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Chapter 5 Planetary Motion
I.
Historical Description of Planetary Motion
A.
Greek Philosophers’ model (300 B.C)
1) Earth is at the center of the Universe
2) Sun, Moon, Stars are fixed in concentric spheres revolving around Earth
B.
Planets have retrograde motion
1) Planets appear to move backwards sometimes
2) Ptolemy (200 A.D.) explains with Epicycles
a) Circles not spheres for sun, moon, planets
b) Smaller circular motions on the larger orbit
c) Explained retrograde motion
C.
Copernicus and Galileo: Heliocentric Solar System
1. Sun is center of Solar System, planets including Earth, revolve around sun
2. Explains retrograde motion, plus other of Galileo’s observations
3. Used circles for the orbits: didn’t work for everything
D.
Kepler’s Planetary Motion (1571-1630)
1. Assistant to Tycho Brahe, who had the best observations yet of the sky
2. Devised 3 laws from the data: Testable Rules or Empirical Laws
a) Planetary orbits are ellipses, not circles
b) Orbital radius sweeps out equal areas in equal times
3
4 2
c) r 3  T 2 r
T
2
 constant 
Gm s
3.
4.
II.
These 3 laws accurately predicted the motions of the planets
As Empirical Laws, they still needed to be explained
Newton’s Universal Gravitation
A.
Newton realized planetary motion was like projectile motion
1) Orbit of a planet is just falling from very high
2) If you threw a ball fast enough from a high
enough altitude, it would orbit Earth
3) The moon is a big falling rock!!!
B.
Universal Gravitation
1) W = mg, so mass must be involved
2) Gravity is inversely proportional to distance
FG 
1
r2
3)
Force of Gravity can be calculated
FG 
4)
Gm1m2
r2
G = universal gravitational constant = 6.67 x 10-11Nm2/kg2
Cavendish, 1731-1810
5)
C.
G is very small, so m1 or m2 must be large for us to notice F
Weight and Gravity
1) Earth is very large, so its attraction force is very large mE = 5.98 x 1024 kg
2) Radius of the earth: rE = 6.37 x 106 m
Gm1m2
3) W = FG
FG 
 mg  W
r2
Gme Nm 2 / kg 2 kg kgm / s 2 m 2 / kg 2 kg
2
g 2 


m
/
s
m2
m2
re
4)
Calculate W for 50 kg person 2 different ways
W = mg
FG 
Gm1m2
r2
III. Moon and Satellite motion
A.
Moon orbits Earth according to Kepler’s Laws = Satellite
1) Phases of the moon
a) Full
b) Half
c) New
2)
B.
Eclipses
a) Lunar: Earth’s shadow covers the moon
b) Solar: Moon blocks the sun from the Earth
Tides: Moon’s Gravitation affects oceans, creating bulges
1) High Tides: closest and farthest from the moon
2) Low Tides: midway from the moon
C.
Other Satellites
1) Anything in orbit of the Earth is a satellite: many man-made objects
3
2
2) They obey Kepler’s Laws: r  constant  4
T2
3)
Gm e
We can manipulate r and T to get any distance or period we want
a) Sychronous orbit: T = 24 h, satellite stays over same place all day
b) Calculate r for a synchronous = 42,000 km (7 times re)
c) Make r shorter, T becomes shorter
d) Make T shorter, r becomes shorter