KEPLER1

Name

kepler1

Purpose (one Line Only)

Solve Kepler's Equation (small eccentricity)

Description

Solve Kepler's Equation. Method by S. Mikkola (1987) Celestial
Mechanics, 40 , 329-334.
result from Mikkola then used as starting value for
Newton-Raphson iteration to extend the applicability of this
function to higher eccentricities, Courtesy of Joern Wilms.

Calling Sequence

kepler1,m,ecc,eccanom

Inputs

m - Mean anomaly (radians, can be an array)
ecc - Eccentricity

Optional Input Parameters

Keyword Input Parameters

THRESH - stopping criterion for the Newton Raphson iteration; the
iteration stops once abs(E-Eold)<thresh

Outputs

eccanom - Eccentric Anomaly (radians)

Keyword Output Parameters

Common Blocks

Side Effects

Restrictions

Procedure

Modification History

2002/05/29 - Marc W. Buie, Lowell Observatory. Ported from fortran routines
supplied by Larry Wasserman and Ted Bowell.
2002/09/09 -- Joern Wilms, IAA Tuebingen, Astronomie.
use analytical values obtained for the low eccentricity case as
starting values for a Newton-Raphson method to allow high
eccentricity values as well
2005/09/14, MWB, modified kepler1 to incoporate Wilms keplereq routine.
2013/08/16, MWB, fixed error with parameter validation
2015/03/10, MWB, inserted kludge to prevent infinite loop on very high
eccentricity orbits (~7-8 9's). If you hit this spot
in the code you will get a warning about non-convergence
and the code will press on. The answer in this case
may well not be right.