Question

At what point in an elliptical orbit is the acceleration maximum? At what point is it minimum? Justify your answers.

Short answer

A planet acceleration will be the most when the distance of planet and sun is least and acceleration will be the least when the distance of planet and sun is highest because of the force of the gravity.

Step-by-step solution

Introduction

All the celestial bodies orbit in hyperbolic, parabolic, elliptical, or circular paths around the heavenly bodies in space.

Out of these celestial bodies, theplanet of our solar system moves in an elliptical orbit around the star sun. Inanelliptical orbit, two axes are present—theperihelionand Aphelion

Perihelion is the shortest distance between planet and sun,whereas aphelian is the longest distance between sun andearth.

Earth is a planet of the solar system and it orbit around the sun in an elliptical orbit. All the other planets such as Mercury, Venus, Jupiter, Saturn, Uranus, Neptune, Mars also revolve around the sun in elliptical orbit.

Discussion

In the elliptical orbit around sun, when any planet will be at its furthest distance from the star Sun, the least amount of gravity will be get applied on it, it is showing that the force of gravity is strongest when planet and sun is closest.

In the figure, x and yare axes, O is the meeting point of the axes, e is eccentricity, and a is the distance of perihelion and aphelion from the point O.

The acceleration follows the same principal, meaning that a planet acceleration will be the most when the distance of planet and sun is least and acceleration will be the least when the distance of planet and sun is highest.