Kepler's First Law: Planetary Orbits are Ellipses


Geometry of the Ellipse


  • a = semi-major axis 
  • b = semi-minor axis
  • e = eccentricity
  • F, F' = foci
  • r, r' = foci distance
  • theta = true anomaly
Orbit is defined by a and e

Position is defined by r and theta

Equation of the Ellipse





Orbital Eccentricities
Earth e = 0.017 b/a = 0.99986
Venus e = 0.007 b/a = 0.999975
Pluto e = 0.25 b/a = 0.968
Comets e = 0.995 b/a = 0.01



rp = a(1-e)
ra = a(1+e)

Mars
Earth
e=0.093, a=1.524 AU e=0.017, a=1.000 AU
Perihelion = 1.382 AU Perihelion = 0.983 AU
Aphelion   = 1.666 AU Aphelion   = 1.017 AU