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+## Copyright (C) 2018-2020 Philip Nienhuis
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{ecc} =} n2ecc (@var{n})
+## This returns the eccentricity given the third flattening (n).
+##
+## Examples:
+##
+## Scalar input:
+## @example
+##  n_earth = 0.0016792;
+##  ecc_earth = n2ecc (n_earth)
+##  => ecc_earth = 0.081819
+## @end example 
+##
+## Vector input:
+## @example
+##  n_vec = [ 0.0016792 0.033525 ];
+##  ecc = n2ecc (n_vec)
+##  => ecc =
+##	 0.081819     0.35432
+## @end example
+##
+## @seealso{n2ecc}
+## @end deftypefn
+
+## Function supplied by anonymous contributor, see:
+## https://savannah.gnu.org/patch/index.php?9566
+## For background see https://en.wikipedia.org/wiki/Flattening
+
+function ecc = n2ecc (n)
+
+  if (nargin < 1)
+    print_usage ();
+  end
+  if (! isnumeric (n) || ! isreal (n) )
+    error ("n2ecc.m: numeric input expected");
+  elseif (any (n < 0) || any (n > 1))
+    error ("n2ecc.m: n should lie in the real interval [0..1]" )
+  else
+    ecc = sqrt (4 * n ./ (1 + n) .^2);
+  end
+  
+endfunction
+
+%!test
+%!
+%! n_earth = 0.001679221647179929;
+%! n_jupiter = 0.03352464537391420;
+%! n_vec = [ n_earth  n_jupiter ];
+%! assert (n2ecc (n_earth) , .081819221456 , 10e-12); 
+%! assert (n2ecc (n_vec), [0.08181922 0.3543164], 10e-8)
+
+%!error <numeric input expected> n2ecc ("n")
+%!error <numeric input expected> n2ecc (0.5 + 3i)
+%!error <n should lie> n2ecc (-1)
+%!error <n should lie> n2ecc (2)
+%!error <n should lie> n2ecc (-Inf)
+%!error <n should lie> n2ecc (Inf)
+