Universal Gravitation

What causes the planets to orbit the sun?

What causes an apple to fall from a tree?

Isaac Newton – 1642 - 1727

Newton’s Universal Law of Gravitation

A gravitational force exists between all objects with mass.

3 things can affect the amount of gravitational force between 2 objects:

mass of object 1 (m) - directly proportional Fg α mmass of object 2 (M) - directly proportional Fg α Mthe distance between their centers (r) - inversely proportional

Fg α 1r2

Put it together!

Fg α m*M r2

Ex: Sandy and Bob an standing near each other such that the gravitational force between them is 6 x 10-8 N. If Years later Sandy is now 2/3 her original weight and Bob’s weight quadruples. The distance between them is ¼ the original distance. What is the new gravitational force between them?There are many ways to solve this problem. Here are a couple methods:

1. Multiply each variable by the number given in the problem. From math class: what you do to one side, you do to the other. Multiple the gravitational force by the new proportion.

Fg α m*M r2

2/3*4 Fg α 2/3m*4M(¼)2 (¼r)2

Fgnew = 2/3*4 * 6x10-8 = 2.56 x 10-6 N (¼)2

2. Create a proportion.

Fg new (2/3)m*4M

(¼r)2 _________ = ______________

Fg old mM r2

Cancel the mM and cross multiply.

r2

Fgnew (2/3)*4

(¼)2 _________ = ______________

Fgold 1 Fgnew = (2/3)*4 x Fgold

(¼)2

Fgnew = (2/3)*4 x 6x10-8 = 2.56 x 10-6 N (¼)2

Turn a Proportion into an Equation

A constant must be added to the proportion.Henry Cavendish (1731-1810) and his Torsion Balance Experiment found the value of this constant.

Torsion Balance Experiment

Universal Gravitation Constant

G = 6.67 x 10-11 N m2/kg2

Fg = G mM r2