Is Gravitational Force A Central Force: Why, How And Detailed Insights


In this article, let us discuss whether gravity is a conservative force or non-conservative, and secondly, is gravitational force a central force or non-central.

Gravitational force is said to be a conservative force because the work done on the object to travel from one position to another is independent of the time taken and the magnitude of the force is constant.

What is Gravitational Force

The gravitational force is one of the fundamental forces in nature and is the weakest force of attraction.

The two objects having mass exert a force of attraction on each other, and this force is centralized at a focus between the line joining the two objects. As the distance between the two increases, this gravitational pull among the both becomes weaker and weaker by the square of the distance separating them both.

The law of Gravitation states that “Every object attracts every other object in the universe by the force which is directly proportional to the product of the two objects and inversely proportional to the square of the distance between the two” and is denoted by the equation:

F=G*(m1m2)/r2

G=6.67*10-11

Where

m1 is mass of object 1

is mass of object 1

m2 is mass of object 2

is mass of object 2

‘r’ is a distance between the two objects

At r=∞, the gravitational force will be equal to zero.

Why Gravitational Force is Central Force

When the two bodies are bounded by the gravitational force of attraction, the force imposed is equal in magnitude and acts in opposite directions towards each other separated by a distance.

Consider a satellite revolving around the Earth. The mass of the satellite compared to the Earth is very negligible and hence the Earth will accelerate at a very minute rate than that of the satellite. The gravitational attraction between both will tend the satellite having less mass than the Earth to revolve around the Earth in a circular orbit. This follows Kepler’s 2nd Law, according to which “the line joining the satellite to the planet Earth will sweep equal areas in equal interval of time”.

For a body to keep in a continuous motion the force has to always act towards the center and the velocity of the object radially pointing outward. The magnitude of the force at the focus depends upon the length of the separation between the centers of gravities of both systems. The gravitational pull between the two keeps the satellite revolving around the Earth in a circular orbit, hence gravitational force is a central force.

is gravitational force a central force
Satellite revolving around planet Earth; Image Credit: Quora

The satellite around the planet will move in uniform circular motion under the action of a centripetal force given by

Fc=mv2/r

Equating this with equation of gravitational force

mv2/r =G*(Mm)/r2

‘v’ is the speed of orbiting satellite around the Earth.

The cycle maintains its momentum while riding is actually because of the central force absorbed by the spinning wheels that help to keep the momentum of the cycle constant and hence the rider is able to keep the cycle in a vertical position. If the momentum applied to the cycle is equal to zero then the cycle will fall on the ground. The direction of the angular momentum lies along the axis of rotation. The greater the speed of the wheels more will be the momentum of the cycle. We can ride a bicycle as the momentum is conserved because of the circular motion of the wheels.

In the same manner, the momentum of the satellite is conserved due to the central force acting due to the gravitational force between the Earth and the satellite.

Why Gravity is Conservative Force

Gravity is a force of attraction experienced by objects towards the center of the Earth. Every object having mass possesses a center of gravity and is bonded to one another by the gravitational pull of attraction. The gravitational force is a long-range force between the two bodies having mass and does not depend on any field and therefore is a non-contact force.

The weight of any object on the Earth will be the mass times the acceleration due to gravity. The potential energy of the object at a certain height above the surface of the Earth is P.E. = mgh. Work done in bringing the object from height ‘h’ to the surface of the earth is the same as the potential energy associated with that object at a particular height ‘h’.

The body at rest has some potential energy associated with it, if there is a slight change in potential energy then it is obvious that there is some work done by the system. The work done in a close path is always zero as the force experienced on the bodies is independent of a path taken and hence the gravitational force is conserved.

Work done to displace the object from one place to another is

Work done to displace the satellite from point 1 to point 2 is

Since work is associated with the potential energy, Potential Energy U= -G*(m1m2)/r2

The negative sign indicates that the gravitational force is always attractive.

ThereforeForce F=-dU/dr;

In central force, the total energy T.E. = K.E. + P.E. =(1/2)mv2+mgh

The angular momentum between the two masses L=r*mv=Constant

This implies that the momentum of the object in orbit is conserved and no work is done in this process hence the total energy is conserved. Therefore a gravitational force is conservative.

Unit of Gravitational force

The unit of gravitational force is Newton, named after the scientist Isaac Newton for his discovery.

The value of the universal gravitational constant G is 6.67*10-11 N.m2/kg2. In the CGS unit we have

Therefore, the unit of the gravitational force is Newton.

Read more on Is Gravitational Force A Contact Force: Why, How, When and Detailed Facts

Frequently Asked Questions

What is the force of gravity acting on the object having a mass of 1.5kg on the surface of the Earth?

We know:

Mass of the Earth ME=5.98*1024 kg

Mass of the object m=1.5kg

The radius of the Earth r=6.38*106m

Acceleration due to gravity g=9.8m/s2

Gravitational constant G=6.67*10-11Nm2kg2

Solution:

What is the range of gravitational force?

The gravitational force is equal in magnitude and acts in opposite directions towards each other.

The range of the gravitational force is infinite. The gravitational force is strongest between the objects having high masses and are closest to each other; the same becomes weaker if the distance between the objects is much larger and at an infinite distance, no gravitational force is observed.

What is a central force?

Spring force, electrostatic force, gravitational force, centripetal forces are some examples of the central forces.

Force acting on the object is directed along the line joining the object and the origin is called central force.

Will you observe a change in your weight if you move from Goa to Greenland?

Yes. Greenland is located near the North Pole of the Earth.

As the acceleration due to gravity is greater at the poles there will be a slight increase in the weight than your weight measured in Goa.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122

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