- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Environmental Science
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- articles and Answers
- Effective Resume Writing
- HR Interview articles
- Computer Glossary
- Who is Who

# Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?

**Johannes Kepler** studied about the planets motion and their positions and. He noticed that motion of th e planets follows a certain law. He gave three laws describing the planetary motion.

These are known as Kepler’s laws which are as follows:

**Kepler’s First law : **The orbit of planet is an ellipse with sun at one of the foci. The figure below illustrates the elliptical orbit of earth with sun at its focus.

**Kepler’s Second law : **The line joining the planet and the Sun sweeps equal areas in equal intervals of time.

In the above figure $A_1 = A_2$ according to law

**Kepler’s Third law : **The Square of its period of revolution around the Sun is directly proportional to the cube of the mean distance of a planet from the Sun.

If ‘r’ is the average distance of the planet from the sun and ‘T’ is the period of revolution then according to third law

$T^2 ∝ r^3$ ie

$\dfrac{T^{2}}{r^{3}} = constant = k$

** Inverse S quare law of gravity : **We know that centripetal force F is given by ;

$ F = \dfrac{mv^{2}}{r}$

Where $v$ = velocity of the planet = $\dfrac{Distance travelled}{TimeTaken}$

Distance travelled in one revolution = $2πr$

Where $r$= radius of the orbit.

$V = \dfrac{2πr}{T}$

$F = \dfrac{mv^{2}}{r}$

$= \dfrac {m \left( \dfrac {2πr}{T} \right)^2} {r}$

$= \dfrac{4 m \pi^{2} r^{2}}{rT^{2}}$

$= \dfrac{4 m \pi^{2} r}{T^{2}}$

according to kepler's third law,

$\dfrac{T^{2}}{r^{3}} = constant = k$

$F = \dfrac{4 m \pi^{2} r^{3}}{T^{2}r^{2}}$

$F = \dfrac{4 m \pi^{2}}{ \left( \dfrac { T^{2}}{r^{3}} \right)r^{2}}$

$F = \dfrac{4 m \pi^{2}}{ Kr^{2}}$ ( By Kepler,s third law).

But $F = \dfrac{4 m \pi^{2}}{K}$ is constant.

Therefore $F = \dfrac{1}{r^{2}}$

And this is the **newton’s inverse square law** which states that the centripetal force acting on planet is inversely proportional to the square of the distance (‘r’) between the sun and the planet.

ads