Investigate Newton's Law of Gravitation, this simulation allows you to vary the coefficient of distance in the force equation. The simulation shows that for smaller powers of distance the moon is deflected from it's original path, whereas for larger powers it spirals in towards the earth.

You should find that the inverse square relationship causes the moon to move in a fixed elliptical orbit around the earth, the special thing about this orbit being that the areal velocity (the area swept out between the earth and moon in unit time) is constant. Different powers of r give different patterns of motion - some of which are ellipses - but none of which have constant areal velocity. The first-power case
F = GMmr¹ gives an interesting result - harmonic motion of the moon through the earth!

Instructions :

• There are two viewpoints, a plan view in the top-left corner and a 3D view.
• The 3D view can be rotated by clicking on the earth with the left mouse button and dragging the mouse left and right or up and down (with the button pressed down).
• The 3D view can be zoomed in and out by clicking on the earth with the right mouse button and dragging the mouse up and down.
• The moon initially obeys an inverse-square law of gravitational attraction with the earth (as indicated by the -2.0 to the left of the equation).
• This value can be changed up or down in steps of 0.1 by clicking on the up and down arrows next to the equation.
• The moon can be reset to it's starting position by cleft-clicking the Restart button.