Kepler proposed that the distance relationships between the six planets known at
that time could be understood in terms of the five Platonic solids.

Actually his model and book explains little if only that their orbits were
inside one another.
And the function is still called, SolveKepler,
original data :
 from Keith Burnett translated a few times.

My question is, what should he be known for? Something that is not this ....
sort of mechanical meditation in which he engaged, while attepmting to discover
the equations ...

If he was any kind of mathematician his model could have looked like this.
#macro SolveKepler(M,ec)
  #local E = M;
  #local d = E - ec * sin(E) - M;
  #while (abs(d) > 0.00000001)
    #local delta = d / (1.0 - ec * cos(E));
    #local E = E - delta;
    #local d = E - ec * sin(E) - M;
  #end
E
#end

#macro orbital(id)
 #if (id)
  #local M = days * radians(val(elements[id][5]));
  #local p = radians(val(elements[id][3]));
  #local M = M + radians(val(elements[id][7])) - p;
  #local e = val(elements[id][6]);
  #local E = SolveKepler(M, e);
  #local r = IDS(au2km(val(elements[id][4]))) * (1.0 - e * cos(E));
  #local vv = 2.0 * atan(sqrt((1.0 + e) / (1.0 - e)) * tan(E / 2.0));
  #local o = radians(val(elements[id][2]));
  #local i = radians(val(elements[id][1]));

  #local vv = vv + p - o;
  #local e = sin(vv);
  #local p = sin(o);
  #local o = cos(o);
  #local vv = cos(vv);
  #local M = cos(i);
  #local _v = <r * (o * vv - p * e * M), r * e * sin(i), r * (p * vv + o * e *
M)>;

  #local result = pop_matrix4(orbitmatrix,_v);
 #else #local result = <0,0,0>;#end
 result
#end
//    0      1             2             3           4          5            6
        7
//Epoch,inclination, ascending node, perihelion, axis au, daily
motion,eccentricity, longitude,
// size-earthrads, name, host-id
/*

composite -depth 8 -stereo keplerR.png keplerL.png kepler.png

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