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9/7/06 1
Lecture 3 :
Cosmology of the Scientific
Revolution
Tycho Brahe
Kepler
Galileo
Newton
http://www.physics.fsu.edu/users/Lind/AST1002/ 9/7/06 2
Tycho Brahe (1546-1601)
- Flamboyant and to science tyrranical aristocrat, but devoted
- (^) DenmarkLived and observed on island off the coast of
- Last of the great “naked eye” observers
- Made planetary observations much more accurate than any previous
- Observed 1572 “new star” (Tycho’s supernova) in
- Demonstrated that comet was beyond Moon orbit ’s
- From parallax observations of new star, comet:
- knew they were not in Earth’s atmosphere
- evidence that heavens were not immutable 9/7/06 3
Tycho’s cosmological model
Tycho used parallax observations to explore heliocentric model:
If Earth moves, then parallax of stars should be observable Tycho could not detect any significant parallax; he concluded Earth is stationary In fact, stellar parallax is 100× too small for naked-eye observation to measure; largest values are about 1 arcsecond=(1/3600)°
Tycho settled on combined geo/helio-centric model
Sun orbits Earth; all other planets orbit Sun http://clyde.as.utexas.edu 9/7/06 4
Johannes Kepler (1571-1630)
Born in Germany; originally planned to be ordained as Lutheran minister Convinced God made the Universe according to a mathematical plan; saw his Christian duty as understanding works God had created Studied mathematics; published in 1596 his Mystery of the Cosmos proposing that planetary orbits lie in spheres nested within series of the Platonic solids (wrong!) a Was hired as Tycho Brahe’s assistant in Prague; his job was to make sense of Brahe’s extremely accurate observations of Mars Kepler became Imperial Mathematician after Brahe’s death (1601) Kepler’s “war with Mars” amounted to a thousand sheets of arithmetic; resulted in publishing Kepler’s “First Law” and “Second Law” in 1609 as part of his New Astronomy Kepler as part of his’s “Third Law Harmony of the World ” was published in 1619 9/7/06 5
Kepler’s first law
Planets move around the Sun in
ellipses, with the Sun at one focus.
perihelion aphelion^ 9/7/06 6
Kepler’s second law
The line connecting the
Sun and a given planet
sweeps out equal areas in
equal times.
Therefore, planets move
faster when they are nearer
the Sun
Consequence of angular
momentum conservation. http://home.cvc.org/science/kepler.gif
9/7/06 7 Kepler’s second law with high- and low- eccentricity orbits 9/7/06 8
Kepler’s third law
The square of the period P of the orbit is
proportional to the cube of the semi-major
axis R
Period ( P ) = time it takes for planet to
complete one orbit
Semi-major axis ( R ) = half of the length of
the “long” (i.e. major) axis of the ellipse.
P^2 =constant × R^3
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For the Earth, we know that:
P =1 year =3× 107 seconds R =150 million km (1 Astronomical Unit, A.U.)
Kepler’s 3 rd^ law says that, for other planets,
(^23)
!!^ =
AU
R
yr
P
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Solar system orbits
Inner planets Outer planets + http://www.rasnz.org.nz/SolarSys/Orbits06.htm Note the low eccentricities! 9/7/06 11
Kepler in perspective
Based on Tycho Brahe’s accurate observations, Kepler calculated and thought his way to a major breakthrough in cosmology Kepler’s three laws of planetary motion
Represented a very simple (and correct!) model of the solar
system
Swept away thousands of years of prejudice – and his own
previous pet theory!
Were driven fundamentally by the data , including Tycho’s
error estimates
Unlike previous models which quantified only what was observed already, Kepler’s Laws had predictive power, consistent with modern idea of a meaningful scientific theory 9/7/06 12
Galileo Galilei
Born in Pisa; worked as professor of mathematics Built one of the first telescopes in 1609 Published “The Starry Messenger” with first telescopic discoveries in 1610 Telescopic observations:
Saw craters and mountains on the Moon
Realized sunspots were on surface, not foreground; rotated
with Sun
Identified four satellites of Jupiter (“Galilean moons”)
Saw rings of Saturn
Resolved the diffuse Milky Way into many faint stars
Observed phases of Venus including gibbous and full
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Isaac Newton (1643-1727)
Attended Cambridge University, originally intending
to study law, but reading Kepler, Galileo, Descartes
Began to study mathematics in 1663
While Cambridge was closed due to plague (1665-
1667), Newton went home and
began to work out foundations of calculus realized (contrary to Aristotle) that white light is not a single entity, but composed of many colors began to formulate laws of motion and law of gravity
Became professor of mathematics starting in 1669
(age 27!)
Worked in optics, publishing “Opticks” (1704)
invented reflecting telescope showed color spectrum from prism recombines into white light with a second prism analyzed diffraction phenomenon Isaac Newton in 1689, by Sir Godfrey Kneller.
Father of
modern
physics and
cosmology
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Newton’s history, cont.
In 1687, published Philosophiae naturalis principia mathematica, or “Principia” publication was prompted (and paid for) by Halley partly in response to claim by Hooke that he could prove gravity obeyed inverse-square law included proof that inverse square law produces ellipses generalized Sun all matter attracts all other matter with a force proportional to the product of ’s gravity law to universe law of gravitation: their masses and inversely proportional to the square of the distance between them many other applications, including tides, precession, etc. laid out general physics of mechanics -- laws of motion showed that Kepler’s laws follow from more fundamental laws
The Principia is recognized as the greatest scientific book ever
written!
Retired from research in 1693, becoming active in politics and
government
9/7/06 21
Next time…
Newton’s laws
Laws of motion
Law of universal gravitation
start reading Chapter 3 of text
