1. Newton’s “4 th law”

2. Law of Universal Gravitation 1.Gravity is universal: ALL objects attract each other. 2.The force of gravity is directly proportional to the masses of both objects. 3.The force of gravity is inversely proportional to the square of the distance.

3. F g α m 1 m 2 If you want to know how Fg changes with mass simply multiply the changes in mass. Ex. 1: If the force of gravity is 18N, what would be the new force if one of the masses was tripled? Since Fg α m 1 m 2 then (3m 1 )(m 2 )=3Fg The new force of gravity is 3(18)= 54N.

4. F g α m 1 m 2 Ex.2: If the force of gravity is 18 units, what would be the new force if one mass is cut in half? Since Fg α m 1 m 2 then (1/2m 1 )(m 2 )=1/2Fg The new force of gravity is 1/2(18) = 9 units

5. F g α m 1 m 2 Ex.3: If the force of gravity is 18 units, what would be the new force if both the masses were doubled? Since Fg α m 1 m 2 then (2m 1 )(2m 2 )=4Fg The new force of gravity is 4(18) = 72 units

6. F g α 1/d 2 Ex.4: If the force of gravity is 60 units, what would be the new force if the distance between is doubled? Since Fg α 1/d 2 then (1/(2d) 2 )=1/4Fg The new force of gravity is 1/4(60) = 15 units If you want to know how Fg changes with distance square the distance and divide by it.

7. F g α 1/d 2 Ex.5: If the force of gravity is 60 units, what would be the new force if the distance between cut in half? Since Fg α 1/d 2 then (1/(1/2d) 2 )=1/(1/4)Fg =4Fg The new force of gravity is 4(60) = 240 units

8. Fg α m 1 m 2 /d 2 Fg = 12 units if m 1 is tripled and d is doubled, what is the new Fg? Since Fg α m 1 m 2 /d 2 then (3m 1 )(m 2 )/(2d) 2 =3/4Fg The new force of gravity is 3/4(12) = 9 units

9. Real Numbers To get Fg to equal Newtons, you must multiply the proportion by a conversion factor. Fg = G(m 1 m 2 /d 2 ) G = 6.67 ×10 -11 Nm 2 /kg 2 m 1 and m 2 are measured in kg d is measured in m

10. Satellites The distance is always measured from the center of planet to the satellite. d = distance above Earth + radius of Earth Use meters!