Motions of the Planets ASTR 2110 Sarazin

Motion of Planets Retrograde Motion Inferior Planets: Mercury, Venus Always near Sun on Sky Retrograde motion when very close to Sun on sky (Every other time) Superior Planets Mars, Jupiter, Saturn (Uranus, Neptune) Can be near or far from Sun Retrograde motion when opposite Sun on sky

Greek Theory of Solar System What is center of Solar System? Aristarchus: Sun Sun is largest object in Solar System Aristotle: Earth Main argument was lack of observable parallax from Earth

Parallax If Earth travels around Sun, we view stars from different angles The stars will appear to shift back and forth every year

Parallax

Parallax If Earth travels around Sun, we view stars from different angles The stars will appear to shift back and forth every year Effect decreases with increasing distance

Parallax Hipparchus found NO measurable shift for stars each year Aristarchus: Earth orbits around Sun, but stars are VERY far away, so parallax too small to measure Correct explanation, but required that stars be > 1000 times further away than planets (actually millions of times further) Aristotle, Hipparchus: Earth is center of Solar System, Sun orbits Earth Stars could not be so far away

Hipparchus (160-127 BCE): Greatest of the Ancient Astronomers Invented magnitudes for star brightness Determined accurate sizes and distances for Sun and Moon Determined accurate length of year Very good orbit for Moon and Sun Refined eclipse predictions (within 1 hour) Compiled star catalogue

Hipparchus (cont.) Found Sun didn t move at a constant speed Discovered precession of Earth s axis

Ptolemy (100-170 AD)

Ptolemy (Cladius Ptolemaeus) Compiled previous measurements by Hipparchus and others (most original sources lost) Made improved measurements Systemized the constellations Measured distance to Moon to 3% using parallax Constructed first complete theory of motion of planets Compiled all in series of 13 volumes: The Almagest (from Al Magisti, Arabic for The Greatest). Main source of information about Greek astronomy

Ptolemy s Theory of Planetary Motions Starting points 1. Earth is center of Universe Geocentric theory No measurable parallax Hipparchus, Aristotle 2. Orbits are circles Most perfect plane figure Plato, Aristotle

Problem: No retrograde motion No inferior and superior planets

Ptolemy s Theory 1. Orbits are Epicycles circles within circles Sun and Moon do not have epicycles Earth planet

Ptolemy: how epicycles produce retrograde motion

Ptolemy s Theory 1. Orbits are Epicycles circles within circles Sun and Moon do not have epicycles 2. Earth is off set from center only one retrograde motion period per orbit

Ptolomy s Epicycles

Ptolemy s Theory 1. Orbits are Epicycles circles within circles Sun and Moon do not have epicycles 2. Earth is off set from center only one retrograde motion per orbit 3. Epicycles of inferior planets tied to Sun Mercury, Venus center of epicycle point to Sun

Inferior Planets Venus Sun Earth

Ptolemy s Geocentric Universe

Negatives Wrong! Ptolemy Theory Very complex, epicycles within epicycles, offsets, Required complex tables Did not predict planetary motions correctly for long times, had to be corrected by adding more epicycles Not a physical, scientific theory (descriptive)

Positives Ptolemy Theory Survived for ~1300 years! Worked OK, given enough effort

Time Flies When You re Having 1300 year pass Fun... Ptolemy s work spreads through Roman Empire Western Roman Empire falls Dark Ages in Europe, much of science lost Arab astronomers translate Almagest into Arabic, make new observations, update theory Muslim invaders in Europe (e.g., Spain) carry Greek books back to Europe, Almagest

Alphonsine Tables Last hurrah of Ptolemy King Alphonse X, Toledo, Spain, ~1270 AD Collects astronomers, mainly from Moorish Spain Translate Almagest Updates Ptolemy s theory, tables Very complex, ~130 epicycles If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler. - King Alphonse X

Funny, I didn t see that coming Ptolemy s geocentric universe becomes part of Catholic doctrine!!

Renaissance Astronomy ASTR 2110 Sarazin Astronomical Clock in Prague

A Timeline for Astronomical Discovery

Nicholas Copernicus (1473-1543)

Heliocentric Theory Copernicus argues that: 1. Sun is center of Solar System 2. Earth and Moon together orbit Sun, as do all the other planets

Nicolaus Copernicus Studied church law, medicine, & astronomy Latinized his Polish name Assistant to Bishop (his uncle) Commentariolis (~1514) informal notes De revolutionibus orbium coelestrium ( On the revolutions of the celestial bodies ) book

Copernican Cosmology

Copernicus Theory 1. Sun is center of Solar System

Copernicus Theory 1. Sun is center of Solar System 2. The further a planet is from the Sun, the slower it moves

Copernicus Theory 1. Sun is center of Solar System 2. The further a planet is from the Sun, the slower it moves Ptolemy: Complex apparent motion is real motion Copernicus: Complex apparent motion is result of simple real motion seen from moving Earth

Retrograde Motion

Like passing a car Retrograde Motion relative motion relative motion

Retrograde Motion Passing occurs when two planets are closest Retrograde motion occurs when planet is closest to Earth Inferior planets: near Sun on sky Superior planets: opposite Sun on sky The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file Mars Venus Earth

Why are inferior planets always close to Sun on sky? Orbit closer to Sun than Earth

Sidereal and Synodic Periods Period = time for planet to orbit the Sun Sidereal period = real period Synodic period = apparent period as seen from Earth

Periods: Ptolemy s Theory 0.32 1.60 1,0 2.14 1.09 1.03 1.0

Periods: Copernicus Theory 0.24 0.62 1.00 1.88 11.86 29.41

Computing relative sizes of orbits in the Copernican system

Astronomical Unit (AU) Right-sized distance unit for Solar System, exoplanetary systems, binary stars Average distance from Earth to Sun 1 AU = 1.50 x 10 13 cm = 1.50 x 10 11 m ~92 million miles, 150 million km

Advantages of the Copernican System Simpler in concept Natural explanation for the annual motion of the Sun against the background stars Natural explanation of retrograde motion Relative spacing of planetary orbits determined, periods made sense Natural explanation for motion of Venus and Mercury relative to the Sun But: not more accurate than Ptolemaic tables (because circular orbits assumed)

The Copernican Revolution Cosmic Connection We live on a planet like many others moving about a star like many others in a galaxy like many others. We are part of the Universe. We are not special. Simplicity of nature Natural laws are simple, but can result in complex phenomena Predictive power of theories

The Empire Strikes Back Catholic church moves to suppress new thinking, due in part to the Reformation Giordano Bruno: builds on Copernicus. Suggests other planets may also have intelligent life

A Timeline for Astronomical Discovery

Galileo Galilei (1564-1642)

Galileo First great experimenter Theories must correctly predict the results of experiments Predictions must be quantitative Studied motion and gravity Inertia (heavier objects harder to stop) Gravity (all things fall at the same rate) Time (pendulum) Relativity First astronomy telescope

Telescopic Observations Galileo did not invent telescope, but was first to use it for astronomy Observations called into question the Ptolemaic cosmology First described in book Sidereus Nuncius

Aristotelian Concept: Celestial bodies are perfect Observation: mountains, craters, valleys on the Moon The Moon

The Sun Aristotelian Concept: Celestial bodies are perfect Observation: Sunspots, rotation of the Sun

The Milky Way Aristotelian Concept: Stars are located on a fixed celestial sphere Observation: Many more stars than visible to the naked eye. Suggest stars are very distant

The moons of Jupiter The View through a telescope Everything does NOT orbit the Earth A page from Galileo s notes

Key Observational Test: Proves that Venus shines by reflected sunlight Phases of Venus Provides an absolute, yes or no test of Ptolemy vs. Copernicus

Phases of Venus- Copernicus

Phases of Venus - Ptolemy

Final Jeopardy, for all the money Perfect observational test 1) If Venus ever has gibbous phases (more than half full), then Ptolemy is wrong 2) If Venus never has gibbous phases, then Copernicus is wrong

Phases of Venus

Phases of Venus- Copernicus

Galileo: Troubles with Catholic Church First book Sidereus Nuncius controversial Galileo ordered to stop defending Copernican theory In 1632, published Dialogo dei Due Massimi Sistemi (Dialogue Concerning the Two Chief World Systems) Put on trial by Inquisition, ordered to recant, put under house arrest

Galileo s Finger