Keplers Laws of Planetary Motion

1
Keplers Laws of Planetary Motion

• A Cultural Look at

Brian Kurtz, Kim Moyer, Danielle Shelton, Bilin
Wu
2
Pre-Kepler Views

• The Universe is geocentric
• (Earth Centered)?
• All orbits are perfect circles
• Deferents and epicycles were used
  to explain Retrograde Motion

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Flaws in Pre-Kepler Views Involving Geocentricity

• Planets show phases just like the moon, therefore
  the universe cannot be geocentric
• If a planet, such as Venus, was between the Earth
  and the Sun, then Venus would always be in the
  crescent phase
• However, Venus displays all phases.

4
Flaws in Pre-Kepler Views Involving Epicycles

• It took many epicycles to accurately describe the
  motion of the planets
• The messiness of the
• model indicates that it
• is most likely incorrect

5
Keplers First Law (Law of Ellipses)?

• All planets orbit in ellipses with a star at one
  focus
• The path of a planet around
• the sun is not circular instead,
• it takes the form of an ellipse
• An ellipse has two foci
• The sun is at one of these points

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Keplers Second Law (Law of Areas)?

• A line joining a planet and its star sweeps out
  equal areas during equal intervals of time
• Perihelion- point in the orbit where the planet
  is closest to the sun
• Aphelion- point in the orbit where the planet is
  farthest from the sun
• The time interval between positions
• B A is equal to that of the time
• interval between positions C D
• The two triangles in are equal in area
• This means that the planet moves
• faster at perihelion than at aphelion

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Keplers Third Law (Law of Periods)?

• The squares of the periods of the planets are
  proportional to the cubes of their average
  distance from the sun
• Also written as P2 a3 , where P is the period
  and a is the average distance of the planet from
  the sun
• This explains that the planets
• farther from the sun mover
• slower and have a longer path
  to follow

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Post-Kepler Discoveries

• Kepler's work confirmed years later by Newton's
  discovery of gravity
• Kepler's laws can be derived from Newton's laws
• Kepler's work is the foundation for most modern
  astronomy