Question

Out of aphelion and perihelion, where is the speed of the earth more, and why?

Answer 1

Hint: The areal velocity of the earth around the sun will always be constant. Hence, the speed of the earth at aphelion is less than the speed of the earth at perihelion. The earth will be at a longer distance from the sun in case of aphelion and distance will be less in case of perihelion. In all cases when the earth revolves around the sun in elliptical orbit its areal velocity will be constant. That here the angular momentum is conserved.

Complete answer:
Thus perihelion and aphelion are the two positions of the earth around the sun where the distance from the sun is minimum or maximum. That is, the perihelion has maximum distance from the sun, where the distance is less in case of aphelion. The areal velocity of earth around the sun will always be constant. Hence, the speed of earth at aphelion is less than the speed of earth at perihelion. The earth will be at a longer distance from the sun in case of perihelion and distance will be less in case of aphelion. In all cases when the earth revolves the sun in elliptical orbit its areal velocity will be constant. That here the angular momentum is conserved.
This is an important application of Kepler’s first law of planetary motion. This law states that every planet revolves around the sun in an elliptical orbit with the sun as its one of its foci. Thus the position of earth at shortest and longest distance are perihelion and aphelion. And Kepler’s second law is a consequence of conservation of angular momentum. That is, the real velocity of a planet around the sun is constant.
Gravitational force, $F=\dfrac{GMm}{{{R}^{2}}}$
Where, G is the gravitational constant.
M is the mass of earth.
m is the mass of the planet revolving around earth.
R is the radius of earth.

Note: As the distance from the sun to the planet increases the velocity of the planet decreases and as the distance between sun and the earth decreases the velocity increases. Thus perihelion and aphelion are the two positions of the earth around the sun where the distance from the sun is minimum or maximum. That is, the perihelion has maximum distance from the sun, where the distance is less in case of aphelion. The areal velocity of earth around the sun will always be a constant according to Kepler’s second law.