Kepler's Third Law

time

8

Kepler's third law states that the square of the period of revolution

P

of a planet is proportional to the cube of the semimajor axis

a

of the planet's elliptical orbit around the Sun. In symbols,

2

P

∝

3

α

or

2

P

=k

3

α

. The constant

k

can be taken as 1 for simplicity, equivalent to measuring

P

in years and

α

in astronomical units. In this Demonstration the ellipses have different eccentricities; the value of

α

is chosen to equal 5, so that the period is equal to

3

5

≃11.18

.