Geocentric Model of the Universe – Ptolemy (et al.)
5 known planets
(excluding Earth)
Sun is beyond Venus
(note that Venus and
Mercury are closer to the
Sun than Earth).
Stars are beyond planets
and not moving wrt each
other.
Claudius Ptolemais (~150 BC)
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Built on Eudoxus (~408 BC),
Aristotle (384-322BC),
Hipparchus and others
Almagest (Al Magest), vastly
influential
introduced equant (uniform
angular movement)
40 epicycles and deferents
Equants and eccentrics for all
planets (including Sun&Moon)
Predicted motions well
• Demo 1 2 3 Details 4
Ancient Greece: not all geocentric
Pythagoras (~550BC)
• Non-geocentric model
• Taught that spheres are the
perfect shape
• Earth and other celestial
bodies were spherical
• Revolved around central fire
• Counter-Earth (antichthon),
blocks view from central fire
• Ten spheres (perfect number?)
• ‘Music of the spheres’
Ancient Greece: not all geocentric
Aristarchus of Samos (?310-250BC)
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Sun was >20 times farther away than Moon
Heliocentric model
Details not known, secondary sources
Earth rotates daily
Earth revolves around Sun
Stellar parallax not observed because stars are
too far away
• Model not accepted, too ‘radical’.
Why a geocentric model might be
considered preferable
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More intuitive, ego-centric, gives man importance
Spinning Earth left would create fast E-W winds
We don’t feel Earth spinning
What keeps Earth spinning? Earth too big to move (no
rotation, no revolution)
Aristotle’s ‘natural tendency’ (earth/water fall, air/fire rise)
If stars are too far away for stellar parallax, universe would
be too big.
No stellar parallax observed
Stars’ brightness should change with season
Falling objects would take curved paths
Moon would be left behind
Copernicus (1473-1543)
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De Revolutionibus Orbium Coelestium
("On the Revolutions of the Celestial
Orbs"), published 1543
Wished to eliminate Ptolemy’s equant
(violated uniform circular motion,
unaesthetic)
Heliocentric model
Earth rotates daily and revolves
around Sun annually
Still assumes uniform circular motion
Retains epicycles (48, i.e. 8 more than
Ptolemy)
Objections to Copernicus
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Predictions not better than before
More epicycles than Ptolemy
Religious objections (not just Catholic church)
Rotational and orbital speed of Earth must be
incredibly large (~1600km/h, equator, and
30km/s)
• No difference in stellar brightness observed
(should be there if distance varies)
• No stellar parallaxes observed.
Tycho Brahe (1546-1601)
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Danish nobleman
Pro-Aristotle, anti-Copernicus
Lost part of his nose in duel
Most precise pre-telescope
observations (1-2’)
Crucial planetary motion data
(Mars)
Observations of supernova
(1572) and comet (1577),
‘change in the sky’
Best measurements yet of
stellar parallax, found none ->
geocentric universe
Moon and Sun revolve around
Earth
Planets revolve around Sun
Brahe’s geo(helio)centric universe
• Found no stellar parallax,
two choices, chose wrong
one
• Geocentric model
• Earth unmovable at
center
• Sun and Moon revolve
around Earth
• Other planets revolve
around Sun
• Epicycles and equants
Johannes Kepler (1571-1630)
• Became assistant to
Brahe in 1600
• Did not get along with
Brahe, competition
• Mars data, 1601-05
• ‘listened’ to data
• Sought ‘celestial
harmonies’
• Published his 3 laws in
1609 (Astronomia Nova,
Law 1 and 2) and 1618
(Harmonice Mundi, Law
3)
Kepler’s laws of planetary motion,
First Law
The orbits of the planets are ellipses, with the
Sun at one focus of the ellipse.
Demo
• AF1305.html
• AF1307.html
Kepler’s laws of planetary motion,
Second Law
The line joining the planet to the Sun sweeps
out equal areas in equal times as the planet
travels around the ellipse. Link
Demo
• AFc1307.html
Kepler’s laws of planetary motion,
Third Law
The squares of the planets’ periods of
revolution are proportional to the cubes of
the semimajor axes of their orbits.
P2 ~ a3
Galileo Galilei (1564-1642)
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Mathematician, observer,
experimenter
Anti-Aristotelian
Did not invent, but made his own
telescopes (1609 …3x – 30x)
Cannonballs, Pisa
Craters and mountains on Moon > perfect shape?
Moons of Jupiter
Phases of Venus (Ptolemy, Brahe)
Milky Way is made up of stars
Odd shape of Saturn
Breakthrough for Copernican
model
Inquisition, house arrest, forgery
‘Eppur si muove’ and still, it moves
Isaac Newton (1643-1727)
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Graduated at age 23.
Did fundamental work at age 23
(published later), see paradigm
shift
Most well-known for his work
on calculus and
gravitation/mechanics
Provided quantifiable, causable
explanations for the movements
of the planets
Could explain planetary
motions by three simple laws of
motion
All motions!!! Apple,
remember?
Philosophiae Naturalis Principia
Mathematica (1687)
Altitude Satellite Types
Miles
100-300 shuttles, space stations, spysats,
navsats, hamsats
300-600 weather sats, photo sats
600-1,200 spysats, military comsats, hamsats
3,000- science sats
6,000
6,000- navsats
12,000
22,300 communications, broadcast, weather
(stationary)
250-50,000 early-warning, Molniya broadcast,
(elliptical) communications, spysats, hamsats