Wednesday, 18 Sep 2024

# Kepler’s Law And Rotational Motion

Johannes Kepler explained the motion of planets in the solar system with his laws of planetary motion. These laws are called the Kepler’s laws of planetary motion. Kepler himself did not number these laws. The three laws of planetary motion are

• Kepler’s first law – The law of orbits
• Kepler’s second law – The law of equal areas
• Kepler’s third law – The law of periods

These laws can be expressed mathematically using Newtonian mechanics and the law of universal gravitation.

## Kepler’s first law of planetary motion

According to the first law, all planets move about the sun in an elliptical orbit with the sun at one of its foci. In other words, the law says that the path of the planets around the sun is an ellipse or oval-shaped and it is not a circle. The elliptical path will have two foci and according to the law, the sun is in one of the foci.

## Kepler’s second law of planetary motion

A radius vector joining from the sun to any planet sweeps out an equal area in an equal interval of time. The planets do not move at a constant speed around the sun. Rather, the speed of the planets varies so that the line joining the centre of the sun and the planets sweep out equal areas in equal intervals of time. This means that the planets move faster when they are closer to the sun and move slower when it is away from the sun. The point on the orbit of the sun closest to the sun is called the perihelion and the point on the orbit farthest from the sun is called the aphelion.

## Kepler’s third law of planetary motion

Kepler’s third law states that the square of the time taken by the planet to go around the sun is directly proportional to the cube of the mean distance from the sun to the planet. This means shorter the distance between the planet and the sun, shorter will be time taken to complete one revolution. The innermost planet Mercury takes 88 earth days to revolve around the sun, the earth takes 365 days and Neptune takes 60,190 earth days to go around the sun.

## Uses of Kepler’s laws

The knowledge of these laws, especially the second law helped Sir Issac Newton in the development of the universal law of gravitation. Newton proved with his universal law of gravitation that the same law rules both the heaven and the earth. He said the same rules can be applied for the objects on the earth. The usefulness of Kepler’s law extends to the motion of extrasolar planets, stellar systems, artificial satellites and natural satellites. Kepler’s law is applied to all inverse square law forces.

 Do check BYJU’S pages to find some related topics like rotational motion and translational motion. Pure rotational motion occurs when all the particles of the object move in a circular path about a single line. This single line is called the axis of rotation. Purely translational motion is one in which all the particles of the body move with the same instantaneous velocity. Then the path traced by every particle is parallel to each other.