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)

• 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 geocentricPythagoras (~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 geocentricAristarchus of Samos (?310-250BC)

• 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

• 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)• 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

• 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)

• 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)• 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)• 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 Miles

Satellite Types

100-300 shuttles, space stations, spysats, navsats, hamsats

300-600 weather sats, photo sats

600-1,200 spysats, military comsats, hamsats

3,000-6,000

science sats

6,000-12,000

navsats

22,300 (stationary)

communications, broadcast, weather

250-50,000 (elliptical)

early-warning, Molniya broadcast, communications, spysats, hamsats