World Builders™                                                                          Session One  --  Astronomy  

   
Finding the Mass of Your Planet
                                         
The mass of your planet = the volume (how much matter there is) times the density.


      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 =  volume of a sphere formula

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 =volume of a sphere formula

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

  • Find the Mass of the Sphere

Mass = Volume * Density

The mass of your planet = 2.14 * 5.2 = 11

  •  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          =   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 =volume of a sphere formula

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

  • Find the Mass of the Sphere

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.


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© 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.