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) 
= 

(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
© 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.
