This document discusses Newton's law of universal gravitation and the development of models of the universe. It explains that Kepler analyzed Brahe's astronomical data and discovered that planets orbit the sun in ellipses. Newton then formulated his law of universal gravitation, which states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The document provides examples of applying this law and gives homework problems.

1. CHAPTER 7
Gravitation

2. UNIVERSAL GRAVITATION
 What is Newton’s Law of Universal Gravitation and
how do I apply it?

3. DEVELOPMENT OF THE MODEL OF THE
UNIVERSE
 Original model?
 Copernicus – 1543
 Brahe – 1560
 No
telescopes, measurem
ents over 20 years

4. KEPLER
 Brahe’s assistant
 Applied geometry to the
data
 Sun is in the center
 Orbits are ellipse shaped
 Planets move faster
closer to the sun

5. NEWTON
 The apple falls, where does this force come from?
 How does this apply to the motion of planets?

6. NEWTON
 Third Law
 Can be thought of as a force of attraction
 Directly proportional to the masses of the objects
 Can also be called gravitational force
 Newton’s Law of Universal Gravitation

7. LAW OF UNIVERSAL GRAVITATION
• Measures the force of attraction between
any two objects
• As small as electrons, as large as planets

8. RELATIONSHIPS BETWEEN THE VARIABLES


9. INVERSE SQUARE LAW


11. SOLVING FOR VARIABLES


12. EXAMPLE
 Find g if r = 1.5
m, density = 3.3 x 103
kg/m3
 What would happen if
the prince jumped
upward?

13. HOMEWORK
 Page 191
 # 55 – 60, 64

14. G ?!
 100 years after Newton
 Cavendish – 1798
 Confirmed that there is a
gravitational attraction
between two objects
 Enabled the calculation of
the mass of the Earth

15. MEASURING G
 Original spheres were
lead
 Worked for any
materials

16. HOMEWORK
 Worksheet