Johannes Kepler Space Astronomy Physics

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 ($P$) 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