Johannes Kepler Space Astronomy Physics

Planetary Motion

• Path of an object through space is called an orbit
• Ptolemy's geocentric model was accepted until Copernicus' heliocentric model finally got adopted
  • Johannes Kepler's laws and moving to ellipses helped adoption

Johannes Kepler's Three Laws of Orbits

1. Each planet orbits the Sun in an ellipse
   • Circular orbits didn't fit the observations made by Tycho Brahe
   • Discovered orbits had a flattened shape (ellipse)
   • Sun is at one focus of the ellipse
2. Straight line joining a planet and the Sun sweeps out equal areas in space and equal areas in time
   • Eg. in 60 days a planet will move the same amount of area, no matter how close it is to the body it orbits
   • The Law of Equal Areas
   • 
   • Discovered by observing orbits speeding up as a planet gets closer to the Sun
   • Consequence of the conservation of angular momentum
   • Figure skater law
3. A planet's orbital period ($P$) squared is proportional to the semi-major axis ($a$) of its orbit cubed
   • $P^2 \propto a^3$
   • When $P$ is measured in years and $a$ is measured in astronomical units, the two sides are equal
   • Applies to all objects orbiting the Sun
   • Provides means for calculating objects relative distances from the Sun
   • Law of harmonies

Newton's Addition to the Third Law

• Isaac Newton realized that the Sun's mass and a planets mass come into play with regards to the third law
• The proper formula is $a^3 = (M_1 + M_2) \times P^2$
  • $M_1$ is the mass of the Sun
  • $M_2$ is the mass of the planet
  • Both $M_1$ and $M_2$ are expressed in units of the Sun's mass