v } ( t ) = 0$
B) $\frac { d } { d t } ( \mathbf { r } ( t ) \times \mathbf { v } ( t ) ) = 0$
C) $\mathbf { r } ( t ) \bullet \mathbf { v } ( t ) = 0$
D) $\frac { d } { d t } ( \mathbf { r } ( t ) \cdot \mathbf { v } ( t ) ) = 0$
E) $\frac { d } { d t } ( \mathbf { r } ( t ) \bullet \mathbf { v } ( t ) ) = 1$

Quizplus · Accepted Answer

The condition $\frac { d } { d t } ( \mathbf { r } ( t ) \times \mathbf { v } ( t ) ) = 0$ implies that the angular momentum of the planet about the center of attraction is conserved. This conservation of angular momentum ensures that the motion of the planet remains in a plane.

Which of the Following Equation Implies That the Motion of a Planet