5.4.3 Planetary motion

• Kepler’s 1st law: the orbit of a planet is an ellipse with the Sun at one of the two foci.
• Ellipse: a ‘squashed’ or elongated circle, with two foci. The orbits of all the planets are elliptical.
• • Most of the planets have low eccentricity (how elongated circles are) so orbits modeled as circles.
• Aphelion: the furthest point from the Sun.
• Perihelion: the closest point to the Sun.
• Kepler’s 2nd law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• • Speed is not constant on orbit. The planet moves faster when closer to the Sun (between P & Q).
  • The planet moves slower between P & Q.
  • If the time interval is equal between P & Q, and X & Y than areas are equal.

  
• Kepler‘s 3rd law: the square of the orbital period $T$ of a planet is directly proportional to the cube of its average distance r from the Sun.