NEWTON’S LAW OF

UNIVERSAL GRAVITATION

Newton’s Law ofUniversal Gravitation

Newton’s law of universal gravitation:The force of attraction between two objects is

directly proportional to the product of the masses and inversely proportional to the square of the distance between the center of the masses.

FORMULA Fg = Gm1m2

r2

F- force (N)m- mass (kg)r- distance between objects(m)G- universal gravitational constant (6.67 x10-11Nm2/kg2)

EXAMPLE: What is the force of attraction between the Earth and the Moon?

r

Fg = 6.67x10-11(5.98x1024 kg)(7.35x1022kg) (3.85x108m)2

Fg = 2.93 x 1037

1.48 x 1017

Fg = 1.98 x 1020N

Inverse square proportion:

Earth

r2r

3r4r

1N ¼ N 1/9 N 1/16 N

As the distance between the objects increases theforce decreases.

F

r

GravityAs you increase the distance from the center of the earth, your weight will decrease slightly. On mountain tops you weigh a little bit less.

If you are in a valley the effects of gravity will be slightly more.

If you could drill a tunnel through the center of the earth, your weight would decrease as you fell through. At the center of the earth your weight would be zero.