1. Describe the universal gravitational law.

2. Evaluate the techniques and models used by Ptolemy and Copernicus to explain the setup of the universe.

3. A child picks up a tennis ball tied to the end of the rope. He swings the rope around, over his head, in a circle. Once the ball is spinning, he lets go of the string and the ball goes flying. Explain which of the following images correctly shows which may the ball fly and why.

1. The law of universal gravitation is , where F=force, G=gravitational constant, m=mass, r=radius. It's an inverse square law, because there's a squared term in the denominator. It's really neat because it's basically the same thing as Coulomb's law () but just with big things instead of small ones!

2. Ptolemy was a Greek mathematician who believed in a geocentric model, or that the earth was the center of the universe and the sun revolved around it. Copernicus believed in a heliocentric model, which is exactly the opposite. Of course we now agree with Copernicus. Both scientists used extensive proofs and logic to come to their conclusions, but ultimately Copernicus was correct.

3. The first image, Path A, shows how the ball will fly. This is because of Newton's laws: the object will keep going in the direction it was last going. The force is not circular; the force is basically tangent to the circle at every point. Just try doing this with your bike (I do this in my driveway) by spinning in circles, then just stopping: you will go along Path A. Also, this is the centripetal force, which says that the force is towards the inside; this causes the ball to go outwards when you let go.