Chapter 12: Gravitation Newton’s Law of Gravitation.

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Presentation transcript:

Chapter 12: Gravitation Newton’s Law of Gravitation

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

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

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

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  ???

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

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

Projectile

Projectile

Circular orbit

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.

Geometry of an ellipse

Elliptical orbit

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