1. Chapter 6 - Gravitation Newton’s Law of Gravitation (1687)
Kepler’s Laws
Implications of Newton’s Law of Gravitation
Gravitation near the Earth’s surface
Superposition of forces
Justification for Kepler’s second and third law
Gravitational Potential Energy

2. Newton’s law of (universal) gravitation

3. Cavendish Experiment (1798)

4. Vector Form of Newton’s Law of Gravitationby on

5. Superposition of Forcesm1 m2 m0 m3

6. Problem 1
Three masses are each at a vertex of an isosceles right triangle as shown. Write an expression for the force on mass three due to the other two. m1 r r m3 m2

7. Gravity near the earth’s surface

8. Kepler’s Laws The Law of Orbits The Law of Areas The Law of Periods
All Planets move in elliptical orbits, with the sun at one focus.
The Law of Areas
A line that connects a planet to the sun sweeps out equal areas in equal times.
The Law of Periods
The square of the period of any planet is proportional to the cube of the semi major axis of its orbit

9. Kepler’s 2nd Law The Law of Areas
A line that connects a planet to the sun sweeps out equal areas in equal times.

10. Justification of Kepler’s third law
(for circular orbits around the sun)

11. Problem 2
Verify Kepler’s third law for the earth revolving around the sun.
distance from sun to earth = x 1011 m
mass of sun = 1.99 x 1030 kg. r Ms

12. Problem 3
What would be the height of a satellite with a period of one day
mass of earth = 5.98 x 1024 kg. h Re r me

13. Gravitational potential energy again

14. Escape velocity