1. Newton’s Law of Gravitation

2. Newton concluded that gravity was a force that acts through even great distances Newton did calculations on the a r of the moon and its F r Found the F r inversely proportional to the square of the radius of orbit

3. Since F r is caused by gravity, the force of gravity is inversely proportional to square of radius Newton also realized that the force of gravity depends on the mass – directly proportional to the mass of the two objects being attracted

4. Law of Universal Gravitation Every part in the universe attracts every other part with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

5. Equation F G = Gm 1 m 2 / r 2 G = universal constant = 6.67 x 10 -11 N m 2 /kg 2

6. Example 1 A 50 kg person and a 75 kg person are sitting on a bench so that their centers are about 50 cm apart. How much gravitational force is there between them?

7. Example 2 What is the force of gravity acting on a 2000 kg spacecraft when it orbits two Earth radii from the Earth’s center? Radius = 6380 km Mass of earth = 5.98 x 10 24 kg

8. Acceleration F G = Gm 1 m 2 / r 2 On the earth m 2 is the mass of the earth and m 1 F G = mg mg = Gm 1 m 2 / r 2 m 1 cancels g = Gm 2 / r 2

9. Example 3 What is the acceleration due to gravity on the moon which has a mass of 7.4 x 10 22 kg and a radius of 1750 km?