Units

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Planetary Orbits Keplers Laws
2
Announcements

• The first homework due on Tuesday (start of
  class)
• available for download on website
• Can be turned in early to a box located outside
  of room 330 Kuiper
• It is the slot just above the white sign that
  says
• Giacalone
• Do not turn them into the lettered slots!!
• If turned in after class (for a small penalty)
  you can also turn it into this box
• Mission update volunteers?
• Note taker please see me at the end of class
• Reading for next class
• Review (or finish) Ch. 2 and 4

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Todays Topics

• Finish discussion on Earth-centered vs.
  Sun-centered solar system
• A long-standing Earth-centered view of the solar
  system is turned on its head with the invention
  of the telescope
• Phases of Venus
• The modern view of the solar system and the
  epiphany that gravity is important!
• Keplers revision to the system devised by
  Copernicus
• Keplers Laws
• Galileos experiments on gravity
• Newtons law of universal gravitation

4
Activity 1 (based on reading assignment)

• Consider the diagram. Which of the following
  statements is true?
•  
• The asteroid exerts a LARGER force on the Earth
  than the Earth exerts on the asteroid.
• (B) The asteroid exerts a SMALLER force on the
  Earth than the Earth exerts on the asteroid
• (C) The asteroid exerts the SAME force on the
  Earth as the Earth exerts on the asteroid.
• (D) The force exerted by the asteroid on the
  Earth is different from the force that Earth
  exerts on the asteroid, but that is all that can
  be said based on the information provided.

Circle the correct answer and also give a brief
reason for it
5
Aristotle dismissed the heliocentric system he
saw no parallax
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Parallax Shift
Only small apparent shifts can be seen using the
Earths rotation to change the observing
point. Larger shifts can be seen using Earths
orbit around the Sun (but still to small to be
noticed without a telescope)
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• Ptolemy introduced the concept of epicycles to
  explain the motion of Sun and planets

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Retrograde motion of planets

• When observed from one night to the next, a
  planet appears to move from West to East against
  the background stars most of the time.
• Sometimes it will appear to reverse direction.
  For a short time, it moves from East to West
  against the background constellations.

• This reversal is known as retrograde motion. All
  planets exhibit this behavior as seen from Earth.
  It is due to the relative motion of Earth and
  the planet.

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Ptolemys Universe

• The epicycle picture explains the retrograde
  motion of the planets
• This picture lasted 1000 years!
• Newtons physics has only been around for about
  400 years and Einstein has already corrected it !
• But, as we now know, it is flawed.

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The Ptolemaic system had to be modified somewhat
to explain the inner planets Venus and
Mercury. The morning and evening star (Venus)
was long thought to be 2 different objects until
Pythagoras discovered that it was one object
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The Copernican RevolutionA short list of key
people
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Nicholas Copernicus

• 1473-1543, Polish
• Re-proposed heliocentric theory
• Put the Sun at the center, but still believed the
  orbits of the planets were circles epicycles
• He felt that this was a more natural explanation
  of the solar system

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Tycho Brahe

• 1546-1601, Danish
• Nose cut off in duel by a fellow student
• Observed a supernova, and periodic comets
• Proof that the stars and planets are not
  constant, as the ancient astronomers believed
• Best pre-telescope (naked-eye) observer
• Given island of Hven to build an observatory
• Best, most observations
• Still no parallax

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Galileo Galilei

• 1564-1642, Italian
• Used telescope
• Jupiters moons
• Lunar mountains, sunspots
• Phases of Venus
• Saturns Ears
• Experiments on motion
• Including attempts to measure the speed of light
• Famous gravity experiment using the leaning tower
  of Pisa

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Jupiter and 3 of the Galilean satelites (only
Callisto is missing from this amateur
photograph) This is what Jupiter looks like
through a standard amateur telescope. Galileo
probably saw it similarly
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Phases of Venus
Galileos observations of Venuss gibbous
(full-ish) phase definitively ruled out
Ptolemys geocentric model !
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The phases of Venus in the Ptolemaic Modelonly
a crescent Venus is possible(no gibbous phase)
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The Phases of Venus in the Heliocentric Model
including the gibbous phase of Venus, as observed
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Conclusion

• The 1000-year-old paradigm of a Earth-centered
  solar system, was proved incorrect as the result
  of simple observations made by a new technology
  -- the telescope.
• New technologies often lead to re-writing of
  textbooks.
• Current new technologies include
• Space age
• Super computers

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Johannes Kepler proposed elliptical pathsfor the
planets about the Sun

• Using data collected by Tycho Brahe, Kepler
  deduced three laws of planetary motion
• the orbits are ellipses
• a planets speed varies as it moves around its
  elliptical orbit
• the orbital period of a planet is related to the
  size of its orbit

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Keplers First Law

• The planets move about the sun in elliptical
  orbits with the Sun at one foci of the ellipse

Aphelion
Perihelion
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Semi-major axis
The Semi-major axis is ½ the long width of the
ellipse Planetary fact sheets usually quote the
semi-major axis of the orbit
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• Eccentricity a measure of how oblong an ellipse
  is.

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Perihelion and Aphelion

• Semimajor axis average distance between planet
  and Sun
• Often denoted by the symbol a
• Perihelion point in orbit closest to the Sun
• Rper a(1-e)
• Aphelion point in the orbit farthest from the
  Sun
• Rap a(1e)

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Activity 2

• Consider the table of planetary orbital
  eccentricities at the right
• Which 2 planets in the solar system would
  experience the largest change in orbital speed
  and which 2 would experience the smallest change
  in orbital speed?
• Describe the extent to which that you think
  Earths orbital speed changes throughout a year?
  Explain your reasoning.
• which orbit below most-closely represents the
  orbit of the Earth?

C
A
B
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Extra slides

• The rest of these are slides were not covered in
  class, but are included for your notes

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• The orbits of most of the planets are nearly
  circles (low eccentricity). But other objects,
  especially comets, have orbits with high
  eccentricities.

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Keplers Second Law

• The Planet sweeps out equal areas of the
  elliptical orbit, in equal time intervals
• The planet moves fastest when it is closest to
  the Sun and slowest when it is farthest away

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Activity 3
The orbit of a fictitious planet in a Keplarian
orbit is shown below. The twelve positions shown
(1-12) are each exactly one month apart.

• Does the planet appear to be traveling the same
  distance each month?
• At which position would the planet have been
  traveling the fastest? The slowest? How can you
  tell?
• At position number 4, is the speed of the planet
  increasing or decreasing as time goes on? How
  can you tell?
• Provide a concise statement that describes the
  relationship that exists between a planets
  orbital speed and the distance from its companion
  star

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Keplers Third Law

• The square of a planets period (P) is
  proportional to the cube of its semi-major axis
  (a).
• or
• The farther a planet is from the Sun, the longer
  it takes to go around the sun

P the period (in years) a semi-major axis
(in AU)
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(No Transcript)
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• A warning about this formula !
• It only applies to planetary motion about the
  Sun! Also, the units must be P in years, and a
  in AU. Otherwise you will NOT get the correct
  result

P the period (in years) a semi-major axis
(in AU)
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Acceleration Due to Gravity

• Galileo discovered that the higher an object is
  dropped, the greater its speed when it reaches
  the ground
• All falling objects near the surface of the Earth
  have the same acceleration (9.8 m/s2)
• The acceleration of gravity on the surface of
  other solar-system bodies depends on their mass
  and radius
• Mars and the Moon have a smaller acceleration of
  gravity
• Saturn is about the same as Earth
• Jupiter is more than Earth

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Objects fall at the same rate independent of
mass !

• Galileos famous experiment
• Showed that objects of different masses dropped
  from the same height arrive to Earth at the SAME
  time
• Disproved Aristotles theory
• Did he really do it ?
• The experiment was also performed by an astronaut
  on the moon?

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Astronaut Alan Bean
Perfomed Galileos experiment on the Moon