1. Newton’s Law of Universal Gravitation

2. Who Found It?

3. Universal Law of Gravitation

4. Universal Law of Gravitation

5. Universal Law of Gravitation

6. Universal Law of Gravitation

7. Universal Law of Gravitation

8. Universal Law of Gravitation

9. Universal Law of Gravitation

10. Universal Law of Gravitation

11. Cavendish

12. The Statement of the Law
Magnitude: Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Direction: This force acts along the line joining the two particles.

13. Gravity Near the Earth’s Surface

14. Moon: Special Satellite

15. Earth: the Satellite of the sun

16. Kepler’s Laws
Johannes Kepler discovered 3 laws from the motion of the planets as mapped by Tycho Brahe
Planetary orbits are elliptical not circular
Orbits sweep out equal areas in equal times
T2 /r3 = k where k = “constant”

17. The orbits of the planets are ellipses, with the sun at one focus.
(Law of Ellipses)
The closer the planets are to one another,
the more circular the orbit.

19. Kepler’s 2nd Law
An imaginary line drawn from the center of the sun to the center of the planet will
sweep out equal areas in equal intervals of time.
(Law of Equal Areas) Deals with speed…
faster when closer to the sun.

20. Kepler’s 2nd Law

21. Kepler’s 3rd Law
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (Law of Harmonies) (TA /TB)2= (rA /rB)3

23. Satellite Motion
If a projectile moves fast enough, it falls at the same rate that the Earth curves

24. Satellites
What keeps a satellite up?
Its high speed
How they move?

25. How fast are satellites moving?

27. Weightlessness What is gravity in outer space?
Where space shuttle orbits…g = 8.7m/s How come astronauts
are “floating” then?
g = F/m