“Every object in the universe attracts every other object in the universe”

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

Universal Gravitation Key Points These ideas should be able to be combined. In order for it to be successful, two important things happened: 1. Newton invents a new branch of calculus 2. Henry Cavendish determines a gravitational constant G = 6.67 x

Universal Gravitation Formulas Force of Universal Gravitation: F g = G x m 1 x m 2 d 2 ( m must be in “kg”; d must be in “m”) Gravitational Acceleration: A g = G x m d 2 (m = mass of bigger object)

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.

F g α m 1 m 2 Ex.2: If the force of gravity is 18 N, 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 N

F g α m 1 m 2 Ex.3: If the force of gravity is 18 N, what would be the new force if both 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 N

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

F g α 1/d 2 Ex.5: If the force of gravity is 60 N, what would be the new force if the distance between masses is 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 N

Fg α m 1 m 2 /d 2 Ex.6: If the force of gravity is 12 N, what would be the new force if m 1 is tripled and d is doubled? 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 N If both variables change, simply apply both relationships