Kepler, Galileo: Moving Forward

Question 1

Tycho Brahe

Answer 1

1546-1601
Most accurate naked eye data in human history
Collected data not just at special points (opposition, quadrature etc) but at all times
Data needed for Kepler to discover elliptical orbits
Observed 1572 supernova - heavens are changeable
argued that Comet of 1577 smashed idea of crystalline celestial spheres (comets aren’t sub lunar)

Question 2

Why didn’t Tycho believe in heliocentric model?

Answer 2

For that, would have to see stellar parallax
Observed NONE
So distance to stars is > 1000 AU
That’s way too big!

Question 3

Tycho’s model

Answer 3

Hybrid geocentric and heliocentric
Earth in centre, sun around earth, planets around sun
Observationally indistinguishable

Question 4

Kepler

Answer 4

1571-1630
Gifted mathematician and astronomer
Super religious
Believed God made universe according to mathematical plan, called Kepler to discover and reveal
Copernican model: sun=father, stars=sun, rest=Holy Spirit
First astrophysicist

Question 5

Mysterium Cosmographicum

Answer 5

Cosmic mystery
Kepler published in 1596
Caught tycho’s eye, so Kepler became his student

Question 6

Keplers first big “discovery”

Answer 6

Each of 5 Platonic solids, inscribe and circumscribe it with spheres, getting a shell whose thickness is proportional to radius
Tightly nest shells in appropriate order and find relative radii of 6 planets
Destroyed when Uranus was found

Question 7

The physics Kepler knew

Answer 7

Aristotle:
V proportional to F
Motion caused by consciousness (soul, intelligence, instinct)
Consciousness of heavenly bodies is serene, causing uniform circular motion
William Gilbert:
Theory of magnetic soul of earth
Magenetism + consciousness causes planetary motion

Question 8

Math Kepler knew

Answer 8

Archimedes:
Finding areas under curves using limits of inscribed and circumscribed polygons (inspired nested Platonic solids)
Nicholas of Cusa (1400s):
Equivalence in limit of straight line with circle of infinite radius, or infinitesimal arc and chord

Question 9

Astronomy Kepler knew

Answer 9

Ptolemy
Copernicus
He revived the sacrilegious Equant

Question 10

Kepler’s goal

Answer 10

To completely reform astronomy

• perfect accuracy in reproducing observations
• unified model based on physical causes

Question 11

Vicarious hypothesis

Answer 11

Trying non equal eccentric and Equant, running all the math, finding it wrong, trying something else (took ages)
Gave right longitudes, wrong latitudes and distances
To get right distances, it gave wrong longitudes (unacceptable error)

Question 12

What did Kepler eventually realize?

Answer 12

Observations of Mars depend on earth’s orbit
But earth’s orbit = Suns orbit and epicycles in ptolemy’s model
So understanding earth’s orbit is key
Copernicus - all planets except earth have epicycle
Kepler - all planets must be treated with same, unified physical theory

Question 13

What did Kepler do to find earth’s orbit?

Answer 13

Deduced it from tycho’s data (real tricky)
Improved theory of earth’s motion suggested all planets are Ptolemaic with equal eccentric and Equant (foci of ellipse)
This unification conclusively demonstrated superiority of heliocentric over geocentric

Question 14

Kepler’s distance law

Answer 14

Speed proportional to 1/r at ap sides
So time to traverse equal arcs proportional to r
Assumed wrongly that v proportional to 1/r at all points

Question 15

How did Kepler justify his distance law?

Answer 15

Wrong physics
Planets driven around by rotating filaments from sun, like spokes of wheel
Magnetic like solar force spreads out in a plane, diminishes as 1/r
Aristotle v proportional to F proportional to 1/r, made sense
Solar force can only push in circles
Explained radial oscillations as magnetic effect (Gilbert’s magnetic soul)

Question 16

Keplee’s area law

Answer 16

About same as distance law
Used it to simplify calculations but still believed distance law
Computed longitudes of Mars using this area law (and circle + eccentric + Equant) got errors as big as 8’
Realized orbit is NOT a circle

Question 17

What did Kepler do once he realized orbit isn’t a circle

Answer 17

Tried oval
Reverted to epicycles to produce oval shape, cooked up weird magnetic physical mechanism
Tedious calculations so replaced oval with ellipse
Thought area law and ellipse were approximations to simplify calculations
After many more iterations, hit ellipse as true orbit, with sun at 1 focus

Question 18

Other things Kepler did?

Answer 18

Music of the spheres

Question 19

Kepler’s 1st law

Answer 19

1st ellipse law: planets travel on elliptical orbits with the sun at one focus

Question 20

Kepler’s 2nd

Answer 20

Area law: a line drawn from sun to a planet sweeps out equal areas in equal time intervals

Question 21

Astronomy Nova

Answer 21

New astronomy
Kepler published in 1609
Has his 2 laws

Question 22

Kepler’s 3rd law

Answer 22

Period law
The squares of the sidereal orbital periods of the planets are proportional to the cubes of the semi major axis of their orbits

P^2 = Ka^3
For objects orbiting sun, K=1yr^2/AU^3

Question 23

Harmonies Mundi

Answer 23

Harmony of the world
Published by Kepler in 1619
Has his 3rd law

Question 24

Galileo

Answer 24

1564-1642
Why believe earth is in motion rather than sun?
Cop+Kep are theory
Direct experimental evidence from 1700s, but Galileo provided first indirect evidence using newly discovered telescope
First modern scientist

Question 25

Sidereus Nuncius

Answer 25

Starry messenger Galileo published it in 1610 Has his first observations

Question 26

Galileo's observations: moon and sun

Answer 26

Moon is not smooth and perfect -calculated heights of mountains based on shadows and trig -"uneven, rough, crowded with depressions and bulges" Observed sun spots (more imperfections) Challenged idea of separation between heavens and earth, need for perfect uniform circular motion of heavenly objects

Question 27

Galileo's observations: Milky Way

Answer 27

Milky Way consists of numerous faint stars - sketch of Orion's Belt along with a bunch of individual stars invisible to naked eye - stars really ARE a great distance from the sun (resolved parallax issue)

Question 28

Galileo's observations: planets

Answer 28

Planets show as small disks, not points like stars -planets seem to be distinct from stars, may be world's like earth Challenged idea of separation between heavens and earth

Question 29

Galileo's observations: Jupiter

Answer 29

Jupiter has orbiting moons of its own - one objection to heliocentric model is multiple centres of motion, but if Jupiter has moons, there has to be multiple centres - so the rationale for geocentric is undermined

Question 30

Galileo's observations: Venus

Answer 30

Venus has phases like the moon Largest when new, smallest when full Together with kepler's modifications of Copernican model, killed Ptolemaic model

Question 31

Galileo's observations: Neptune

Answer 31

Maybe???? Discovered in 1612, 243 years before official discovery by Le Verrier/Adams/Galle in 1846

Question 32

What can 3rd Kepler's law be used for?

Answer 32

Estimate mass of supermassive black hole at centre of Milky Way