1. Kepler

2. Geocentric vs Heliocentric: How do we know?
Is the Earth or the Sun the center of the solar system?
How do we decide between these two theories?
Invoke the scientific method:
both theories make (different) predictions
NOT about planetary motion BUT phases of Venus
Compare to observations
Decide which theory explains data

3. Phases of Venus
Heliocentric
Geocentric

4. Aristotle easily falsified by experiment – but emphasis was not on observation
How people thought about projectiles up until the Renaissance: the cannonball moves in almost a straight line, until it runs out of impetus and falls on the house. WRONG!

5. Galileo gets it right
Strobe photograph
Galileo Galilei’s notebook
In fact, all projectiles fall in exactly the same way, regardless of what they are or weigh!

6. Tycho Brahe – The Data Taker
Key question: Where are things?
Catalogued positions of planets in Uraniborg and Prague
Working without telescope
Data ten times as accurate as before
Died at banquet binge drinking
TYCHO BRAHE (Danish)
collects detailed and accurate (1-2 arcmin accuracy) observations of stellar and planetary positions over a period of 20 years
shows that comets and novas are extralunar contra Aristotle; comets pass through planetary spheres
His research may have cost 5-10% of the total GNP of Denmark at that time!
JOHANNES KEPLER (German) reduces Tycho's data and by triangulation determines the orbits of the planets, including Earth's. The "baseline" is given by the Earth moving in its orbit.
Not a simple problem, since the orbit of the Earth was not known beforehand, and the other planets don't sit still while the Earth is moving around!
Tycho Brahe (1546–1601)

7. Tycho Brahe Tycho Brahe observing
collects detailed and accurate (1-2’ accuracy) observations of stellar and planetary positions over a period of 20 years
His research costed 5-10% of Danish GNP
shows that comets and novas are extralunar contrary to Aristotle
Shows that stars can change
(Supernova of 1572)
Proves that comets are superlunar
TYCHO BRAHE (Danish)
collects detailed and accurate (1-2 arcmin accuracy) observations of stellar and planetary positions over a period of 20 years
shows that comets and novas are extralunar contra Aristotle; comets pass through planetary spheres
His research may have cost 5-10% of the total GNP of Denmark at that time!
JOHANNES KEPLER (German) reduces Tycho's data and by triangulation determines the orbits of the planets, including Earth's. The "baseline" is given by the Earth moving in its orbit.
Not a simple problem, since the orbit of the Earth was not known beforehand, and the other planets don't sit still while the Earth is moving around!
Tycho Brahe observing

8. Measuring distances with the Parallax
The closer an object is, the more relocated it appears with respect to the fixed stars from different points on Earth

9. Johannes Kepler–The Phenomenologist
Key question:
How are things happening?
Major Works:
Harmonices Mundi (1619)
Rudolphian Tables (1612)
Astronomia Nova
Dioptrice
Johannes Kepler (1571–1630)

10. Kepler’s Beginnings Astrologer and Mystic
Tried to find “music in the skies”
Tried to explain distances of the 6 known planets by
spheres resting on the
5 mathematical bodies
 pre-scientific

11. Kepler’s First Law: Orbit Shape
The orbits of the planets are ellipses, with the Sun at one focus
Orbits turn out not to be circles nor eccentric circles but ellipses (which can be made with string and thumbtacks as shown)
The sun is at one focus (not the center).
A foreshortened circle 11

12. a = “semimajor axis”; e = “eccentricity”
Ellipses
a = “semimajor axis”; e = “eccentricity”
Orbits of most planets are nearly circular and have small e (Mercury and Pluto most notable exceptions) 12

13. Conic Sections
From Halley’s book (1710)

14. Kepler’s Second Law: Motion in Time
An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal times
conservation of angular momentum: same effect makes skaters speed up when they draw in their arms 14

15. Kepler’s Third Law: Relating Orbits
The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis:
P 2  a Jupiter: 53 / 122 = 125/144 ~ 1
a P
Planet Semi-Major Axis Orbital Period Eccentricity ____ P2/a3
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
(A.U.) (Earth years)
more distant planets move more slowly and have longer "years".
Kepler can determine ratio of sizes of the planets' orbits but not the actual sizes; this is because he uses orbit of Earth as baseline for triangulation. If we know the size of one planet's orbit, we can find the rest.
Earth's orbit (1 AU)=93 million mi=150 million km=8 light minutes. Nowadays determined by radar ("radio detection and ranging") bounced off Venus. 15