The Discovery of Gravity
The Legacy of Greek Astronomy
• Rejection of supernatural explanations
• Development of mathematics, logic
• Large body of accurate observations
• Understanding of Earth shape & size, lunar phases,
eclipses
• Ptolemy’s model reproduces Solar System motions well
Ptolemy's geocentric model
"The latest thing"
130 AD
Ptolemy's geocentric model
"The latest thing"
130 AD
1500 AD
Ptolemy's geocentric model
"The latest thing"
130 AD
1500 AD
1300 years with ~0
scientific progress
Timeline of the [Second] Scientific Revolution
Timeline of the [Second] Scientific Revolution
Observers
Interpreters (mathematicians, theoreticians)
Copernicus (1473-1543)
Copernicus’ Study
Copernican Heliocentric Model
from“De Revolutionibus”
Earth - Moon
Sun
Copernicus' Heliocentric Universe:
Structure
• The Sun is stationary at the center of the
solar system
• Earth is a planet, like the 5 others known
– Not at a central location
– Properties of matter universal? Revived atomism?
– "Gravity" is not a product of Earth's location in the universe
• Orbits of planets in order from Sun: Mercury, Venus,
Earth, Mars, Jupiter, Saturn
Copernicus' Heliocentric Universe:
Motions
• Introduces concept of relative motion (described in Lec. 4)
– Observed "apparent" motions are affected by motion of Earth
– Earth has two motions: spin and orbital motion around Sun
• Earth spins on its polar axis, producing the "diurnal" motion
– Universe is stationary; Earth need not be at center
– Universe can be very large (even infinite)
• Planets orbit the Sun in the same direction
– Orbital speed decreases with orbit size
• Earth's orbital motion produces the apparent "retrograde"
loops of other planets on the sky
– We are seeing the "reflex" of Earth's motion
Copernican model: animation
Puzzlah # 23
How does the size of the "retrograde" loop of Saturn
as seen on the sky compare to that of Mars?
(A) Larger
(B) Smaller
(C) The same
Puzzlah # 23
How does the size of the "retrograde" loop of Saturn
as seen on the sky compare to that of Mars?
(A) Larger
(B) Smaller
(C) The same
The “Copernican Principle”
Scientific arguments should assume that
human beings have a typical, rather than
special, perspective on the universe.
Is now known to be correct on three cosmic
scales:
1. Solar system
2. Galactic
3. Extra-galactic
The Parallax Puzzle
• If Earth orbits the Sun, as in the Copernican model,
there must be a parallax effect in the positions of
nearby stars relative to more distant ones
Triangulation to Determine Distances
Stellar Triangulation: “Parallax”
Use radius of Earth’s orbit as a baseline to
determine stellar distances by triangulation.
Measure shift in position of nearby star against
positions of distant stars over several months.
• Parallax Java Animation
The Parallax Puzzle
• If Earth orbits the Sun, there must be a parallax effect
in the positions of nearby stars relative to more
distant ones
• No parallax effect was detectable to the naked eye
– The largest stellar parallaxes are about 1 arc-sec and were not
even measured with telescopes until 1838.
• Therefore, either:
– Stars are VERY DISTANT (> 2,000 AU)
– OR: Earth does NOT orbit the Sun
• Greeks, Copernicus, Tycho --- all were aware of this
difficulty for a heliocentric interpretation
– (Most) Greeks and Tycho: Earth does not orbit the Sun
– Copernicans: stars are very distant
Thomas Digges’Copernican Universe (1576)
Thomas Digges’Copernican Universe (1576)
Stars extending
to infinity
"This orb of stars fixed infinitely up extendeth itself in
altitude spherically, and therefore immovable, the
palace of felicity garnished with perpetual shining
glorious lights innumerable, far excelling our sun both
in quantity and quality, the very court of celestial
angels, devoid of grief and replenished with perfect
endless joy, the habitacle for the elect."
--- Thomas Digges (1576)
Tycho Brahe
(1546-1601)
Tycho’s Nose
Tycho’s Supernova,
1572
Parallax distance:
beyond Saturn
Comet of 1577
Parallax distance:
beyond Moon
Tycho’s Parallax Estimate of Distance for
Comet of 1577
Tycho's profound revelation:
The universe beyond the Moon is not
perfect and changeless
Tycho's profound revelation:
The universe beyond the Moon is not
perfect and changeless
Astronomy suddenly became a lot more
interesting than it was before
Uraniborg,
Tycho's Observatory
Tycho instrument:
“equitorial armillary”
Angular precision possible:
about 1 minute of arc
Tycho’s “skysphere”
(6-foot diameter)
Tycho Observing
Produced a huge volume of
precise, continuous observations
of planetary motions
Tycho's Geocentric Universe
Earth stationary at center, but all other planets orbit the Sun.
Rationale for geocentrism? Tycho could not measure stellar parallax.
Puzzlah #24
If the Sun had been situated in the dense center of our
Galaxy rather than on the outskirts, Tycho would
probably have accepted the Copernican model because
he could have measured the parallaxes of other stars.
(A) True
(B) False
Puzzlah #24
If the Sun had been situated in the dense center of our
Galaxy rather than on the outskirts, Tycho would
probably have accepted the Copernican model because
he could have measured the parallaxes of other stars.
(A) True
(B) False
Literary footnote
Tycho's family:
a source for
Shakespeare?
Literary footnote
Tycho's family:
a source for
Shakespeare?
Galileo (1564-1642)
Galileo: a "triple threat"
An experimental physicist
An observational astronomer
A successful popularizer of science
Galileo's Falling Body Experiments
Predecessors to Newton's Laws of Motion
Experimental Results
Acceleration under gravity:
motion is the same for all
objects, independent of mass;
downward velocity increases
in proportion to time
Galileo Telescopes (~ 1 inch aperture)
Galileo: Thousands of “New” Stars
Modern Image of Milky Way
Galileo:
Sunspots
The sun is not
a perfect sphere
Galileo:
Surface Features
on Moon
The Moon is not a
perfect sphere
Lunar mountains in
a modern photograph
Galileo:
Phases of
Venus
(over 4
months)
The phases of Venus prove that Venus orbits the Sun,
contrary to Ptolemy’s model
Gibbous
Crescent only
Crescent
Galileo’s Notes
on the Moons of
Jupiter
The 4 “Galilean” moons orbiting Jupiter prove that
there can be a “center of motion” other than the Earth
Galileo's unprecedented discoveries
were a powerful argument for
EMPIRICISM
"You must read the book of Nature...In
other words, observe and do experiments.
This is against the medieval idea of
scholasticism---that all wisdom and
knowledge are best found in ancient
authorities." --- Galileo
Kepler
(1571-1630)
Turbulent times: The Sack of Magdeburg (1631) during the Thirty Years' War
The 5 Perfect Polyhedra (“Platonic Solids”)
Kepler: Is the spacing of planetary orbits determined
by inscribed Platonic solids?
Kepler’s Greatest
Methodological Contribution
Models (hypotheses) must agree with the observations
within the observational uncertainty (or “error”).
This is the fundamental basis of
modern empirical science.
Page of calculations
from Kepler’s
notebooks
Eight years of work
to resolve an 8'
discrepancy in the
orbit of Mars.
(8’ is 1/2700 of a full circle)
Kepler’s Three (Empirical)
“Laws” of Planetary Motion
1. Planetary orbits are ellipses with the Sun at one focus
2. A line joining a planet as it moves to the Sun sweeps out
equal areas in equal times.
–
A given planet moves faster in its orbit when nearer the Sun
3. The squares of the orbital periods of different planets are
proportional to the cubes of the orbital sizes
–
Velocities of planets in larger orbits are slower
Geometry of an Ellipse
Kepler’s Second Law
Kepler’s Third Law:
Orbital Speed Depends on Orbit Size
Vel
P2
A3
A
Puzzlah #32
You are planning a mission to Mars, and you want
your spacecraft to encounter Mars when the planet
is moving the least rapidly in its orbit. You therefore
arrange for the encounter to occur at ...
(A)
(B)
(C)
(D)
Aphelion (farthest from Sun)
Perihelion (nearest Sun)
Halfway between aphelion & perihelion
It doesn't matter, since Mars always moves
at the same speed.
Puzzlah #32
You are planning a mission to Mars, and you want
your spacecraft to encounter Mars when the planet
is moving the least rapidly in its orbit. You therefore
arrange for the encounter to occur at ...
(A)
(B)
(C)
(D)
Aphelion (farthest from Sun)
Perihelion (nearest Sun)
Halfway between aphelion & perihelion
It doesn't matter, since Mars always moves
at the same speed.
UMd Solar System Visualizer
K #2
K #1
K #3
The Sun is the key: it
must exert some kind of
FORCE on the planets
to control their orbital
motions.
"There will certainly be no lack of human pioneers when we
have mastered the art of [space] flight....Let us create
vessels and sails adjusted to the heavenly ether, and there
will be plenty of people unafraid of the empty wastes. In the
meantime we shall prepare, for the brave sky-travelers,
maps of the celestial bodies."
---- Johannes Kepler (1610)
"There will certainly be no lack of human pioneers when we
have mastered the art of [space] flight....Let us create
vessels and sails adjusted to the heavenly ether, and there
will be plenty of people unafraid of the empty wastes. In the
meantime we shall prepare, for the brave sky-travelers,
maps of the celestial bodies."
---- Johannes Kepler (1610)
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