Question

It is found that the speed of the earth around the sun increases when it is close to the sun.
A. The angular velocity of the earth is constant.
B. The areal velocity of the earth is not constant
C. The areal velocity of the earth is constant
D. None of these.

Answer 1

Hint: Planetary motion around the sun is understood with the help of Kepler’s law. There are three of Kepler’s laws. Kepler’s second law talks about the areal velocity of the planets around the sun. The law states that the imaginary line connecting earth and the sun covers an equal area in an equal period of time. Since the orbit of the earth is elliptical and the sun is at its focus therefore when the earth reaches near the sun, to cover an equal area in equal time the earth’s speed increases.

Complete step by step answer:
Step 1:
Kepler’s first law states that each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the orbital ellipse. The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit.

Step 2:
Kepler’s second law states that the imaginary line joining a planet and the Sun sweep equal areas of space during equal time intervals as the planet orbits. That planets do not move with constant speed along their orbits. Rather, their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times. The point of the nearest approach of the planet to the Sun is termed perihelion. The point of greatest separation is aphelion, hence by Kepler's Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.

Step 3:
The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.

Step 4:
According to the first and second Kepler’s law, it is clear that the earth moves fastest at perihelion where it covers the maximum area in a particular time period. The areal velocity of the earth is constant.

Hence, the correct answer is option (C).

Note: Angular velocity of the earth is not constant because the linear velocity of the earth is not constant and the path of the earth is elliptical. The areal velocity of the earth is constant.