1. Newton’s Fourth Law Universal Gravitation UniversalUniversal Universal Gravitation

2. What is Gravity? Attractive force between two objects with mass Strength of attraction depends on: –Mass of each object (in kilograms) –Distance between the objects (in meters) –Gravitational Constant (G = 6.67 x 10 -11 N∙m 2 /kg 2 )

3. Gravitational Proportions The force of gravity is DIRECTLY proportional to the masses of the objects attracted to one another If the mass of one object is doubled, the force of gravity is… If the mass of BOTH objects is doubled, the force of gravity is…

4. Gravitational Proportions The force of gravity is INVERSELY proportional to the SQUARE of the distance between the objects attracted to one another If the distance between the objects is doubled, the force of gravity is… If the distance between the objects is tripled, the force of gravity is…

5. Examples What happens to F g in the following cases? -Double one mass 2X -Double both masses 4X -Triple one mass 3X -Triple both masses 9X -Halve one mass ½ X -Halve one mass and double the other 1X -Double the distance ¼ X -Triple the distance 1/9 X -Halve the distance 4X -Quarter the distance 16X -Double one mass and double the distance 2x ¼ x  ½ x -Double both masses and double the distance 4x ¼ x  1x -Halve one mass and halve the distance ½ x 4x  2x Triple one mass and quarter the distance 3x 16 x  48x

6. 3000 m 4 x 10 5 kg 6 x 10 5 kg F g = 1.78 x 10 -6 N

7. Gravitational Fields Objects with MASS produce gravitational fields Field lines point inward from ALL DIRECTIONS