## Copyright (C) 2018 Anonymous
##
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; see the file COPYING. If not, see
## .
## -*- texinfo -*-
## @deftypefn {Function File} {@var{n} =} ecc2n (@var{ecc})
## This returns the third flattening given an eccentricity
##
## Examples:
##
## Scalar input:
## @example
## e_earth = .081819221456;
## n_earth = ecc2n ( e_earth )
## => n_earth = 0.0016792
## @end example
##
## Vector input:
## @example
## e_vec = [ .081819221456 0.3543164 ]
## n = ecc2n ( e_vec )
## => n =
## 0.0016792 0.033525
## @end example
##
## @seealso{n2ecc}
## @end deftypefn
function n = ecc2n ( ecc )
if nargin < 1
print_usage ( );
end
if ( ischar ( ecc ) )
error ('ecc2n.m: numeric input expected');
elseif ( ecc > 1 )
error ('ecc2n.m: eccentricity should be <=1')
else
B=(4 ./ ecc .^2 - 2); %Taken from e^2=4n/(1+n)^2
%Use to get in the form n^2-Bn+1=0
%From testing the other definition of third flattening (a-b)/(a+b)
%Use the - version for the quadratic equation
n=( B - sqrt( B .^2 -4 ) ) ./ 2;
end
%! test
%!
%! ecc_earth = .081819221456;
%! ecc_jupiter = 0.3543164;
%! e_vec = [ ecc_earth ecc_jupiter ];
%! assert ( ecc2n ( ecc_earth ) , 0.001679222 , 10e-10 );
%! assert ( ecc2n ( e_vec ), [0.0016792 0.03352464],10e-8)
%! error ecc2n ("ecc")
endfunction