## Kepler's Third Law

Demonstrate an understanding of Kepler's third law relating planetary distances to orbital periods and perform simple calculations using the formula: T^{2}= R

^{3}where T is in years and R is in AU

#### 3. The orbital period of a planet squared is proportional to its mean distance from the Sun cubed, when different planets are compared.

There is a relationship between the distance of a planet and the time it takes to orbit the Sun.

**Terms you need to know first...**

**SQUARE** = a number multiplied by itself e.g. 2 x 2 = 4. 4 is the square of 2

**CUBE** = a number multiplied by itself and then multiplied by itself again. e.g. 3 x 3 x 3 = 27. 27 is the cube of 3.

**T** = Period/ Time it takes to orbit the Sun

**r** = mean radius from Sun

Although we use the Sun as our example, this equally applies to any primary body e.g. the Earth and calculating the orbit of the Moon around it.

Kepler's Third Law is this: The square of the Period is approximately equal to the cube of the Radius.

**T**^{2} = r^{3}

^{2}= r

^{3}

###### Summary

**T ^{2} = r^{3}**

Note: Incidentally some astronomers, textbooks and websites uses "P" for Period rather than "T" for Time. Don't worry if you see this being used elsewhere

###### Links

Bill Drennon, Central Valley Christian High School Animated Kepler's Laws

Davidson's WebPhysics Animations

UBC's Interactive Mathematics Interactive Simulator