• After the Greeks, civilization in the WEST (Western Europe) flourished thanks to the Roman Empire (~100 BCE to 500 ACE).
• Romans where engineers not scientists.
• Rome decays and after getting sacked a few times by barbarian tribes the structure Rome imposed on Europe falls apart.
• For almost 1000 years Western Europe falls into a pit of poverty and dispair (The Dark Ages).
• Europe in the hands of the Catholic Church and feudal lords. Battle for papacy = battle for power.
• Ruthless extermination of "heresies"
• Learning confined to monastaries where the few books that exist are held and copied by hand.

 

 

• The rest of the world is doing quite fine thank you.
• Flourishing cultures in Africa, Mesoamerica, the Near East (the Islamic empire, the Eastern Roman empire) India and Asia.
• Slowly, thanks to Islamic, Jewish, and Christian scribes in Spain the Greek texts are rediscoved. Aristotle, Ptolemy etc are known again to the west.

By the 15th century exploration of new trade routes via sea-going ships begins in earnest.

New navigation technologies are needed (based on astromical knowledge)

Money is made in new ways challenging the old power structure.

The Catholic Church's power begins to erode. People begin asking for a new way of worship. Protestant Reformation!
 

Copernicus was born in Poland but traveld to Italy to study (like everyone else at the time)

His inspiration came less from the sky than from books!

Printing Press invented 30 year before his birth

It changed everything!

Because of his reading of Greek philosophers, Copernicus was offended by the Equants of Ptolemy. Restore uniform circular motion!

He was also a "sun-worshiper" in the sense that a movement called neo-platonism was growing which saw the Sun as a symbol for the highest ideals

"In this most beautiful temple who would place a lamp in another or better position than that from which it can light up everything at the same time? For the the sun is not inappropraitely called by some people the latern of the universe, its mind by others, and its ruler by still others"

The plan -> Sun at center surrounded by planets on uniform circular orbits.
 

1. All spheres revolve around sun
2. Earth-Sun distance much smaller than Earth-Stars distance
3. Earth spins on its Axis
4. Motion of Earth on Orbit explains Ecliptic/Zodiac
5. Retograde Motion explained by relative motion of planets

Point 2: Explains lack of Parallax

Point 3: Explains daily rotation of sun and stars

Point 4: Explains yearly motion of Sun against stars.

Point 5: Retograde motion is a "catch and pass" effect.
 

Planets move at different speeds with inner planets moving faster than outer ones.

Faster planets lap slower ones

From point of view of fast planet (frame of reference) slow moving ones appears to stop in sky and change direction twice.
 

This also states that when a planet is in midst of retograde motion it should be "opposition" to Earth meaning it is opposite the sun as well as closest and therefore brightest.
 
 

In the Ptolemic model there was no inherent size-scale. It all depended on how tightly you choose the spheres (orbits) to be nested.

The geometry of the Heliocentric model allowed distances to be derived

Example - Venus: Recall that you can only see Venus near sunset or sunrise.

When Venus is catching up to us it appears to move eastard realative to stars.

When Venus is moving away from us it appears to move westward realative to the stars.

Because it is closer to the sun than we are Venus has a maximum elogation on the sky -> A maxium angular distance from the sun.

That allows its distance to be calulated via trigonometry.
 

Using the observed angle between Venus and the Sun the radius of Venus' orbit (R_v) can be determined in terms radius of Earth's orbit (R_e)
 

(Earth-Sun distance = 1 Astronomical Unit = 1.5x10¹³ cm)

Using these kinds of methods the distance to the stars was thought to be 1.5 million times R_e.
 

When it came to predicting observations Copernicus' model was really no better than Ptolemy's.

It also had to be rigged as well with little epicycles to make things work better.

Still the aesthetic captured the minds of other astronomers.
 

Copernicus will not publish the work until he is dying!

Instant censure:
 

Brahe, danish noblemen, was the best "naked eye" astronomer to ever exist at that point.

Seeing a predicted solar eclipse at age 13 sets him onto astronomy
 

Discovery/Observations of a Nova (1572) made him famous. He shows via lack of parallax that sphere of stars can change

With a ton of gold given to him by King of Denmark he builds Uraniborg, the Castle of the Heavens, a massive observatory complex.

At Uraniborg he makes the most accurate most complete tables of the astronomical observations.

Did not fully buy the Copernican model.

Tycho was an observer not a theorist: he needed someone to turn the data into a model.

That person was Johannes Kepler

Before his death he grants Johannes Kepler access to the observatory and its records setting the stage for the triumph of the heliocentric model.
 

Kepler was a theortist meaning his speciality was mathematics.

He was moved to mystical rapture by the harmonies he saw in the spacing of planetary orbits and saw in this a reflection of a subtler harmony in the construction of the world.

Plato's Doctrine of Ideals: the world we see is a shadow of a more perfect world of ideal forms. Mathematics best expresses those ideal forms.

While teaching a high school class he realizes that the ratio of Saturn and Jupiter's orbits in the Coperinican model can be decribed as spheres nested in a triangle.
 

From this he attempts to build a model where the orbits of the planets are each built from spheres inscribed around the five platonic solids (Cube, Solid Triangle...)

When confronted with Tycho's data Kepler is forced to abandon this idea.

Battles to find a model for Mar's orbit for 8 years!

Success comes with a geometrical figure called the ellipse.
 

An ellipse is a geometical "object"
 

Like a squashed circle.

Circle has 1 center point, ellipse has two (foci)

Special property of ellipse's: Every point on an ellipse has the characteristic that the sum of the distances from the two foci to the point is constant.
 

• e goes to 0 as the ellipse gets more squashed
• e goes to 1 as the ellipse gets more circular

Family of ellipses with eccentricities

{0.25, 0.36, 0.46, 0.57, 0.67, 0.78, 0.88, 0.99}

in order of light to dark shade.

Kepler's discovery of the laws of planetary motion sealed the fate of the geocentric model.

Kepler also believed that FORCES between the sun and the planets were responcible for the 3 laws. This set the stage for Newton 50 years later.