A planet moving along an elliptical orbit is closest to the...

A planet moving along an elliptical orbit is closest to the sun at a distance $\mathrm{r}_{1}$ and farthest away at a distance of $\mathrm{r}_{2}$. If $\mathrm{v}_{1}$ and $\mathrm{v}_{2}$ are the liner velocities at these points respectively, then the ratio $\left(\mathrm{v}_{1} / \mathrm{v}_{2}\right)$ is $\ldots \ldots \ldots \ldots$ (A) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)$ (B) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)^{2}$ (C) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)$ (D) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)^{2}$

A planet moving along an elliptical orbit is closest to the sun at a distance $\mathrm{r}_{1}$ and farthest away at a distance of $\mathrm{r}_{2}$. If $\mathrm{v}_{1}$ and $\mathrm{v}_{2}$ are the liner velocities at these points respectively, then the ratio $\left(\mathrm{v}_{1} / \mathrm{v}_{2}\right)$ is $\ldots \ldots \ldots \ldots$
(A) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)$
(B) $\left(\mathrm{r}_{1} / \mathrm{r}_{2}\right)^{2}$
(C) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)$
(D) $\left(\mathrm{r}_{2} / \mathrm{r}_{1}\right)^{2}$

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Key Concepts

Elliptical Orbits

Elliptical orbits describe the paths of celestial bodies moving under the influence of gravity in a shape that is an elongated circle. In these orbits, there are two key points: the perihelion, where the orbiting object is closest to the focal point (such as the sun), and the aphelion, where it is farthest away. Understanding the geometry of ellipses and the variation in orbital distances is fundamental to analyzing the dynamics of planetary motion.

Conservation of Angular Momentum

Conservation of angular momentum is a key principle in orbital mechanics which states that when no external torque acts on a system, the angular momentum remains constant. In the context of an elliptical orbit, this principle leads to the relationship that the product of the radial distance and the tangential velocity remains constant at any two points along the orbit. This concept is pivotal in understanding how the velocity of a planet changes as its distance from the central body varies during its orbit.

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