Universal Gravitation Equation
Thus, according to Newton’s law of gravitation, Every particle in the universe attracts every other particle with a force whose magnitude is,
Directly proportional to the product of their masses i.e.
F ∝ (m1 × m2) …..(1)
Inversely proportional to the square of the distance between their centres (Also known as Inverse Square law) i.e.
F ∝ (1 / r2) ……(2)
On combining equations (1) and (2) it is obtained that,
F ∝ (m1 × m2) / r2 ……(3)
Therefore, from equation (3), it can be said that the gravitational force or force of gravity between two particles or objects is proportional to the product of their masses and the square of the distance between them.
F = G × (m1 × m2) / r2
where,
G is the proportionality constant, also known as the Gravitational constant,
F is the force of gravity,
m1 is the mass of one object,
m2 is the mass of the other object and
r is the distance between those objects.
Gravitational Constant
Gravitational Constant is a proportionality constant, and it is used in Newton’s Universal Law of Gravitation. It is denoted by G. It can also be defined as a force of attraction between any two unit masses separated by unit distance. From Newton’s Universal Law of Gravitation i.e. from equation (4), the expression for G is,
F = G × (m1 × m2) / r2
G = F × r2 / (m1 × m2)
When,
r = 1 m and m1 = m2 = 1 kg then,
G = F
Dimensional Formula for G is [M-1L3T-2].
Its values in SI units is 6.67 × 10-11 Nm2 kg-2 and in the CGS system is 6.67×10-8 dyne cm2 g-2.
Universal Law of Gravitation
Universal Law of Gravitation or Newton’s law of Universal Gravitation as the name suggests is given by Sir Isaac Newton. This law helps us to understand the motion of very large bodies in the universe. According to this law, an attractive force always acts between two bodies that have masses. The strength of the force is directly proportional to the mass of the object and is inversely proportional to the square of the distance between them.
In this article, you are going to read about everything related to Universal Law of Gravitation including its definition, what Gravitational Law states, weight vs. Gravitational Force, etc.
Table of Content
- What is the Universal Law of Gravitation?
- Universal Gravitation Equation
- Vector Form of Universal Law of Gravitation
- Principle of Superposition of Gravitational Forces
- Newton’s Law of Gravitation from Kepler’s Law
- Weight and Gravitational Force
- Universality of Gravity
- Importance of Universal law of Gravitation
- Solved Examples
- FAQs