World Builders™ World Builders™ Session One  --  Astronomy Session One  --  Astronomy Circle Talk              Circle Talk           Circle Equations and Planet Designing Tips           Circle Equations and Planet Designing Tips
 Some basic information:        =3.14 r = the radius The radius is the distance from the center of a circle to the line that encloses the circle.

Here are some circle formulas that might be useful to you

The Circumference of a Circle
(the distance around the outside)

#### 2 p r

The Area of a Circle
(the flat surface on the inside)

The Surface of a Sphere
(the outside of a ball)
The Volume of a Sphere

(the space inside a ball)

How will we use these formulas?

Note how the numbers change in the examples below.

A change in the radius has quite an effect on the other measurements.

The radii are red  in the formulas.

*  means multiplication in the computer.

Use this for the earth with a radius of one earth radius

Circumference of the Circle

#### 2r

2 * 3.14 * 2 = 12.56

2 * 3.14 * 1 = 6.28

2 * 3.14 * .5 = 3.14

Area of a Circle

3.14 * (2 * 2) =

12.56

3.14 * (1 * 1) =

3.14

3.14 * (.5 * .5)

= 0.785

Surface of a Sphere

4 * 3.14 * (2 * 2) =

50.48

4 * 3.14 * (1 * 1 )

=  12.56

4 * 3.14 * (.5 * .5 )

=   3.14

Volume of a Sphere
(the inside)

4 * 3.14 * (2 * 2 * 2)
3

33.49

4 * 3.14 * (1 * 1 *1) 3

=   4.18

4 * 3.14 * (.5* .5 .5)
3

=  0.52

NOTE:  Using these numbers the volume of the earth = 4.18

When you work out the numbers for your own planet, you can use these formulas.

If you let the radius of the earth = 1 you can compare the sizes of the planets with each other without getting entangled in enormous numbers.

Using the radius of the earth = 1, a larger planet might have a radius of, perhaps, 1.3.

A smaller planet might have a radius of, perhaps, 0.75.

Check the page on Statistics on Planets and Moons to get some ideas of possible sizes.