1. Universal Law of Gravitation

2. So because of Newton’s 3 rd law every body in the universe exerts a force of attraction on every other body. This is Newton’s Universal Law of Gravitation The force between two objects, due to their masses, is called the gravitational force (F g )- in this case it’s not Earth specific and is not 9.81 m/s 2 ).

3. Masses of the 2 objects Distance between the objects Universal Gravitational Constant- 6.67 x 10 -11

4. What is the gravitational force between the Earth and the Moon? m Earth = M = 6.0 x 10 24 kg m Moon = m = 7.4 x 10 22 kg r = 3.8 x 10 8 m G = 6.67 x 10 -11

5. What if the distance between the Earth and the Moon was doubled? What if the distance between the Earth and the Moon was tripled? What if the distance between the Earth and the Moon was quadrupled?

6. What is the gravitational force between the Earth and Venus? m Earth = M = 6.0 x 10 24 kg m Venus = m = 5.0 x 10 24 kg r = 3.8 x 10 10 m G = 6.67 x 10 -11

7. Solving the ULG equation using variables: = 100 N F g ’ = ? If M’ = 3M, and r’ = 2r F’g = GmM’ r’ 2 = Gm3M (2r) 2 = Gm3M 4r 2 = 3 GmM 4 r 2 = 3 (100 N) 4 75 N

8. There is also a way to determine the gravitational field around one object: For one object this is weight, so this becomes… == This is now the gravitational Field Strength

9. For the Earth the gravitational field strength should be 9.81 m/s 2 …find it. Radius of the Earth – 6.37 x 10 6 m

10. For the Moon the gravitational field strength should be 1.6 m/s 2 …find it. Radius of the Moon – 1.7 x 10 6 m

11. Both the ULG and the GFS follow the Inverse square law: ULG-If the distance between two objects is doubled the gravitational attraction is (1/4) of the original. OR GFS-If we travel beyond the Earth by a distance that is double it’s radius than we will only feel a quarter of Earth’s gravitational pull (9.81 m/s 2 /4 = 2.45 m/s 2 ).

12. 2x3x4x 1/4 = 2.24 1/9 = 1.09 1/16 =.61 1x r = 6.4 x 10 6 m 9.81 m/s2

15. HW: The gravitational attraction between the Earth and Mars is 8.7 x 10 16 N. The distance between the two planets is 5.5 x 10 10 m. Earth has a mass of 6.0 x 10 24 kg. What’s the mass of Mars?