# The Weird Science of Johannes Kepler's 3 Laws of Planetary Motion

If you think the orbit of any planet that moves around the Sun is a perfect circle, then you need to think again! The truth is that, the orbits of planets are ellipses, and on this basis, the three Laws of Planetary Motion are formulated by Johannes Kepler.

UniverSavvy Staff

Last Updated: May 15, 2018

Inspired by Law of Periods!

Based on Kepler's third law, which states that the farther the planet is from the Sun, the weaker will be its forces; Newton formulated The Law of Gravitation.

Based on the properties of ellipses, Johannes Kepler devised three laws that explain the motion of planets around the Sun.

Kepler's First Law

**The Law of Orbits**. As discussed earlier, an ellipse has two foci. While studying the motion of planets around the Sun, Kepler explained that the path followed was elliptical, with the Sun as one of the two foci. In simple terms, the law can be stated as:

**All planets move in elliptical orbits, with the Sun at one focus.**

Kepler's Second Law

**The Law of Equal Areas**. As the Sun is one of the foci, it is clear that the Planet-Sun distance will be changing. But, the planet covers up for the increase in the distance by moving faster when it is closer to the Sun. This indicates that planets do not move at a uniform speed. The second law states that:

**The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.**

Kepler's Third Law

**The Law of Periods**and

**Harmonic Law**. This law relates the time required by a planet to make a complete trip around the Sun to its mean distance from the Sun. This law can be simply stated as:

**The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.**

**P**

^{2}∝ a^{3}Here, 'p' is the orbital period while 'a' is the semi-major axis of the orbit.

To convert this equation into a ratio, we introduce a constant of proportionality

**p**/

^{2 }**a**=

^{3 }**1**(

**yr**/

^{2 }**AU**)

^{3}where 'yr' is the sidereal year

*****and 'AU' is the astronomical unit

******.

*****- Time taken by the Earth to complete one trip around the Sun

******- Average Earth-Sun distance, i.e., approximately 149.6×10

^{6}km

The law is commonly represented as,

**T**= (

^{2}**4Π**/

^{2}**GM**)

**R**

^{3}where,

T - Earth years

G - Constant of Gravitation

M - Mass of the larger body

R - Center of mass of two bodies

The third law was applied to Earth satellites. The law stated that, when a satellite is farther from the Earth, it will take a longer time to complete the orbit, and its average speed will be slower.