The force of attraction with which an object attracts another object in the universe is called gravitational force. The law of gravitation was put forth by Sir Isaac Newton in 1687. It is widely believed that the inspiration to formulate the law came to Isaac Newton after he saw an apple fall from a tree. This article provides comprehensive study material on the law of gravitation, the gravitational force, the universality of gravity and the gravitational constant.

The law of gravitation

• The SI unit of G (gravity) is N m2 Kg-2.
• Henry Cavendish, an 18th-century scientist, found the value of G by using the sensitive balance. The value of G is 6.673 x 10-11 N m2 Kg-2.
• According to Newton’s universal law of gravitation, a force along a line joins every particle in the universe to every other article.
• This force that attracts these particles is inversely proportional to the square of the distance between the particles and is directly proportionate to the product of their masses.
• The universal law of gravitation equation is F = G m1m2/r2.

In the above equation, F is the magnitude of the gravitational force, G is the gravitational constant. The gravitational constant remains the same for all celestial bodies in the universe.

• While Newton might have been the first scientist to propose a mathematical form for gravitation, philosopher Galileo Galilei and his contemporaries were also trying to understand and explain the existence of a force that caused the motion of planets.

Universality of gravity

Gravitational force is a universal concept. It exists not only between the earth and other objects on the earth but between objects themselves. The force so applied is directly proportional to the mass of the objects. This concept is essential to study the planetary movements of the solar system. The elliptical orbital pathways of the solar system are also an effect due to the gravitational pull between the planets.

Calculating value of  ‘g’:

g = G M/d2

• Here M is the mass of the earth, and d is the gap between the item and the earth.
• If an item is on or close to the surface of the earth, the space may be equal to R (the radius of the earth). As a result, for objects on or near the surface of the earth,
  • The force of gravity decreases with altitude.
  • It also varies at the floor of the earth, reducing from poles to the equator.
• The cost of acceleration because of the earth’s gravity, g = 9.8 kgm/s².

Mass

• The mass of an object is the degree of its inertia.
• The more the mass, the more is the inertia.
• The mass of an object is constant and does not change with location of the object.

Weight

• The earth draws each object towards its centre with a certain pressure, and this pressure relies upon the mass (m) of the object and the acceleration because of gravity (g).
• The weight of an item is the pressure with which it is attracted toward the earth.

It is denoted through W.

W = m × g

• The SI unit of weight is similar to that of pressure, Newton (N). 
• The weight is a force that acts vertically downwards and has magnitude and direction.
• Weight depends on the location because g relies upon the mass of the planet.

Weight of the object on the moon = (1/6) × its weight on the earth.

Conclusion

In these study material notes on law of gravitation, we discussed the following things:

• 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 = Gm1 m2/r2 

• 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.