Planetary Motion

Johannes Kepler's Three Laws of Orbits

  1. Each planet orbits the Sun in an 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
    • 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 (PP) squared is proportional to the semi-major axis (aa) of its orbit cubed
    • P2āˆa3P^2 \propto a^3
    • When PP is measured in years and aa 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

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 a3=(M1+M2)ƗP2a^3 = (M_1 + M_2) \times P^2
    • M1M_1 is the mass of the Sun
    • M2M_2 is the mass of the planet
    • Both M1M_1 and M2M_2 are expressed in units of the Sun's mass

Space Astronomy Physics