Here are photographs of an astronomy activity by Linda Shore.

Four moons of correct diameter line up across the earth.

Introduction

Start with two identical size, 10 cm diameter, balls of playdough, call one the earth, cut a moon out of the other.

Material

• Two normal size cans of playdough.
• A plastic knife.
• A ruler.

To Do and Notice

Roll each can of playdough into a sphere.

Notice that the spheres are the same size.

Cut a moon-size piece of plsydough out of one of the spheres.

What's Going On?

The Moon has a diameter that is 1/4 the diameter of the earth.

To make a playdough spere with 1/4 the diameter you need only 1/64 of the volume of the original sphere! See the math root.

To Cut out a piece of playdough with 1/64 the volume there are several strategies you can use. You can:

By cutting bits of a yellow earth-size lump in half repeatedly
you can make a yellow piece 1/64 the volume of the red earth lump.

cut the original ball in half making two hemispheres,
Then cut each hemisphere in half
and then cut each of these pieces in half again making eight equalt octants of a sphere.
Then cut the octants in half, then in half again and finally in half a third time to make small pieces with 1/64 the volume of the original sphere.

These little chunks will roll up into spheres with 1/4 the radius of the original earth.

Or

Regan rolls out an earth globe into a cylinder and cuts off 1/64

You can roll the dough out into a long cylinder, make marks at 1/2 the length, then at 1/4,1/8,1/16,1/32, and 1/64 of the length.

Slice off 1/64 using the plastic picnic knife and roll it into a ball.

You can measure the radius of your earth and moon ball using a ruler, or make 4 moon balls and line them up side by side to see that they have the same radius as the earth.

Math Root

The volume, V_e, of the earth sphere of radius R_e is

V_e = 4/3piR_e³

The volume of the moon V_m of a moon with radius R_m = 1/4 R_e is

V_m = 4/3 pi R_m³ = 4/3 pi (R_e/4)³ = 4/3 pi R_e³/64 = V_e/64

Etc.

To many people it seems very strange that it takes 64 moon balls to assemble one earth which is only four times the radius of the moon.

Scientific Explorations with Linda Shore and Paul Doherty

© 2001

31 July 2001