5. Chapter 12: Gravitation
Newton’s Law of Gravitation

6. Gravitational attraction
Note: Two particles of different mass exert equally strong gravitational force on each other

8. Gravitational Forces (I)MM
MM ME
FG = G
r 2
‘‘Attractive Force” ME

10. Cavendish balance
Cavendish(1798) announced that he has weighted the earth

13. Average Density of the Earth
g = 9.80 m/s2
RE = 6.37 x 106 m
ME = 5.96 x 1024 kg
rE = 5.50 x 103 kg/m3
= 5.50 g/cm3 ~ 2 x rRock
 ???

14. The gravitational force is conservative
Note:
Work done is
Path independent!

16. Gravitational potential energy
Note: The gravitational potential is zero at infinity

19. Projectile

20. Projectile

21. Circular orbit

23. Kepler’s Laws
Each planet moves in an elliptical orbit, with the sun at one focus of the ellipse
A line from the sun to a given planet sweeps out equal areas in equal times.
3. The periods of the planets are proportional to the 3/2 powers of the major axis lengths of their orbits.

24. Geometry of an ellipse

25. Elliptical orbit