World Builders™                                                                     Session One  --  Astronomy       
                 Kepler's Laws

                                                                          of Planetary Motion

                               Third Law

This third law will allow you to figure out how long your planet's year will be.

The squares of the sidereal periods of the planets are proportional to the cubes of their semimajor axes.

Let's translate this:  
The squares of   math language for a number multiplied by itself:
Example: 6 x 6 = 36
the sidereal periods of the planets

we would call this the planet's year
It is a journey of one full orbit around the sun.

are proportional to are mathematically related to
the cubes of math language for a number multiplied by itself
and then
multiplied by itself again.
Example: 6 x 6 x 6 = 216
their semimajor axes.

We need a diagram here:

Remember (Kepler's First Law) that the planets move in elliptical paths.

Here is an ellipse.

The major axis of an ellipse is a line drawn

through both foci.

Here you can see the major axis drawn in red.


However, we need to find the semimajor axis.

ellipse with semi major axisSemi means half, so let's cut the major axis in half.

Now we see the semimajor axis in red.

We can use the mean distance of the planet
from its sun as the number for the semimajor axis.

The mean distance of the earth from the sun is 93,000,000 miles.

This is called one astronomical unit, or AU for short.

This law uses the astronomical unit as the distance number for calculating the length of the year.

Now you are ready to calculate the orbital information for your planet,

Find the Life Zone (Habitability Zone) for Your Planet.

Calculate the Year Length When You Know Your Planet's Distance from the Sun

Calculate Your Planet's Distance from the Sun When You Know the Year Length

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© 1998, 2003. Elizabeth Anne Viau. All rights reserved. This material may be used by individuals for instructional purposes but not sold. Please inform the author if you use it at