Day 4 Chapter 2 Gravitation and the Motion of the Planets

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Day 4 Chapter 2Gravitation and the
Motionof the Planets
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Science is the key to understanding

• Science a body of knowledge and a process of
  learning about nature (called the scientific
  method).
• Knowledge is acquired by observations and
  experiments.
• Scientific method is a process for gaining more
  knowledge, that can be tested and accepted by
  everyone.
• Scientific theory is an explanation of
  observations or experimental results that can be
  described quantitatively and tested.
• The theory must make testable predictions that
  can be verified by new observations or
  experiments, and can possibly be refuted.
• Theories can be modified and should be the
  simplest version that explains the observations
  (Occams razor).
• Observe, hypothesize, predict, test, modify,
  economize.

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The Copernican Revolution

• The model of the Greeks (attributed primarily to
  Ptolemy) had the Earth at the center of
  everything.
• Copernicus proposed a model of the solar system
  with the Sun at the center (hence a solar
  system).
• Galileo made a telescope and used it to view the
  sky, and saw that the phases of Venus refuted the
  geocentric model of the Greeks.
• Tycho Brahe and Johannes Kepler developed a more
  detailed heliocentric model with elliptical
  orbits.

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Retrograde motion of a planet occurs over several
weeks, and involves motion to the west, as
compared to prograde (direct) motion, which is
to the east(relative to the stars of the
celestial sphere).
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The Geocentric Model of planetary motion (Greek
philosophy)
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The Geocentric Model does explain retrograde
motion, using concepts like deferent and
epicycle. However, it does not predict the
motion with much accuracy, and does not predict
phases of Venus (seen with a telescope).
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Ptolemys Model of planetary motion used
deferents (big circles) and epicycles (little
circles centered on a point that moves on the
deferent). This involved up to 80 circles to
describe 7 objects!
Occams Razor says Simplify this!
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Nicholas Copernicus and his Heliocentric model of
the Solar System explained this in a simpler way
with the Sun at the center.
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Retrograde motion is seen in this model, using
Earth and Mars as the example.
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Retrograde Motion of Mars as seen from Earth
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Galileo Galilei and the Birth of Modern
AstronomyGalileo built a telescope in 1609 and
looked at the sky.
Four objects The Moon The Sun Jupiter Venus
(and much more)
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Galileo looked at the Moon and saw mountains,
craters, valleys, and topography like you might
find on the Earth. The Moon was perhaps an
object like the Earth!
By projecting an image of the Sun, he could see
imperfections on the Sun. Sunspots could be seen
to move from east to west on the Sun and he
deduced that the Sun rotated about once a month.
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Galilean Moons of Jupiter Small point of light
could be seen near Jupiter. By observation
during several weeks he deduced that these were
moons and that they revolved around Jupiter.
Perhaps this planet was like the Earth, with
several moons of its own. It also seemed like
a miniature model of the heliocentric solar
system.
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Venus Phases in the Heliocentric modelThese are
consistent with the observations in a telescope.
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Venus Phases in the Geocentric model are
obviously wrong as soon as you observe with a
telescope. This refutes Ptolemy!
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Both described the positions and movement of the
Sun, Moon, and 5 visible planets, as seen without
a telescope. The geocentric theory was too
complicated (80 circles!). (Occams razor could
be invoked to seek a simpler way.)Once the
telescope was used to observe Venus, the
geocentric theory could not explain the phases of
Venus. The heliocentric theory of Copernicus
explained many of Galileos observations, but
also used circular orbits. More accurate
measurements did not agree with the simple theory
of Copernicus (circles had to be replaced by
ellipses in the newer theory of planetary
motion).
Geocentric vs. heliocentric theories
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After Copernicusand Galileo, two major
figureschanged the way we come to understand
the Universe Keplers laws of planetary
motionNewtons laws of mechanics
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More detailed observations were made by Tycho
Brahe (commonly called Tycho, 1546 - 1601). He
made observations of a supernova in 1572 which
convinced him that it was a distant star. He
received an island and built an observatory to
measure planetary motion to high accuracy over a
period of more than 20 years. His observations
were inherited by an assistant, Johannes Kepler,
when Tycho died in 1601.
Further development of the heliocentric theory
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Tycho Braheobtained data over a period of 21
years that were later used by his assistant
Johannes Keplerto determine thatplanetary
orbits are NOT circles, but are ellipses.
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Johannes Kepler and the Laws of Planetary Motion
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Kepler used decades of Tychos observations in
his mathematical calculations, to determine the
shape of the planetary orbits, and the speed of
the planets as they went around the Sun. This
massive effort resulted in three major statements
about the characteristics of planetary orbits
Keplers three laws of planetary motion.
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Keplers three laws of planetary motion

• Orbital paths of the planets are ellipses.
• An imaginary line connecting the planet with the
  Sun sweeps out equal areas of the ellipse in
  equal intervals of time.
• The square of a planets orbital period is
  proportional to the cube of its semi-major axis.
  
• Kepler published this in 1609, the same year that
  Galileo built his first telescope.

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Keplers first law The orbital paths of the
planets are elliptical, with the Sun at one
focus. Keplers second law An imaginary line
connecting the Sun to any planet sweeps out equal
areas of the ellipse in equal intervals of
time.Keplers third law The square of the
planets orbital period is proportional to the
cube of its semimajor axis.
Keplers laws of planetary motion
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An Ellipse can be drawn with string and TWO foci
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For an ellipse, r1 r2 2a The
eccentricity is defined as e c/a A
circle results when e 0 GeoGebra
demonstration http//people.ucalgary.ca/louro/
geogebra/ellipse.html
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Some Properties of Planetary Orbits
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Keplers first law The orbital paths of the
planets are elliptical, with the Sun at one
focus. Keplers second law An imaginary line
connecting the Sun to any planet sweeps out equal
areas of the ellipse in equal intervals of
time.Keplers third law The square of the
planets orbital period is proportional to the
cube of its semimajor axis.
Keplers laws of planetary motion
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Keplers Second Law equal areas in equal
timeThis also means higher speed at closer
distances.
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Another graphic on Keplers Second Law
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The Astronomical Unit is about 150,000,000 km
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Keplers first law The orbital paths of the
planets are elliptical, with the Sun at one
focus. Keplers second law An imaginary line
connecting the Sun to any planet sweeps out equal
areas of the ellipse in equal intervals of
time.Keplers third law The square of the
planets orbital period is proportional to the
cube of its semimajor axis.
Keplers laws of planetary motion
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Keplers Third Law P2 (in years) a3 (in
a.u.)Basically, it means that large orbits have
long periods.
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Real orbits have the center of mass as one
focus For the Sun and planets, this is not a
large effect. For binary stars, the center of
mass may be near the middle of the line
connecting them.
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Lets review Keplers Laws. Review  see if you
can tell what these are simulating 
http//webphysics.davidson.edu/physlet_resources
/bu_semester1/c17_kepler2.html http//webphysics.
davidson.edu/physlet_resources/bu_semester1/c17_pe
riods_sim.html http//webphysics.davidson.edu/phy
slet_resources/bu_semester1/c17_solar_sim.html
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Newtons Laws of Physics

• First law inertia
• Second law F ma
• or acceleration force / mass
• Third law Action and Reaction
• means that forces occur in pairs.
• These can be used to show that orbits should obey
  Keplers 3 laws.

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Isaac Newton developed a quantitative and
explanatory theory of mechanics, explaining the
motion of objects resulting from forces.
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Newtons Second Law F maThe acceleration of
a mass is proportionalto the total force acting
upon it, and inversely proportional to the mass
of the object.
Newtons First Law The law of inertia. An
object will continue in its motion without
change of velocity unless it is acted on by a
net external force.
Newtons Third Law Action-reactionFor every
force acting upon an object (action), there is a
force acting on another object (reaction) which
has the same magnitude (size) but points (acts)
in the opposite direction.
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Newton also developed the universal law of
gravity. Gravitational force varies with the
distance between the objects.It depends on the
product of the two masses, i.e., m1 x m2 and
on the inverse of the square of the distance
between the masses (assuming they are small
compared with the distance). 1/r2
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The Suns gravity causes planets to move on a
path called an orbit. These orbits obey
Keplers Laws.
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• Newtons Laws explain Keplers Laws
• Newtons Laws account for all three of Keplers
  Laws.
• The orbits of the planets are ellipses, but it is
  also possible to have orbits which are parabolas
  or hyperbolas. (conic sections)
• Edmond Halley predicted a comet would return in
  1758 and every 76 years after that. (seen in
  1910, 1986, and will return in 2061) Halleys
  comet has an elliptical orbit extending out past
  Neptune.
• William Herschel discovered Uranus in 1781 by
  accident.
• After 50 years it was seen to deviate from an
  elliptical orbit, and a calculation led to the
  discovery of Neptune in 1846.
• To be precise, elliptical orbits would only occur
  if there were only the Sun and one planet. There
  are 8 planets and other objects which cause
  deviations from the perfect elliptical orbit.

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The first exam is on Thursday, Feb. 4 (next
week!) We will have about 30 minutes of class
before the exam.Then you will take the exam
(which uses a Scantron). The exam is multiple
choice and true/false questions. Coverage is
Chapters 1 and 2 in your textbook. To review,
look at the chapter summaries, my day notes, and
a study guide that I will post this weekend.