General Astronomy
Historical Attempts to Model the Solar System
The Historical Quest to
Model the Solar System
• The Theme through the Ages has
been:
– What is it?
– How does it work?
– How is it going to affect ME?
• For each different era, there is a
different emphasis
Ancient Astronomy
Babylon
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(Religious-Mystical)
The earth is a flat disk which rises out of the ocean with an
inverted bowl (sky) over it. The stars are fixed into place on the
bowl.
The planets move about against the steady background (major
gods)
Astronomy began as a systematic study when the priestastrologers started to keep a careful watch on the movements of
the gods in order to warn their kings about what the gods might be
planning.
Babylonians are responsible for dividing the sky into 12 equal zones
(zodiac) through which the gods moved.
Calendar was Lunar; a month started at sundown on the day that
the crescent moon was first seen in the west. This leads to 29-30
day months with 12-13 months per year.
Ancient Astronomy
Egypt (Religious-Mystical)
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Even less scientific approach
No system at all; everything is blamed on or due to the gods.
– The Sky is the goddess Nut; Stars are part of her body.
– Horus, the hawk-headed god identified with the Pharaoh, had his left
eye damaged in battle with Set, the god of hostility and chaos. His eye
was later restored by Thoth, the ibis-headed god of the moon. This
loss and restoration, of course, explains the phases of the moon.
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The major contribution was a Solar calendar having 12 months of
30 days each (adjusted at year’s end)
– primary use was agriculture; i.e., when Sirius rose in the east just
before the sun, the Nile would flood.
Ancient Astronomy
Greece
(Mystical-Scientific)
The Greeks inherited volumes of data and observations
from the Egyptians and Babylonians. At a formal level,
at least, astronomy was still linked to religion; e.g., the
sun was Apollo’s chariot.
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Thales of Miletus
(640? - 546BC)
– Thought the earth was flat, but still gave the first
recorded prediction of a solar eclipse.
– Believed the sun to be self-luminous and the moon to shine
by reflected light.
– Taught the Greeks to navigate using the ‘Little Dipper’
(close to the pole at that time).
Greek Astronomy
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Pythagorus
(582 - 500 BC)
– A mystic who believed that mathematics was all that was needed (Numerology).
• For example, since 10 is a ‘perfect’ number, 1+2+3+4 = 10, and he could only
identify 9 heavenly bodies, 5 planets, the sun, moon, earth and fixed-stars,
then there must be a 10th, the ‘counter-earth’ which revolved opposite the
earth - forever out of sight. It was on the other side of the ‘Central fire’
about which everything revolved; including the sun.
• The friction of revolution caused the Music of the Spheres which played
for the gods on Olympus.
• Taught that the Earth was round based on the belief that the sphere is
the perfect shape used by the gods.
• Had some success in developing a relation describing the lengths of the
sides of a right-triangle.
B
A
C
A2 + B2 = C2
Greek Astronomy
• Eudoxus of Cnidus
(4th century BC)
– Geocentric Model
– Modeled solar system as spherical shells each rotating
independently from the center out (Fails to explain variation in
brightness of planets)
Greek Astronomy
Aristotle
(384 - 322 BC)
The greatest of all philosophers! Succeeded in single-handedly setting
back the course of astronomy and geology for centuries.
– Regarded the earth as a sphere; the sun and moon as pure (emphasis
on purity) aether instead of matter
• Aether is a substance whose ‘natural motion’ is circles about the
earth.
• Matter is a substance whose ‘natural motion’ is up and down.
• Since matter can only move if pushed, the moon and planets had
animate souls whose job it was to steer these bodies about the
sky.
– Geocentric Model of Solar System
• Failure to observe parallax
Aristotole's Universe
Greek Astronomy
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Aristarchus of Samos
(300BC)
– Determined the relative distances of the sun and moon from
the earth
• Showed that the sun was much further away than the moon despite
the similar apparent sizes
– Estimated the relative sizes of sun and moon (Timed lunar
eclipses)
– Estimated distance to the sun (using a solar eclipse)
– Created a heliocentric model of the solar system
– In his Sand-Reckoner, Archimedes (d. 212 BCE), discusses how
to express very large numbers. As an example he chooses the
question as to how many grains of sand there are in the cosmos.
And in order to make the problem more difficult, he chooses
not the geocentric cosmos generally accepted at the time, but
the heliocentric cosmos proposed by Aristarchus of Samos (ca.
310-230 BCE), which would have to be many times larger
because of the lack of observable stellar parallax.
Greek Astronomy
Eratosthenes
(276 - 196 BC)
– 1st to determine the Earth's Diameter
He noted that at Syene (Aswan) on June 21
the sun shown directly down a deep well; on
the same date at Alexandria, it hit the wall
of the well at 7 degrees. Knowing the
distance between Syene and
Alexandria was 7/360 of the earth's
circumference he could calculate
the diameter.
Greek Astronomy
Hipparchus
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(150 BC)
Created the first formal observatory
Devised a system of Magnitudes
Created the first Star Catalog
Determined that the Earth was precessing
Invented trigonometry
Geocentric Model
– Wanted perfect circles with uniform circular motion, so
he invented epicycles
Geocentric Model
Epicycle
Earth
Deferent
Geocentric Models
Why were Aristotle, Hipparcus and others insisting
on the Earth being at the center of the Solar
system?
1. Parallax
It was clear to them that if the earth was orbiting the Sun,
the stars should exhibit parallax. However, the stars
are much farther away then they imagined and the
parallax much too small to be seen with the naked eye.
2. If the earth were moving, one should sense the
motion.
3. How would the moon stay in orbit if the earth
was moving away from it?
Geocentric Models
What observations must be explained
by the model?
• Retrograde motion
• Variation of brightness
• Mercury and Venus never stray too
far from the Sun (28° and 48 °
respectively)
Motions of Inner Planets
Motions of Inner Planets
Motions of Outer Planets
The Retrograde motion of the planets presents a challenge for the
geocentric model.
The Geocentric Model: Convolutions
Greek astronomers invented the epicycle and
deferent scheme to account for retrograde motion.
Greek Astronomy
Ptolemy
• Adapted and improved Hipparchus'
geocentric model to account for
discrepancies found by improved
observations.
• Produced the Almagest, which both
summarized the state of
Astronomy and extended it.
• Used eccentrics and equants to
refine the model
The Ptolemaic Universe
Ptolemy's geocentric (earth-centered) model of the universe.
Middle Ages
Europe
• The earth is a flat disk which rises out of
the ocean with an inverted bowl (sky) over
it. The stars are fixed into place on the
bowl.
• In 1200 AD, Aphonso X of Castile had the
planetary position tables calculated. In
noting the ~88 epicycles, equants and
eccentrics necessary, is reported to have
stated " Had I been present at the
Creation, I could have offered excellent
advice…"
Islam
Astronomy kept alive due to
need to know the direction of
Mecca
Carried forward Greek
astronomy
Developed new Mathematics,
aided calculations
Great observers - Many star
names are Arabic.
Painting, 1581
Nicolas Copernicus (1473 - 1543 AD)
• Chiefly a mathematician, he attempted to summarize
all the existing models
• Developed the idea of relative motion. This having
been done, he realized that the sun moving about the
earth and the earth moving about the sun results in
the same observations.
• Developed a new model of the solar system in a book,
De Revolutionibus
– Generally considered a 'crank'
Nicolas Copernicus
• Had life-long association with the church - was
a Canon.
• The church did not immediately view his model
as radical.
• His model was simply a hypothesis. It was
simpler mathematically and easier to use.
• De Revolutionibus was not forbidden by the
church until 73 years after publication.
• It became forbidden in 1616 after word of
Galileo was getting around.
Copernicus proposed a
heliocentric (sun-centered)
model for the universe.
Opponents argued, in
addition to earlier parallax
and other items, that if
earth were revolving about
its axis it would 'fly apart'
His answer was that
the Celestial spheres
would do the same,
even faster since they
are larger.
Heliocentric Hypothesis
• There were some preconceptions:
– The Universe is spherical
– All heavenly bodies must move in combinations of perfect
circles
– All heavenly bodies must move in uniform circular motion
• He placed them in order:
– Sun, Mercury, Venus, Earth (and Moon), Mars, Jupiter
and Saturn.
– He deduced that the nearer the planet to the sun, the
faster its motion.
– He worked out the approximate scale of the solar system
– He can account for the three observations we noted
earlier in a much simpler manner - without epicycles
Heliocentric Hypothesis
Looking at the Inner
Planets from Earth
At any point in Earth's
orbit, the maximum
elongation of Mercury
is limited - We can
never see it too far
from the Sun
The same effect for Venus, only the elongation is larger
Heliocentric Hypothesis
Variation in Brightness
occurs when planets are
1. Closer together and
2. are better illuminated
by the Sun
Heliocentric Hypothesis
Retrograde Motion is now easily seen without the
use of epicycles:
D
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B
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C
B
A
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Observation
Tycho Brahe (1546 - 1601 AD)
Tycho Brahe's contributions to astronomy were enormous.
•He not only designed and built instruments, he also calibrated them and checked
their accuracy periodically.
•He thus revolutionized astronomical instrumentation.
•He also changed observational practice profoundly.
•Whereas earlier astronomers had been content to observe the positions of
planets and the Moon at certain important points of their orbits (e.g.,
opposition, quadrature), Tycho and his cast of assistants observed these
bodies throughout their orbits. As a result, a number of orbital anomalies
never before noticed were made explicit by Tycho. Without these complete
series of observations of unprecedented accuracy, Kepler could not have
discovered that planets move in elliptical orbits.
•Tycho was also the first astronomer to make corrections for atmospheric
refraction. In general, whereas previous astronomers made observations accurate
to perhaps 15 arc minutes, those of Tycho were accurate to perhaps 2 arc
minutes, and it has been shown that his best observations were accurate to about
half an arc minute.
Instruments
Tycho Brahe observed a supernova, bright enough to
see in the daytime. He attempted to use parallax of a
supernova to test the Copernican model.
Results of the parallax experiment
No parallax observed
Stars either very far away, or not moving at all
Led him to reject the heliocentric model
Actual parallaxes are 100 times smaller than he could
detect
Tycho's Model
• Hybrid model – combined geocentric and
heliocentric
– Earth in center; Sun orbits Earth
– Other planets orbit the Sun (and so, also
the Earth)
– Tychonic system adopted by Catholic Church
for many years as official Astronomical
conception of universe
Tycho's Model
Tycho Brahe's model is a
combination of the
Geocentric and
Heliocentric.
The Earth is at the center
about which orbit the Sun
and Moon. All other
planets (and Tycho's
Comet) orbit the Sun
and Theory
Johannes Kepler (1571 - 1630 AD)
Kepler worked on a number of
projects. He was basically a
mathematician. As can be seen
from his model of the spacing of
the planets:
Spacing was according to some
mystical use of regular
polygons
Kepler
• Kepler was hired by Brahe (by direction of Brahe's patron)
• He was assigned the analysis of the orbit of Mars.
– This was the most difficult of all the planetary orbits
– Many feel that Brahe assigned this one to Kepler because he
was afraid that this bright, young man would upstage him.
• The choice of Mars was fortunate. While difficult it leads directly
to Kepler's Laws of Planetary Motion
• When Brahe died, Kepler had access to volumes of measurements –
20 years worth – for analysis
Kepler's Laws
First Law:
The orbits of the planets are ellipses
with the Sun at one of the foci.
Kepler's Laws
Second Law:
Equal Areas of the orbit are swept
out in equal intervals of time
one month
difference
one month
difference
Kepler's Laws
Third Law:
The square of the period is equal to
the cube of the average distance
P2 = a3
This assumes units of 1 earth year for period
and 1 Astronomical Unit (AU) for average distance
Searching For The
Underlying Laws
Galileo Galilei
“I do not feel obliged to
believe that the same
god who has endowed us
with sense, reason and
intellect has intended us to
forgo their use.” - Galileo
• Foundations of experimental
physics
• Falling bodies
• Discovered:
 Mountains, 'Seas' and Craters
on the Moon
 Sunspots
 Moons of Jupiter
 Phases of Venus
Galileo’s telescope revealed
that Jupiter had moons which
orbited Jupiter instead of
Earth.
Gasp! Not all heavenly bodies
orbited about the Earth!
telescopic
of Venus
the Ptolemaic
model.
If theThe
system
wasappearance
geocentric,
Venusin would
look like
this:
The telescopic appearance of Venus in the Copernican model.
Galileo saw Venus like this, a heliocentric system:
Searching For The Underlying Laws
Sir Issac Newton
Newton's Laws of Motion
1.
An object in a state of rest or
uniform motion will remain in that
state unless acted on by an external
force
Inertial mass
2.
F=m a
3.
Every action has an equal and
opposite reaction
Newton’s 1st Law
At rest – until acted on!
Uniform motion – until acted on!
Newton’s Second Law
• F=ma
• “Mass resists acceleration”
Newton’s Third Law
Forces have equal strength, but accelerations may differ:
MAN’S FORCE ON BOAT
FORCE
BOAT’S FORCE ON MAN
FORCE
MORE MASS,
LESS
ACCELERATION
Searching For The Underlying Laws
Newton's Law of Universal Gravitation
Gravitational mass
F=
GmM
r2
Mass
versus
Weight
• Mass is a measure of the total amount
of material in the object
Remains the same everywhere
• Weight is the force with which an
object is
pulled down while on the ground (due to
gravity’s attraction)
Changes depending on the body you are
standing on
Searching For The Underlying Laws
Newton's Form of Kepler's Third Law
(m + M) P2 = a3
Kepler’s version assumed Solar Mass as a unit since
he used Mars’ measurements
M=1
And since Mars was so small compared to the Sun
m=0
P2 = a3
Back to a basic question…
We've discovered quite a few 'Laws' and
have gathered lots of data.
So how do we prove the Earth is rotating
about its axis?
Any ideas?
Foucault's Pendulum
Consider a pendulum centered
over the north pole. Assuming
it doesn’t slow down and stop,
it will trace out a complete
circle in 24 hours as the Earth
turns beneath it.
Back to another question…
Now how do we prove the Earth is
rotating about the Sun?
Any ideas?
Time out for a Challenge
Let's suppose there is a heavy rain, but no
wind. I'll give you a long, perhaps 8 foot
cardboard tube about 2 inches in diameter.
I want you to run from one side of the
parking lot and back and get a single
raindrop to pass completely down the tube
without striking the side.
How would you do it?
The Aberration of Starlight
• Bradley determined that our
challenge was the same as
looking at a star in a telescope.
Earth is 'running' around and
the light is traveling down a
long tube without striking the
sides. So do we have to tilt
the telescope slightly as Earth
moves?
• Yes – This slight, but
measurable angle proves that
the Earth is orbiting the Sun.
Parallax (again)
• In 1838, Bessel announced that 61 Cygni had a parallax
of 0.314 arcseconds; which, given the diameter of the
Earth's orbit, indicated that the star was about 3
parsecs (9.8 light years) away.
• Again showing that the Earth orbits the sun