The Universal Law of Gravitation

Introduction

We live on the earth, and on it, we can walk and breathe air that does not escape into space. Life on earth is possible because of gravity.

Gravity is also the phenomenon that governs all planetary motion in space. Gravity is the attractive property of any given mass. Gravitation does not depend on the path being followed and is a conservative force. 

Gravitation and Gravity

Gravitation can be defined as the attractive force between two bodies that possess mass. On the other hand, gravity is the property of a single mass’s ability to attract another mass. 

The term ‘gravity’ is used when we consider the environment of a specific gravitational field to study the effect of the attractive pull of subject mass on test mass(es).

A central part of the theorisation of gravitation and gravity is the universal law of gravitation defined by the scientist Issac Newton. Newton is often called the father of gravity. He stated the law of universal gravitation in 1687.

Newton’s law of universal gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:

F ∝ m1 m2r2 

F = G x m1 m2r2 

Where F is the gravitational force and m1 and m2 are the masses of bodies that are r distance apart, and G is the gravitational constant= 6.67 × 10−11 N.m2/kg2.

Other propositions central to Newton’s laws include:

1. Every mass attracts all other masses.
2. Attraction is proportional to the product of the masses of bodies involved.
3. Attraction is inversely proportional to the square of the distance between the centres of the bodies.

Discovering the Gravitational Constant

Henry Cavendish developed the first method for calculating the gravitational constant in 1798. It has been modified several times since to make it more accurate.

In the first method, researchers constructed a metal-coated silicate plate suspended in the air from a wire. Two steel balls create an attraction. The force of gravity was measured by determining the degree of kinking of the wire.

The second method was similar to the first, except that the platter was suspended from a turntable that held the cable in place. In this procedure, the gravitation was measured by registering the degree of rotation of the turntable.

In both methods, the researchers included features to prevent interference from nearby objects and interference from the addition of seismic data.

Weight and the Gravitational Force

Mass and Weight

Although these terms are often used interchangeably, they are not the same. 

Mass is defined as the measurement of matter in an object. Weight, on the other hand, is the measurement of mass due to the function of gravity. A person weighing 60 kg on the earth would weigh 10 kg on the moon. The change is because the moon has a weaker gravitational pull than the earth. 

The gravity of a body is calculated based on how fast it attracts a freely falling body towards it or how it affects the acceleration of a freely falling body. Thus, weight and gravitational force may be used as interchangeable terms in a particular gravitational field.

Acceleration due to gravity

Weight, thus, is a force that measures mass due to gravity. 

Force is an outcome of mass times acceleration. If acceleration due to gravity is 9.8 ms-2, that is the acceleration due to gravity, then force becomes the weight of an object. 

Hence, W = mg  Where W is weight, m is mass , and g is acceleration due to gravity.

Calculating Acceleration due to Gravity

The universal law of gravitation, as we have seen, explains why the moon revolves around the earth and the earth around the sun. Furthermore, the earth’s gravity allows it to hold its surrounding atmosphere in place. 

Let us consider the mass of a test mass to be m and the mass of earth to be M. The test mass is on the earth’s surface, so r is the radius of the earth, and g is the acceleration due to gravity.

Weight of the test mass

F = mg

From the universal law of gravitation, we have

F = G x Mmr2

From the above two equations we get,

mg = G x Mmr2

g = G x Mr2

Putting in the values, 

g = 6.67 × 10-11 N.m2/Kg2 x  5.97219 × 1024 kg(6378.1 x 103 m)2

g = 9.8 ms-2

The gravity of the moon can be calculated by putting in the values of mass and radius of the moon.

g = 6.67 × 10-11  N.m2/Kg2 x 7.34767309 × 1022 kg (1737.4 x 103 m)2

g = 1.62 ms-2

ge/gm =  9.8 ms-21.62 ms-2  =  6.049   6

Thus, acceleration due to gravity on earth is almost six times that on the moon. It explains why a person weighs six times lighter on the moon.

To calculate the acceleration due to the gravity of any other body in space, we can use the following formula.

Let M be the mass of the earth and m be the mass of any other planet or body. R is the radius of the earth and r is the radius of the other planet, and g is the acceleration due to the gravity of any other body in space:

g = G x Mr2

G = g R2/M

 g’ = Gmr2

Therefore we get,

g’ =  g R2M x mr2 

g’ = g mMR2r2 

Since we already know that acceleration due to gravity (g) on earth is 9.8 ms-2.

Universality of Gravity

Gravitational attraction does not only exist between the earth and other celestial objects but also between all objects in general. The strength of gravitational attraction between two objects is proportional to the product of their mass. 

The universal law of gravitation helps scientists study the orbits of planets. Since all objects gravitationally influence each other, minute changes in the elliptical motion of the planets can be explained and analysed.

The force of gravity is inversely proportional to the square of the distance between the centres of the bodies. As distance increases, the effect of the force of gravity reduces. Gravity’s range is considered to be infinite. However, at large distances, it is deemed to be negligible. 

Conclusion

Gravitation depends on the product of masses and the distance between them. Mass can be defined as the measurement of a matter in an object. Weight, on the other hand, quantifies mass in a particular gravitational field.

The universal law of gravitation may be expressed using the formula: F = G x m1 m2r2 

The gravitational constant is the proportionality constant G = 6.67 × 10−11 N.m2/kg2

Gravity may be defined as the acceleration experienced by a freely falling body. 

The discovery of the concept of gravity also helped Einstein define his theory of relativity.