# The Laws of Planetary Motion UPSC

The first Greek scholar Aristotle (384-322 B.C.) presented his concept regarding the movement of the planets, in which he told that the Earth is located in the center of the universe and the Sun is revolving around it. This concept continued till 1530 AD. But, in 1530 AD, Polish scholar Copernicus denied this concept in his book ‘De Revolutionibus‘ and first told that the center of the universe is not the Earth but the Sun, around which the Earth and other planets revolve.
Gravitational force plays an important role in the movement of celestial bodies. Black holes act as centers of gravity to run the universe. Our universe is full of many such black holes. The stars revolve around the galaxy. Our Sun is a star, which revolves around its galaxy Milky Way in 25 crore years.
The bodies which revolve around the Sun in their respective orbits in the sky are called ‘planets’. The celestial bodies that revolve around a planet are called satellites. The object of this rotation is the center of gravity. The black hole located at the center of the galaxy for the stars, the Sun for the planets and the planetary center of gravity for the satellites. This gravitational force is universal. According to Newton, every particle of matter in the universe attracts every other particle towards itself. This all-pervasive force of attraction is called the force of gravity.

## Laws of Planetary Motion

In 1571 AD, Kepler propounded three laws related to the motion of the planets. which are mentioned below. as

### Law of Orbits

All the planets revolve around the Sun in Elliptical orbits and the Sun is at one focus of the orbits. In the figure, the Sun S is at the focus of an elliptical orbit of a planet.

### Law of Areas

The line joining any planet to the Sun covers equal areas in equal intervals of time, that is, the areal speed of the planet remains constant. ,
The second law states that when a planet is farthest from the Sun (Aphelion), its speed is minimum, and when it is closest to the Sun (Perihelion), its speed is maximum.

### Law of Revolution Period

The square of the period of revolution of any planet around the Sun (the time taken to make one complete revolution) is proportional to the third power (cube) of the semi-major axis of its elliptical orbit. Is . That is, this rule states that the more distant the planet from the Sun, the longer its rotation period. * The rotation period of the nearest planet Mercury is 88 days, while the rotation period of the distant planet Neptune is 164.8 years.

## Newton’s findings

On the basis of Kepler’s laws, Newton made the following conclusions

(1) A (centripetal) force acts on the planet whose direction is towards the Sun.
(2) This force is inversely proportional to the square of the distance between the planet and the Sun. ,
(3) This force is directly proportional to the mass of the planet. Since the force between the planet and the Sun is mutual, the force must be directly proportional to the mass of the Sun.

According to Newton, this sequence is applicable not only between the Sun and the planets but also between any two particles in the universe. This is Newton’s law of gravity.
In 1686, Newton stated that every particle of matter in the universe attracts every other particle towards itself. This all-pervasive force of attraction is called ‘gravitation’. Newton gave the following law of gravitation
The force of attraction between two material particles is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. Its direction is perpendicular to the line joining the two particles.

## Acceleration due to Gravity of Earth

When an object is released freely from above, it starts falling towards the earth and the velocity of its fall keeps on increasing. Therefore, acceleration is produced in its motion. This acceleration is called ‘Earth’s acceleration due to gravity’. Thus, the gravitational acceleration of the Earth is the increase in the velocity of an object falling freely towards the Earth in a second. It is denoted by ‘g’. It does not depend on the size, shape, mass etc. of the object.
The unit of gravitational acceleration is ‘metre/second’ or ‘newton/kg’.

Earth’s acceleration due to gravity g = 9.80 m/s*
Earth’s mass = 6.0 x 1024 kg*
Average density of Earth = 5.5 x 103 kg/m*

Changes in the value of Earth’s gravitational acceleration The value of Earth’s gravitational acceleration g varies at different places on the Earth’s surface. The value of g also changes on going up or down from the earth’s surface.
The value of g on the Earth’s surface is lowest at the equator and highest at the poles.
There are two reasons for this – the size of the earth and the rotation of the earth around its axis.

## Shape of the Earth

The shape of the earth is a geoid. Giyad is that surface which passes through the average height of the land masses (i.e. through the middle of the sea level and that land mass) and the average depth of the oceans and seas, i.e. between the ocean floor and the ocean bottom of a place.
Thus the earth is not perfectly round but somewhat flattened at both the poles. Its radius at the equator is about 21 kilometers more than the radius of the poles. We know that the value of earth It is dependent on the radius of .* It is clear that the smaller the value of the radius, the greater the value of g. As we move from the equator towards the poles, the value of radius decreases. Hence the value of g goes on increasing.

The value of decreases on going above the surface of the earth.
The value of g also decreases on going down from the earth’s surface.
Since the value of g changes from one place on the earth’s surface to another, and on going up or down from the earth’s surface. Therefore, the standard value is at the sea level of 45° latitude. Its normative value is 9.80 m/s2.

### Rotation of the Earth

• The earth is rotating around its axis. Therefore, every object located on the earth surface is moving on a circular path. We know that an object moving in a circular path has a centripetal acceleration towards the center of the circle. This acceleration is taken from the gravitational acceleration g, so the observed value of g will be less than the value that would have been at every point on the Earth’s surface in the absence of the Earth’s axial rotation speed.
• If the Earth stops rotating around its axis, then the value of g (the weight of an object) will increase everywhere except the poles. * This increase will be maximum at the equator and will decrease towards the poles. On the contrary, if the angular velocity of the earth increases, then the weight of objects will decrease at every place except the poles. ,
• If instead of 24 hours the Earth starts making one round in 1.4 hours, then the weight of any object on the equator will become zero. But the mass will remain the same.
• In fact, about 65% of the change in the value of g on the Earth’s surface is due to the Earth’s axial rotation and the remaining about 35% is due to the flattening of the Earth’s shape.