Physics

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Physics

• How Copernicus, Tycho, Kepler, and Newton
  revolutionized astronomy

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Aristotle and the Greek Philosophers

• Thales (c. 624 546 BC)
• Anaximander (c. 612 546 BC)
• Pythagoras (c. 560 480 BC)
• Eudoxus (c. 400 347 BC)
• Aristotle (384 322 BC)

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Claudius Ptolemy

• c. 90 168 AD
• Almagest (c. 150 AD)
• Epicycles upon epicycles in a geocentric universe

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Nicholas Copernicus

• 1473 1543 AD
• De Revolutionibus Orbium Coelestium (1543)

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Tycho Brahe

• 1546 1601 AD
• 20 years of observations at observatories he
  designed himself with instruments he designed
  himself

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Johannes Kepler

• From
• to three Laws of Planetary Motion in 10 years
  and thousands of pages of calculations
• Conclusion
• COPERNICUS WAS CORRECT.

http//www.pafko.com/tycho/observe.html

• 1571 1630 AD

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Keplers First Law

• Orbits are

• Orbits are ellipses with the Sun at one focus.

http//www.daviddarling.info/encyclopedia/E/ellips
e.html
http//www.math.rutgers.edu/courses/251/maple_new/
maple3.html
Eccentricity Simulator
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Earths elliptical orbit

• The Earths orbit is slightly elliptical at its
  perihelion it is approximately 147 million km
  from the Sun, and at aphelion it is approximately
  152 million km from the Sun. Which of the
  following is a result of the Earths elliptical
  orbit?
• a. It is summertime at perihelion and
• wintertime at aphelion.
• b. The Earth moves faster in its orbit at
• perihelion and slower at aphelion.
• c. Days are longer at aphelion and shorter
  
• at perihelion.
• d. The Earth spins faster at perihelion and
• slower at aphelion.

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Keplers Second Law

• Equal areas in equal times An imaginary
  straight line between a planet and the Sun sweeps
  out equal areas in equal times as the planet
  moves around the Sun.

http//observe.arc.nasa.gov/nasa/education/referen
ce/orbits/orbit2.html
Simulation of Keplers 2nd Law
http//astro.unl.edu/naap/pos/pos_background1.html
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A different solar system

• Consider two planets, Starsky and Hutch, orbiting
  a distant star. Starsky orbits twice as far from
  the star as Hutch does. How does Starskys
  orbital period compare to Hutchs?
• a. half as long
• b. the same
• c. twice as long
• d. more than twice as long

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Keplers Third Law

• The square of a planets orbital period is
  proportional to the cube of its semimajor axis.

http//jersey.uoregon.edu/kepler/Kepler.html
Simulation of Keplers 3rd Law
Additional Keplers 3rd Law Simulation
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Isaac Newton

• 1642 1727 AD

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Traveling out into space

• Suppose that you are in a spaceship traveling
  past two different planets. You pass a blue
  planet that has twice the mass of the Earth at a
  distance of 1 AU, then you pass a red planet that
  has the same mass as the Earth, also at a
  distance of 1 AU. From which planet will you
  feel the greater gravitational pull?
• a. the blue planet
• b. the red planet
• c. neither the gravitational pull from
• each planet will be equal

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Still traveling

• Suppose that you are in a spaceship traveling
  past two different planets. You pass a blue
  planet that has the same mass as the Earth at a
  distance of 1 AU, then you pass a red planet that
  also has the same mass as the Earth, but at a
  distance of 2 AU. From which planet will you
  feel the greater gravitational pull?
• a. the blue planet
• b. the red planet
• c. neither the gravitational pull from
• each planet will be equal

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Almost home

• Compared to your mass here on Earth, your mass
  out in space between the stars would be
• a. zero.
• b. negligibly small.
• c. the same.
• d. unknown.

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GRAVITY
G M1 M2
F
R2
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Make a distinction

• Gravitational pull of an object
• Surface gravity of an object
• For example

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The Earth, modified
The original Earth
The new Earth twice the radius four times
the mass
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Guiding Questions

• How did astronomers/astrologers/philosophers view
  the universe before Copernicus?
• What did Copernicus propose, and why was it
  heretical?
• How did Kepler show that Copernicus was correct?
• Describe what Keplers Laws tell us about the
  motions of planets in our solar system.
• What makes an ellipse different from a random
  oval?
• Explain how Keplers 2nd and 3rd Laws are
  different.
• What quantities determine the force of gravity
  between two objects?
• Using Newtons Law of Gravity, describe how the
  force of gravity varies based on objects masses
  and distance from one another.
• How does gravity explain Keplers 2nd and 3rd
  Laws?
• What is surface gravity?

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Sample questions

• 1. a. Draw an ellipse with an eccentricity of 0.
• b. Draw an ellipse with high eccentricity.
  Assuming this ellipse is the orbit of a comet
  around the Sun, show where within the orbit the
  Sun is located.
• c. Show where the comet would move the fastest,
  and where it would move the slowest.
• d. Halley's Comet has an elliptical orbit with
  a period of 76 years. Why does this comet only
  spend a small fraction of that 76-year period
  close enough to Earth and the Sun for us to see
  it? (Note there are two reasons)
• 2. If you were able to stand on Saturn (you
  couldn't really, because it is made mostly of
  gas), you would weigh about the same as you weigh
  on Earth (this means the force of gravity on you
  from the Earth is roughly the same as the force
  of gravity on you from Saturn). How is this
  possible Saturn's mass is 95 times the mass of
  the Earth! (You do not need to do any
  calculations, just explain how the correct
  equation works)
• 3. Despite the fact that Saturns SURFACE GRAVITY
  is similar to the Earths, its gravitational pull
  on its moons is much larger than the Earths pull
  on our Moon. Consider Saturns moon Dione,
  located approximately the same distance from
  Saturns center as the Moon is from the Earths
  center. For this question, assume the distances
  are equal.
• a. WHY does Dione feel more gravitational pull
  than the Moon?
• b. What would you expect Diones orbital period
  to be the same as the Moons, larger, or
  smaller? Explain why.