Newton got the idea of gravity by watching an apple drop to the ground (so the story goes) and then, looking at the moon, wondered if it was the same gravity making it go in circles around the earth. Kepler had already found the equal area in equal time and period cubed per radius squared laws and Newton used them to investigate gravity. Look at the lines radiating out of the center of the earth. Using the formula for area of a sphere, where is the density of the lines per square area greatest? If the density represents the relative force of gravity, on which circle is the force of gravity the greatest? Open the link below and after the applet has loaded click the show forces button and then in one motion, click in the white field and drag your mouse, let go and repeat until you get 3 or 4 planets orbiting the red sun.
If the force due to gravity was 1 on a circle of radius r, what is the force on a circle of 2r?
1
1/2
1/4