Gravitation and Kepler’s Laws

Gravitation and Kepler’s Laws



Gravitational force is one of the most basic forces of nature. It is a force that acts between any two objects in the universe and it is always attractive. We call gravitational force attractive since it always tries to bring masses closer and never pushes it away. It is the force with which all the objects are attracted towards the centre of the earth. The motion of the moon around the earth, the earth around the Sun are all governed by the force of gravity.

The universal law of gravitation was first stated by Newton. According to the law, every particle of matter in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

If two particles of masses m1 and m2 are separated by a distance d and F is the force of attraction between them, then

F = G.m1.m2/d2

Where G is the gravitational constant.

Motion of Planets and Satellites

Planets are the celestial body that revolves around the sun while satellites (natural or artificial) are bodies that revolve around the planet. The motion of the planets and satellites can be analysed using the laws of motion and the universal law of gravitation. According to Kepler’s laws of planetary motion, all the planets revolve around the sun in elliptical orbits with the sun at one of the focal points. The force responsible for this motion is mainly the interaction between the sun and a given planet. A good deal of information regarding planetary motion can be obtained by considering the special case of circular orbits. The results obtained can also be applied to the motion of the satellite around a planet.

Kepler’s law

The complete analysis of the motion of the planet is summarised in three important laws known as Kepler’s laws of planetary motion. Kepler’s laws can also be derived mathematically by Newtonian mechanics and universal gravitation.  Let us discuss the three laws of planetary motion in detail here.

Kepler’s first law of motion

Kepler’s first law of motion states that “ All planets move in elliptical orbits around the sun with the sun at one of the focal points. The point on the orbit where the planet is closest to the sun is called perihelion and the point at which the planet is farthest from the sun is called aphelion.

Kepler’s Second law of motion

Kepler’s second law of planetary motion states that “The radius vector drawn from the sun to the planets sweeps out equal areas in equal intervals of time”. According to Kepler’s third law, the angular momentum remains constant since the areal velocity for the planets revolving in elliptical orbits remains constant.

Kepler’s Third law of motion

According to Kepler’s third law of motion “The square of the period of revolution of the planet is directly proportional to the cube of the semi-major axis of the elliptical orbit”

From the third law of motion, we understand that if the orbits are shorter then the time taken by the planets to complete one revolution is shorter.

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