World Builders™                                             e=6>                  Session One  --   Astronomy  

                        Calculate Your Planet's

                                             Year Length                                          

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

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


Let's check Kepler's Third Law again.
The squares of the sidereal periods of the planets are proportional to the cubes of their semimajor axes.

So this means on earth:

(one year) x (one year)
= (one AU) x (one AU) x (one AU)
squares of the sidereal periods
= cubes of their semimajor axes

(sidereal periods)2

= (semimajor axes)3

The numbers work like this:

1 x 1 = 1 x 1 x 1

(1)2 = (1)3


Let's try this with a planet that is twice as far from its sun as the earth, i.e., 2 AU.

This is the Formula
(this planet's year) x
(this planet's year)   
= (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 year length for a planet at 2 AU
squares of the sidereal periods
= cubes of their semimajor axes
(this planet's year) x
(this planet's year)   
= (distance from sun = 2 AUs) x (distance from sun = 2 AUs) x (distance from sun = 2 AUs)
(this planet's year) x
(this planet's year) 
  
=
2 x 2 x 2 
(this planet's year) x
(this planet's year) 
  
= 8     which is the same as (2)3   
So . . . (this planet's year)   
= the square root of 8    or  =

8 ^ 0.5 =

Your answer should be 2.8284271247461903
(You don't need all these decimals)

The length of the year of this planet is about 2.8 earth years.

Multipily 365 earth days by 2.8 to get the number of earth days that it takes for your planet to orbit its sun.

365 x 2.8 = 1,022 earth days



Let's do another example. This planet is 4.5 AUs from its sun.
This is the Formula
(this planet's year) x
(this planet's year)   
= (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 year length for a planet at 4.5 AU
squares of the sidereal periods
= cubes of their semimajor axes
(this planet's year) x
(this planet's year)   
= (distance from sun = 4.5 AUs) x
(distance from sun = 4.5 AUs) x
(distance from sun = 4.5 AUs)
(this planet's year) x
(this planet's year) 
  
=
4.5 x 4.5 x 4.5  
which is the same as (4.5)
3   

Use Calculator:     4.5 ^ 3 =
(this planet's year) x
(this planet's year) 
  
= 91.125
So . . . (this planet's year)   
=

the square root of 91.125     or
  
which is the same as

91.125 ^ 0.5 =

Your answer should be 9.545941546018392
(You don't need all these decimals)

The length of the year of this planet is about 9.5 earth years.

Multipily 365 earth days by 9.5 to get the number of earth days that it takes for your planet to orbit its sun.

Get Another Calculator

365 x 9.5 = 3467.5 earth days


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

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

Kepler's Third Law  


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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.