If you are going to have
a moon, or moons, you will need to know the mass of your planet
to figure out the moon's orbit.
You have already chosen the radius and density of your planet
in How to How to Design Your Solar
System, Part 3. With those numbers you can find the mass,
because
Mass = Volume *
Density
You will need to figure out the volume,
but that is not hard. There are formulas waiting for you at Circle Talk: Math for Your Solar System.
Using
the formula for volume you
will see that if we say the
radius of the earth is 1,
the volume of the earth is
4.18 Then what is the mass?
Part 1 Find the Volume of the Planet
We will use the same formula
to calculate the volume of your planet. You can
pick the radius of your
planet, remembering that the
radius of the earth = 1 for
this project.
The Volume of a Sphere =
To translate, this says
4 * Pi * (radius
of the sphere * radius of the sphere * radius of the sphere)
3
Let's do earth, assuming that the radius = 1
Pi = 3.14, so we will put that
in.
4 * 3.14 * (1
* 1 *1)
= 12.56 =
4.18
3
3
The volume of this sphere = 4.18

Part 2 Find the Mass of the Sphere
We remember that
Mass = Volume *
Density We have the volume
of the planet (in this case, Earth) which is 4.18
We know the density of the planet
(in this case, Earth) which is 5.5
We multiply the
Volume by the
Density
4.18 * 5.5 = 22.99
which we can round to 23
So if the radius of the earth is 1
and its density = 5.5, the mass of the earth is 23. 
Compare this with the
answers that you get for your planet.
Example 1: Find the mass of a planet with a radius of .8 and
a density of 5.2
(We
will say the earth's radius is one and compare your planet's
radius to it.)
This requires 3 steps:
 Find the volume of the sphere
The Volume of a Sphere = which means
4 * Pi * (radius
of the sphere * radius of the sphere * radius of the sphere)
3
Put in the numbers:
4 * 3.14 *(.8 * .8 * .8) = 12.56 *
.512 =
6.43 = 2.14
is the volume of your planet
3 3 3

Mass = Volume *
Density
The mass of your
planet = 2.14 * 5.2 = 11

If you
want to use the mass of the earth = 1, then you need to do
one more step:
Do this:
mass of your planet
= 11 = 0.478
mass of earth if radius= 1
23 
You can now use this
number to calculate the orbits of your moons.
Example 2:
Find the mass of a planet with a radius of 1.4 and a density
of 5.7
(We
will say the earth's radius is one and compare your planet's
radius to it.)
This requires 3 steps:
 Find the volume of the sphere
The Volume of a Sphere = which means
4 * Pi * (radius
of the sphere * radius of the sphere * radius of the sphere)
3
Put in the numbers:
4 * 3.14 *(1,4 * .1,4 * .1.4) = 12.56 *
2.74 =
34.46 = 11.49 the volume of your planet
3
3
3

Mass = Volume *
Density
The mass of your
planet = 11.49 * 5.7 = 65.48

 Correct to make the mass of the earth = 1
If you
want to use the mass of the earth = 1, then you need to do
one more step:
Do this:
mass of your planet
= 65.48 = 2.84
mass of earth if radius= 1
23 
You can now use this
number to calculate the
orbits of your moons.
NOTE:
For comparison, using
earth
volume = 4.18
earth density = 5.5
gives
you 4.18 * 5.5 =
22.99 rounded up to
23 for the mass of the
earth.
A
larger and/or more dense planet
will have more mass.
A
smaller and/or less dense
plant will have less mass.
© 2000, 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.
