Sun, earth and moon
Move the earth by dragging the red point. Check the check box to view the path of the moon. Change the radius of the earth and the radius of the moon. Change the number of months in a year.
Create epicycles without trigonometry
- Place a point
Sunat the origin.
- Enter a circle having constant radius and the point
Sunas centre. Use the tool Circle with Centre and Radius .
- Insert a point
Earthon the circle.
- Make a point
Aon the circle, make sure
Alies on the x-axes; then measure the angle α, as in the picture.
- Make a circle having constant radius and the point
- Make a line through
Earthparallel to the x-axes, then make the intersection point between the circle and the line. Name the intersection point
- You can not move the point
Moonsince it is an intersection point. This is not the point that is going to represent the moon.
- There are 12 months in a year. Every time the earth makes one revolution around the sun, the moon has to make 12 revolutions around the earth. The angle the moon has to the x-axes should hence be 12 times the angle of the earth, i.e. the angle α.
- Rotate the point
Moonaround the point
Earthby using the tool Rotate Object around Point by Angle .
- When you enter the angle, enter 12*α.
- The rotated point
Moon', is the point representing the moon. Rename it to
Moon(the other point will automatically be renamed, two objects must not share the same name).
- Hide all objects that should not be shown. Right-click on
Trace on. You can now show the path of the moon as the earth moves by dragging the earth.
- Right-click on the earth and choose "Animation On".
You can vary the radii of the two circles by using sliders instead of constant numbers. You can also vary the number of months in a year by using a slider instead of the number 12 when rotating the moon. As a final touch you use images instead of points. For more information see GeoGebra Tutorial - Epicycles.
The pattern made by the moon, is the same kind of pattern you can get from a spirograph. To see more spirograph patterns, see Trigonometry - Make a Spirograph.
By repeating the procedure of placing circles around points on circles...you
can create any orbit.
One of the most impressive orbits is this one from YouTube.
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License