function value = kepler ( x )

%*****************************************************************************80
%
%% kepler evaluates a version of Kepler's equation.
%
%  Discussion:
%
%    Kepler's equation relates the mean anomaly M, the eccentric anomaly E,
%    andthe eccentricity e of a planetary orbit.
%
%    Typically, e is a fixed feature of the orbit, the value of M is determined
%    by observation, and the value of E is desired.
%
%    Kepler's equation states that:
%      M = E - e sin(E)
%
%    Suppose we have an orbit with e = 2, and we have observed M = 5.  What is
%    the value of E?  The equation becomes:
%      5 = E - 2 sin ( E ).
%
%    To solve for E, we need to rewrite this as a function:
%      F(E) = 5 - E + 2 sin ( E )
%    and then use a nonlinear equation solver to solve for the value of E
%    such that F(E)=0.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    25 July 2019
%
%  Input:
%
%    real x, the current estimate for the value of E.
%
%  Output:
%
%    real value, the Kepler equation residual F(E).
%
  value = 5.0 - x + 2.0 * sin ( x );

  return
end

