The **key difference** between Kepler and Newton law is that **Kepler law describes the planetary motion around the Sun whereas Newton laws describe the motion of an object and its relationship with the force that is acting on it. **

Kepler’s law and Newton’s laws are very important in physical chemistry regarding the motion of objects.

### CONTENTS

1. Overview and Key Difference

2. What is Kepler Law

3. What is Newton Law

4. Side by Side Comparison – Kepler vs Newton Law in Tabular Form

5. Summary

## What is Kepler Law?

Kepler law is a set of laws described by Johannes Kepler (between 1609 and 1619). This law describes the planetary motion around the Sun. This set of laws modified the heliocentric theory of Nicolaus Copernicus by replacing its circular orbits and epicycles with elliptical trajectories. Moreover, it explains the variation of planetary velocities. This set of Kepler’s laws has three laws as follows:

- The orbit of a planet is an ellipse where the Sun is at one of the two foci.
- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- The square of a planet’s orbital period is proportional to the cube of the length of the semi-major axis of its orbit.

Kepler indicated the elliptical orbits of planets by calculations of the orbit of the planet Mars. Using these calculations, he inferred that other planets in the Solar system also have elliptical orbits. Moreover, the second law of Kepler’s laws helps in establishing the theory that when a planet is closer to the Sun, it can travel faster than usual. According to the third law of Kepler’s laws, farther a planet from the Sun, the slower its orbital speed becomes and vice versa.

Furthermore, Kepler used his first two laws in computing the position of a planet as a function of time. This method included the solution of a transcendental equation named as the Kepler’s equation. When considering the procedure of calculating the heliocentric polar coordinates of a planet as a function of the time, it includes five steps: computing the mean motion, computing the mean anomaly, computing the eccentric anomaly, computing the true anomaly and computing the heliocentric distance.

## What is Newton Law?

Newton’s laws are a set of three laws that describe the relationship between the motion of an object and the forces acting on it. These three laws of motion were introduced by Isaac Newton in 1687. He used these laws for the explanation and investigation of the motion of many physical objects and systems.

The three laws are as follows:

- First Law: An object either remains at rest or continues to move at a constant velocity unless it is acted upon by an external force.
- Second Law: The rate of change of momentum of an object is directly proportional to the force applied or for an object with constant mass where the net force acting on the object is equal to the mass of the object that is multiplied by the acceleration of that object.
- Third Law: When one object exerts a force on a second object, the second object exerts a force that is equal in magnitude and opposite in the direction of the first object.

More importantly, these three laws of Newton were verified by experimental methods and observations for over 200 years and are considered as excellent approximations at the scales and speeds of everyday life.

## What is the Difference Between Kepler and Newton Law?

The key difference between Kepler and Newton law is that Kepler law describes the planetary motion around the Sun whereas Newton laws describe the motion of an object and its relationship with the force that is acting on it.

Below is a summary of the difference between Kepler and Newton law.

## Summary – Kepler vs Newton Law

Kepler’s law and Newton’s laws are very important in physical chemistry regarding the motion of objects. The key difference between Kepler and Newton law is that Kepler law describes the planetary motion around the Sun whereas Newton laws describe the motion of an object and its relationship with the force that is acting on it.

##### Reference:

1. “Kepler’s Three Laws.” *The Physics Classroom*, Available here.

##### Image Courtesy:

1. “Kepler’s law 2 en” By Kepler2.gif: Illustration by RJHall using Paint Shop Proderivative work: Talifero (talk) – Kepler2.gif (CC BY-SA 2.0 at) via Commons Wikimedia

2. “Sir Isaac Newton (1643-1727)” By Godfrey Kneller – (Public Domain) via Commons Wikimedia

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