2. GRAVITATION

3. NEWTON’S LAW OF GRAVITATION There is an attractive force between any two bodies which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. There is an attractive force between any two bodies which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.

4. NEWTON’S LAW OF GRAVITATION mama mama mbmb mbmb FaFa FbFb d

5. Universal Gravitational Constant G = 6.67 X 10 -11 N.m2N.m2 Kg 2

6. NEWTON’S LAW OF GRAVITATION Note : F Grav = F w (The weight of a body is the gravitational force acting on it) F Grav = F w MeMe rere m1m1 = m1gm1g

7. NEWTON’S LAW OF GRAVITATION MeMe rere m1m1 = = g g This expression can be used to find the acceleration due to gravity on any celestial body of known mass and radius. This expression can be used to find the acceleration due to gravity on any celestial body of known mass and radius.

8. NEWTON’S LAW OF GRAVITATION Given that the Earth’s radius Is 6.37 X 10 6 m, find the Earth’s mass. Given that the Earth’s radius Is 6.37 X 10 6 m, find the Earth’s mass. = = g g M e = (9.80 m/s 2 )(6.37 X 10 6 m) 2 6.67 X 10 -11 N. m 2 / Kg 2 M e = 5.96 X 10 24 Kg

9. NEWTON’S LAW OF GRAVITATION The Earth has a mass of 5.96 X 10 24 Kg and the moon has a mass of 7.32 X 10 22 Kg. If the moon orbits the Earth at a distance of 3.8 X 10 5 Km, what force does the moon exert on the Earth? The Earth has a mass of 5.96 X 10 24 Kg and the moon has a mass of 7.32 X 10 22 Kg. If the moon orbits the Earth at a distance of 3.8 X 10 5 Km, what force does the moon exert on the Earth? MeMe MmMm d

10. NEWTON’S LAW OF GRAVITATION m e = 5.96 X 10 24 Kg m m =7.32 X 10 22 Kg d = 3.8 X 10 5 Km = 3.8 X 10 8 m F Grav = 2.0 X 10 20 N F Grav = 2.0 X 10 20 N

11. NEWTON’S LAW OF GRAVITATION F m1m1 m2m2 How far apart would the centers of two 1000 Kg bodies have to be in order for the gravitational attraction between them to be 1.0 N ? F = 1.0 N m 1 = m 2 = m = 1000 Kg G = 6.67 X 10 -11 N.m2N.m2 Kg 2

12. NEWTON’S LAW OF GRAVITATION F grav m1m1 m2m2 d=8.2 X 10 -3 m

13. MOVE ON TO CIRCULAR MOTION