World Builders™                                                                         Session One  --  Astronomy              

                        Calculate Your Planet's

                                   Distance from Your Sun                                          

The third law will allow you to figure out how far your planet is from your sun.


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

This is the Formula
(this planet's year in earth years) x
(this planet's year in earth years)   
=

(distance from sun in AUs) x
(distance from sun in AUs) x
(distance from sun in AUs)

squares of the sidereal periods
= cubes of their semimajor axes

(sidereal periods)2

=

(semimajor axes)3


You need to figure out your planet's year length as it relates to the earth year.

If your planet's year is in earth days right now

(Example:  My planet's year is 112 earth days long) you need to do this:

 My Planet's year in earth days  =
365
 112
 365
 = .3068493

Throw away most of those decimal numbers:  your planet's year = .3 earth years
           (about a third of an earth year. That makes sense)

However, if you already have a number that is about earth years

(Example: My planet's year is 4.7 earth years long) then use that number as it is.

Use Kepler's formula:

This is the Formula
(this planet's year in earth years) x
(this planet's year in earth years)   
= (distance from sun in AUs) x
(distance from sun in AUs) x
(distance from sun in AUs)
squares of the sidereal periods
= cubes of their semimajor axes

(sidereal periods)2

=

(semimajor axes)3


Let's do a couple of examples.

Example 1: My planet's year is .3 earth years long.

Find the distance from the sun of a planet with a year that is 0.3 earth years long.
squares of the sidereal periods
= cubes of their semimajor axes
(this planet's year =0.3) x
(this planet's year =0.3)   
= (distance from sun) x
(distance from sun) x
(distance from sun)

0.3 x 0.3 

Use Calculator: 0.3 ^ 2 =

=
(distance from sun) x
(distance from sun) x
(distance from sun)
0.09  
= (distance from sun) x
(distance from sun) x
(distance from sun)
So . . . this planet's AU   
=
the cube root of 0.09 
Type this on the calculator keyboard: 0.09 ^ .33 =
Your answer should be 0.45175194192142615
(You don't need all these decimals)

The planet's distance from the sun is about 0.45 AUs

Your planet is about half as far from its sun as the earth is from Sol.

Example 2:    My planet's year is 3.7 earth years long

Returning to Kepler's Law:

This is the Formula
(this planet's year in earth years) x
(this planet's year in earth years)   
= (distance from sun in AUs) x
(distance from sun in AUs) x
(distance from sun in AUs)
squares of the sidereal periods
= cubes of their semimajor axes

(sidereal periods)2

=

(semimajor axes)3


Find the distance from the sun of a planet with a year that is 3.7 earth years long.
squares of the sidereal periods
= cubes of their semimajor axes
(this planet's year = 3.7) x
(this planet's year =3.7)   
= (distance from sun) x
(distance from sun) x
(distance from sun)

3.7 x 3.7 
Use Calculator: 3.7 ^ 2 =

=
(distance from sun) x
(distance from sun) x
(distance from sun)
13.69  
= (distance from sun) x
(distance from sun) x
(distance from sun)
So . . . this planet's AU  
= the cube root of 13.69    or


Type this on the calculator keyboard: 13.69 ^ .33 =
Your answer should be 2.371445443
(You don't need all these decimals)

The planet's distance from the sun is about 2.7AUs

Your planet is about two and a half times as far from its sun as the earth is from Sol.


Now, go to the star tables -- I think you know what to do next!

With the star tables and this calculator, it should be easy for you to make a table with the distances and year lengths for all the planets in your system. Go for it!


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

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

Kepler's Third Law


Astronomy Information Menu

Design Your Solar System

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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 eviau@earthlink.net.