1. Conceptual Physics Notes on Chapter 12 UniversalGravitation

2. Universal Gravitation Isaac Newton and the falling apple --- Isaac Newton and the falling apple --- Newton was under a apple tree when a apple hit him on the head and he got an idea that changed the world. Newton was under a apple tree when a apple hit him on the head and he got an idea that changed the world. What was his GREAT idea? …. What was his GREAT idea? ….

3. Universal Gravitation Isaac Newton and the falling moon --- Isaac Newton and the falling moon --- Newton compared a falling Newton compared a falling apple to the moon in orbit around the Earth. He said that the moon fell toward the earth as fast as it moved in a straight line - tangential velocity.

4. Universal Gravitation Newton “generalized” Newton “generalized” his moon findings to ALL objects, and said that ALL objects in the universe attract each other. (Law of Universal Gravitation)

5. Universal Gravitation NEWTON’S LAW OF UNIVERSAL GRAVITATION Every object attracts every other object with a force directly proportional to the mass of each object, but decreases as the square of the distance between masses. Every object attracts every other object with a force directly proportional to the mass of each object, but decreases as the square of the distance between masses. F ~ m 1 m 2 F ~ m 1 m 2 d 2 d 2

6. Universal Gravitation We want the force to equal, so we have to add a constant to the equation. We want the force to equal, so we have to add a constant to the equation. G = 6.67 x 10 -11 kg (Note that the force of gravity is very weak) Henry Cavendish measured G 150 years after Newton’s Law listed above and was said to have WEIGHED the world! Henry Cavendish measured G 150 years after Newton’s Law listed above and was said to have WEIGHED the world!

7. Universal Gravitation

8. So the equation becomes: So the equation becomes: F = G m 1 m 2 d 2 d 2

9. Universal Gravitation Inverse-square Law: The brightness of an object decreases dramatically as we move farther from the source. The result is due to a larger "sphere" of influence. Light from a source like a star shines in all directions, to the area of illumination increases with increasing distance so the total brightness thins out.

10. Universal Gravitation

11. EXAMPLES: 3 2 = 9 but 1/3 2 = 1/9 3 2 = 9 but 1/3 2 = 1/9 2d 2 = 4dbut 1/2d 2 = 1/4d 2d 2 = 4dbut 1/2d 2 = 1/4d (Note that as the distance gets LARGER, the overall force gets smaller )