Summary
Models of our Solar System (Ch. 4)
• Geocentric Model
• Heliocentric Model
Lunar
Eclipse
Yesterday
morning!
Strange Motions in the Sky
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The motions of planets are not easy to explain
Planets may take years to return to the same part of the sky.
Some planets reverse their direction of motion
This is called retrograde motion.
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Ancient people struggled to explain these motions
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Retrograde Motion of Mars
Astronomical Models of Planetary Motion
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To understand this motion, we need to make a model.
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Aristotle devised one of the earliest models of the Solar System
(c. 350 BC)
Earth was at the center of the Solar System
So the model was Geocentric
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The Sun and planets moved around
Earth, each on a different sphere
A “Prime Mover” controlled the stars’
motion.
Astronomy of Ancient Greece
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Greek scientist Ptolemy worked at the Great Library of
Alexandria in Egypt (~140 AD)
His research included astronomy, astrology, geography & music.
Ptolemy came up with an improved geocentric model.
In Ptolemy’s model, the planets traveled along small circles that
move on larger circles.
This can explain retrograde motion.
Ptolomy’s Geocentric model
Ptolemy’s Model
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A planet orbits the Earth on a small circle, called an epicycle,
The epicycle moves along a large circle, called a deferent
Since circles were thought to be “perfect” shapes, it seemed
natural that planets should follow circles in their motion.
anim
The Geocentric Model
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Ptolemy’s views were published in a book known as the
Almagest
Because it could explain retrograde motion, his theory
was very influential in the study of astronomy for a long
time.
The Geocentric Model was not challenged for 1,600
years!
Copernicus’ Heliocentric theory
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We credit Nicolaus Copernicus, a 16th-century Polish astronomer,
with our modern view of the Solar System
Copernicus suggested a heliocentric theory
He proposed the Sun was at the center of the Solar System.
His theory also explained retrograde motion.
“I began to be annoyed that the movements of
the world machine … were not
understood with greater certainty by the
philosophers, who otherwise examined so
precisely the most insignificant trifles of the world.”
Copernicus, Book on the Revolutions, 1543
“… it is just like someone taking from various
places hands, feet, a head, and other pieces, each
very well depicted, but not for the representation
of a single person. In forcing these fragments
together, they created a monster rather than
a man.”
Copernicus, Book on the Revolutions, 1543
The Heliocentric System of Copernicus
heliocentric system
needs no epicycles!
retrograde motion is a
natural consequence
of the relative speeds
of the different planets
(e.g., Earth orbiting
faster than Mars)
anim.
Copernicus’ Heliocentric Theory
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Copernicus’ new theory allowed him to calculate:
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The relative distances to the planets.
The length of time the planets take to orbit the
Sun
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This let him predict the next appearances of
planets in the sky.
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These predictions proved correct, lending support
to Copernicus Heliocentric Model.
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However, Copernicus’ model was no more accurate
than the Ptolemaic model.
A Heretical Idea?
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Copernicus’ Heliocentric theory caused problems with the Church.
The Church had accepted Aristotle & Ptolemy’s geocentric universe.
It agreed with the Christian notion of heaven as a perfect place.
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To question this model was to question the Church’s authority.
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Copernicus died before the full effects of his model were felt
However, astronomers continued to challenge the Church, using their
observations.
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Galileo
Galileo Galilei (1564-1642) was an Italian scientist who studied
many fields.
He is famous for dropping cannonballs from the Leaning Tower of
Pisa
He obtained the first observations to
confirm the Heliocentric Model
More Evidence for the Copernican Model
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Galileo was the first person to use a telescope for
astronomy.
Several of his observations supported the Heliocentric
model of Copernicus:
He discovered moons orbiting Jupiter (not the Earth)
Galileo Galilei
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Galileo also reported seeing crescent and
gibbous phases on Venus
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Gibbous phases are only possible if Venus is
on the other side of the Sun from us.
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This could not happen in the Geocentric model
of the Universe.
Geocentric model
Of Ptolemy
Theory: Venus is always
between the Sun and Earth
Prediction: Venus will always
be seen in crescent phase
Theory: Venus sometimes
goes behind the Sun…
Prediction: Venus will
sometimes be seen in
gibbous phase.
Observation: Venus
does show gibbous
phase when seen with
a telescope
Galileo Challenges the Geocentric Model
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Heliocentric model challenged beliefs held for 2000 years.
The Church felt threatened by this.
Galileo was arrested and tried.
He was not allowed to advocate the Heliocentric Model.
He had reason to fear: Giordano Bruno, another advocate of
the Heliocentric Model, was tried by The Inquisition.
Bruno was burned at the stake for heresy!
However word of Galileo’s discoveries spread….
Tycho Brahe
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Tycho Brahe (1546-1601) was a
Danish nobleman who built his own
observatory on an island.
Has a child, he had witnessed a Solar
Eclipse
He was so impressed that eclipses
could be predicted, that he dedicated
his life to astronomy.
Tycho Brahe
Tycho made the most precise observations
of the planets to date …without using a telescope.
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During his life, Tycho was reluctant to share his precise data.
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He also had a wild lifestyle, and lost his nose in a duel.
He attended many royal parties
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Perhaps one too many…. He died after eating and drinking too much at a
party….
Johannes Kepler
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After Tycho died, his assistant, Johannes Kepler,
took his place.
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Kepler studied Tycho’s precise observations of the
planets
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He noticed patterns in their motion never seen before.
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His first model for the planets involved geometric shapes
At first, Kepler thought the orbits of the planets had the same proportions as
the “5 Perfect Solids” of geometry.
He worked on this idea for years, but finally admitted it was a failure.
Johannes Kepler
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However, Kepler did not give up.
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He found that the planets’ motions could be
explained if he gave up the idea of circular orbits.
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In time he discovered that all planets follow the
same three rules…..
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Kepler’s Laws of Planetary Motion
Ellipse Shapes
Circle
How to draw an Ellipse
Kepler’s First Law
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The major axis of an ellipse is the line within the ellipse
that passes through the two foci.
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The minor axis is perpendicular to the major axis.
The semimajor axis is half the length of the major
axis, and the semiminor axis is half the length of the
minor axis.
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In astronomy, the semimajor
axis is designated: “a”
a
Kepler’s 2nd Law: Equal Areas in Equal times
Suppose a planet moves from
points A to B in a fixed time.
In the same amount of time it
moves from A’ to B’
These two wedges have the
Same Area!