1. NEWTON’S LAW OF UNIVERSAL GRAVITATION Newton’s Law of Universal Gravitation

2. Newton’s law of universal gravitation: The force of attraction between two objects is directly proportional to the product of the masses and inversely proportional to the square of the distance between the center of the masses.

3. FORMULA F g = Gm 1 m 2 r 2 F- force (N) m- mass (kg) r- distance between objects(m) G- universal gravitational constant (6.67 x10 -11 Nm 2 /kg 2 )

4. EXAMPLE: What is the force of attraction between the Earth and the Moon? r F g = 6.67x10 -11 (5.98x10 24 kg)(7.35x10 22 kg) (3.85x10 8 m) 2 F g = 2.93 x 10 37 1.48 x 10 17 F g = 1.98 x 10 20 N

5. Inverse square proportion: Earth r 2r 3r 4r 1N¼ N 1/9 N1/16 N As the distance between the objects increases the force decreases. F r

6. Gravity As you increase the distance from the center of the earth, your weight will decrease slightly. On mountain tops you weigh a little bit less. If you are in a valley the effects of gravity will be slightly more.

7. If you could drill a tunnel through the center of the earth, your weight would decrease as you fell through. At the center of the earth your weight would be zero.