Elliptical Case

CARTESIAN COORDINATES TO KEPLER ORBIT ELEMENTS CONVERSION

Up ] [ Cartesian to Kepler Conversion Primer ] Kepler to Cartesian Primer ]

Compute orbital elements given position and velocity at time t for elliptical motion

  1. Compute the specific angular momentum and check for a degenerate orbit,
  2. Compute the radius, r, and velocity, v,
  3. Compute the specific energy, E, and verify elliptical motion,

  1. Compute semi-major axis, a,
  2. Compute eccentricity, e,
  3. Compute inclination, i, (0 180 ),

7. Compute right ascension of the ascending node, W , (0 360 ),

8. Compute argument of latitude, , (0 360 ),

9. Compute true anomaly, f, (0 360 ),

  1. Compute argument of periapse, w , (0 360 ),
  2. w = (w + f) f

  3. Compute eccentric anomaly, EA, (0 360 ),
  4. EA is in the same half plane as f

  5. Compute time of periapse passage, T,

EA must be in radians