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

Use these equations to help you to calculate the area and volume of your planet.

 

   
 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.

   

Radius = 2

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


Radius = 1

 

 

 

 
Radius = .5

Circumference of the Circle

   2 r

 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.


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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.