Sept 2012 Week 3 1 Sept 2009 PHY 101 Week 3 1

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Historical figures in the Copernican Revolution

Ptolemy – the geocentric model, that the Earth is at rest at the center of the Universe (...lived in Egypt, 90 – 168 AD)

Copernicus – published the heliocentric model.

Galileo – his observations by telescope verified the heliocentric model.

Kepler – deduced empirical laws of planetary motion from Tycho’s observations of planetary positions.

Newton – developed the full theory of planetary orbits.

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Johannes Kepler (1571 – 1630) … discovered three empirical laws of planetary motion in the heliocentric solar system

1. A planet moves on an elliptical orbit, with the sun at one focal point. 2. The radial vector sweeps out equal areas in equal times. 3. The square of the period is proportional to the cube of the radius.

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Isaac Newton

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m

Fa

nF ˆ2

21

r

mGm

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2

rv

ar

2r r

GMmF

2

2

r

GM

r

v

m implies

Fa

r

GMv

GM

r4T

322

32 rT

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(and the true center of mass!)

)( mMG

a4T

322

GM

a4 32

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END