Law of Universal Gravitation

Universal Gravitation

• gravity is a force of attraction between any two masses

• gravity is a UNIVERSAL force– universal meaning of, affecting, or done

by all things in the world.

Newton’s Law of Universal Gravitation

Force between two objects:

F = Gm1m2

d2

m1, m2: masses of the objects

d: distance between objects’ centers of mass

G: universal gravitational constant, 6.67  10–11 Nm2/kg2

Universal Gravitational Constant

G = 6.67x10-11 Nm2/kg2

• The constant is derived from the force that occurs between two 1 kg masses 1 m apart

2 Things to Know about UG:1. As MASS increases, the FORCE

increases

*** If the top of a fraction gets bigger, the whole answer gets bigger as well.

221

d

mmGF

2. As DISTANCE increases, the FORCE decreases

*** If the number on the bottom part of the fraction gets bigger, then the whole answer will get smaller.

221

d

mmGF

Practice Problem

Tom has a mass of 70.0 kg and Sally has a mass of 50.0 kg. Tom and Sally are standing 20m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. Find the force of gravitational between Tom and Sally.

Practice Problem

What is the gravitational attraction between two spheres (m = 1.67 X 10-27 kg) at a distance of 5.0 X 10-15 m?

Practice Problem

A 1 kg mass weighs 9.8 N on Earth’s surface, and the radius of Earth is roughly 6.4 x 106 meters. Calculate the mass of Earth.