Newton’s Law of Gravitation from Kepler’s Law
Suppose a planet of mass m is revolving around the sun of mass M in a nearly circular orbit of radius r, with a constant angular velocity ω. Let T be the time period of revolution of the planet around the sun.
Therefore,
F = mrω2
= mr × (2π/T)2 ……(1)
According to Kepler’s third law, the square of the time period of the planet is proportional to squares of length of semi-major axes and is given as:
T2 ∝ r3
or
T2 = kr3
where k is the proportionality constant, T is the time period of the planet and r is the length of the semi-major axis.
Now apply this in equation (1) as,
F = mr × (4π2 / kr3)
= (4π2 × m) / kr2
But k = 4π2 / GM, substitute this in the above expression as:
F = G (M × m) / r2
which is the equation of Newton’s law of Gravitation.
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