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The Motions
of the
Planets
Historically Speaking
• Until the sixteenth century all astronomy was
done with the naked eye
• The Greeks knew that the Earth was round
because of the shadows on the Moon during
lunar eclipses
• The Greeks worked out reasonable values for
the sizes of the Earth and the Moon, as well as
their separation.
• They also knew that the Sun was much farther
away from the Earth than the Moon.
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The Geocentric Universe
• The Greeks got
one thing wrong
– They put the Earth
at the center of the
Universe
• Some Greeks got
it right but not the
“important” ones
The Heliocentric Universe
• This was the competing theory!
– Based on the Sun being the center of the
Universe
• The dispute was not just about whether
the Earth goes around the Sun or the Sun
goes around the Earth.
– The key difference is whether the other
planets go around the Earth or around the
Sun.
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• Both models focused on the planets
– Greek for “wanderers”
• They knew of five planets plus the Sun
and Moon
– Mercury
– Venus
– Mars
– Jupiter
– Saturn
• They did not think of the Earth as a
planet
But....Which Theory Wins?
• They key was to accurately predict the
future positions of the planets
• The critical motions to explain in order to
make these predictions were:
– The side to side motion of Mercury and Venus
always near the Sun
– The retrograde motion of Mars, Jupiter &
Saturn
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Mercury and Venus
Retrograde Motion
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Ptolemy
• Greek, AD 85 – 165
• He developed a very
sophisticated geocentric
theory based on a series of
more than 80 circles
• Circles were intellectually
satisfying to Greeks, so they
assumed that nature was
based on circles.
• Ptolemy's theory gave very
nearly correct answers. His
equations and tables were
used for over 1300 years to
predict positions of planets.
Ptolemy’s Universe
All together they looked like........
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Copernicus
• Polish, 1473 – 1543
• Recognized as the driving force behind
the acceptance of the heliocentric
theory
• The realization toward the end of the
sixteenth century that Earth is not at
the center of the Universe is referred to
as the Copernican Revolution.
• Copernicus' picture is much simpler
– The Earth behaves in much the same way
as the other planets do.
• But the theory is still based on perfect
circles and did not make predictions
any better than Ptolemy's theory.
Copernicus’ Universe
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Much simpler on the eyes than
Ptolemy’s Universe!
Mercury and Venus
• Copernicus’
Universe indicated
that Mercury and
Venus were simply
the first two planets
nearest the Sun
thus explaining their
motion
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Retrograde Motion
• This too had an explanation in Copernicus’ Universe
Retrograde
Motion Again
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Tycho Brahe
• Danish, 1546 – 1601
• He collected superb data without
telescopes.
• His data involved all angle
measurements
• He did not support Copernicus
but that does not diminish him as
a collector of data
• He also had a student apprentice
Johannes Kepler
• German, 1571 – 1630
• Kepler was a pupil of Tycho Brahe.
• He inherited and analyzed Tycho's
observations in order to look for
the pattern there.
• After 20 years, he discovered that
the crucial point was that the
planets move in ellipses, not
circles.
• From this understanding, Kepler
went on to develop three laws of
planetary motion which summarize
the motions of the planets about
the Sun.
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Kepler’s 1st Law
• The Orbit of a planet around the Sun is an
ellipse with Sun at one focus
The Ellipse
• A circle is
simply a special
case of an
ellipse
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Kepler’s 2nd Law
• A line joining the planet and the Sun sweeps
out equal areas in equal intervals of time
Kepler’s 3rd Law
• The squares of the periods of the planets
are proportional to the cubes of their
semi-major axes
2
T
=
3
ka
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Final Thoughts on Kepler
• Kepler offered no explanation of why
these laws hold.
• The strength of his theory is that it allows
a much more precise prediction of the
positions of planets than did Ptolemy's
theory.
• Also, his three laws are much simpler
than the complicated ones of Ptolemy.
Galileo Galilei
• Italian, 1564 – 1642
• In 1610, Galileo was the first
person to methodically use a
telescope for astronomy
– Invented by Johannes
Lippershey in 1608
• His notebooks survive and still
provide important details about
how the sky looked in the 16
century
• However, several observations
upset followers of traditional
Greek astronomy
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Galileo’s 1st Observation:
Craters on the Moon
He wrote that the Moon is “… not at all of an even, smooth,
and regular surface, as a great many people believe of it and
of the other heavenly bodies, but on the contrary it is rough
and unequal…”
This really made the church mad!!
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Galileo’s 2nd Observation:
Spots on the Sun
Galileo’s 3rd Observation:
The Milky Way
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Galileo’s 4th Observation:
The Moons of Jupiter
Observations
of Jupiter From
Galileo’s
Actual
Notebook
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Galileo’s 5th Observation:
The Phases of Venus
Galileo and the Church
• In 1633, The Inquisition held its final hearing
on Galileo Galilei. Threatened with torture,
imprisonment, and death, he was forced to
reject his heliocentric views. Convicted, he
was sentenced to life imprisonment
(commuted to house arrest).
• Finally...in 1992, the Vatican admitted that
Galileo had been correct in his heliocentric
views which they previously condemned him
for and forced him to denounce!
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Final Thoughts on Galileo
• Galileo also made important experiments
on mechanics (the science of how things
move):
– He showed that heavy and light things fall at
same rate.
– He introduced the idea of acceleration and
realized that friction is what slows things
down.
• Galileo did not try to connect his
astronomy with his mechanics
experiments
Isaac Newton
• English, 1643 – 1727
• Newton is generally regarded as
the greatest physicist ever
• He wrote the book on optics and
mechanics, and invented calculus
• He knew all about Galileo's and
Kepler's discoveries, and looked for
the underlying physical laws that
could make sense of these
patterns
• Newton is also responsible for
bringing together the laws that
explain both the behavior of
planets and of things on Earth
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Newton’s Laws of Motion
• In putting these laws together, Newton
built on the work of Galileo
• They define the concept of a force (a
push or pull) and describe motion which
is used as the basis of classical
mechanics.
• The three laws apply to any matter, not
specifically planets, and they deal with
the way that motions are related to forces
Newton’s 1st Law of Motion
• A body remains at rest
or moves in a straight
line at a constant speed
unless acted on by an
outside force
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Newton’s 2nd Law of Motion
• The acceleration of an
object is proportional to
the force acting on the
object
F=ma
Newton’s 3rd Law of Motion
• Whenever one body exerts a
force on a second body, the
second body exerts an equal
and opposite force on the
first body
"For every action there is an
equal and opposite reaction"
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Newton's Law of Gravity
• Two bodies attract each other with a force
that is directly proportional to the product
of their masses and inversely proportional
to the square of the distance between them
Things Now Explainable as a Result
of Gravity & The Laws of Motion
•
•
•
•
•
•
Stable Orbits
Kepler’s Laws
Motion of Comets
Perturbations of Orbits
Binary Star Systems
Tides
Let’s look at each one of these a bit more....
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Stable Orbits
• Newton's laws
(including gravity)
explained how
orbits work, both
qualitatively
(characteristically)
and quantitatively
(numerically).
Like Our Moon for Example...
• Also, if we can measure how an object moves in
an orbit we can measure the mass of the object
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Kepler’s Laws Revisited
• Newton showed that if you start with his
four laws and consider a small object in
orbit around a large one, one can derive all
three of Kepler's laws exactly
– Note that Newton's laws are much more
fundamental than those of Kepler
• Newton’s laws allow for situations that
cannot be dealt with by Kepler's laws.
Motion of Comets
• Some comets
travel in parabolas
and hyperbolas,
which are foreign
to Kepler's laws,
but entirely
predictable by
Newton's laws
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Perturbations of Orbits
• The orbits of the planets are not exactly ellipses
after all. There are gravitational forces between
the planets as well as between each planet and
the Sun.
Binary Star Systems
• It is possible for two objects of comparable
mass to orbit around each other
• Newton's laws have no problem with this
arrangement.
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The Tides
• Gravitational
forces act on the
Earth
• These forces
cause a "stretch"
of the ocean
surface
• As the Earth
spins each place
on Earth feels a
rising and
lowering of the
tide twice a day
Albert Einstein & Beyond
• Newton's theory of gravitation is not
the last word on gravity
• The theory does not work for very
strong gravitational fields
• Einstein's general theory of relativity
(1912) supersedes Newton's theory
• When we get very strong
gravitational fields Einstein's theory
work better
• Individuals, such as Steven
Hawking, are finding situations
where Einstein's theory is not
working
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End Topic
The Motions
of the Planets
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