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Chapter 7
7.1 Planetary Motion & Gravitation
 Nicholas Copernicus (Polish)
 Pulished Earth-centered model in 1543
 Tycho Brahe (Danish)
 Vowed to be an astronomer after a solar eclips
 Designed and built a device for measuring stellar objects
 Recorded stellar positions for 20 years
 Johannes Kepler (German)
 Brahe’s assistant that inherited amassed data
 Studied inherited data
Kepler’s Laws
 Believed Sun exerted a force on planets
 Discovered laws that govern planetary (and satellite)
motion
 First Law
 Paths of planets are ellipses with Sun at one focus
 Comets also orbit in ellipses with Sun at focus
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Long period – Comet Hale-Bopp (2400 yrs)
Short period – Comet Halley (76 yrs)
Kepler’s Laws
 Second Law
 Imaginary line from Sun to planet sweeps equal
distances in equal time intervals
 Third Law
 Square of the ratio of periods of any two planets
revolving around the Sun is equal to the cube of the
ratio of their average distances from the Sun
Newton’s Law of Universal
Gravitation
 Newton recognized the relationship between the force
of the Sun and the square of the distance to the planet
 Inverse square law
Universal Gravitation
 Falling apple and Moon obeyed the inverse square law
 According to Newton’s 3rd Law, the force the earth
exerts on apple is same the same as the force the apple
exerts on earth
 Gravitational force
 Force of attraction between two objects must be
proportional to the objects’ masses
 Theorized it existed between any two objects with mass
Universal Gravitation
 Objects attract each other with a force that is
proportional to the product of their masses and
inversely proportional to the square of the distance
between them
m1m2
F=G
r2
 Direct vs Inverse relationships
 Pg 175, Connecting Math to Physics
Universal Gravitation & Kepler’s 3rd
 Derivation
Measuring G
 Universal Constant