## Refutation of Einstein General Relativity orbits

define radius function r(theta) of a precessing ellipse

r = alpha/(1+epsilon*cos(x*theta));

multiply by (epsilon*cos(x*theta)+1)

%*(epsilon*cos(x*theta)+1);

divide by r

%/r;

subtract 1

%-1;

divide by epsilon

%/epsilon;

simplify

expand(ratsimp(%));

transform cos to sin by using theorem sin(x)^2 + cos(x)^2 = 1

sin(x*theta)^2 = 1 - cos(x*theta)^2;

insert result above for cos(x*theta)

sin(x*theta)^2 = 1 - (alpha/(epsilon*r)-1/epsilon)^2;

work out square of sum and take common denominator

radcan(%);

simplify

expand(%);

This expression has to be eqated with the result of EGR

E: (2*alpha)/(epsilon^2*r)-alpha^2/(epsilon^2*r^2)-1/epsilon^2+1 =
(alpha/(x*epsilon))^2*(1/b^2-1/a^2+r0/a/r-1/r^2+r0/r^3);

multiply by epsilon^2*x^2

E*epsilon^2*x^2;

It is seen that the left hand side is a polynom of maximum degree 1/r^2 
while the right hand side is one of maximum degree 1/r^3. Both sides can 
never be equal for a certain range of r. However the variable r must be
able to vary because it describes an ellipse - reduction ad absurdum.

Plot of precessing ellipses

r: alpha/(1+epsilon*cos(x*theta));

r1: ev(r, [alpha=1, epsilon=0.2, x=1]);
r2: ev(r, [alpha=1, epsilon=0.2, x=1.1]);

## Orbital Plots

wxdraw2d(user_preamble = "set grid polar; set size square;",
             nticks        = 1000,
             line_width    = 2,
             xrange        = [-1.5,1.5],
             yrange        = [-1.3,1.7],
             title         = "Precessing Ellipse, 2 orbits",
key           = "r(theta), x=1.0",
color         = red,
polar(r1, theta, 0, 4.*%pi),
key           = "r(theta), x=1.1",
color         = blue,
polar(r2, theta, 0, 4.*%pi))$

wxdraw2d(user_preamble = "set grid polar; set size square;",
             nticks        = 1000,
             line_width    = 2,
             xrange        = [-1.5,1.5],
             yrange        = [-1.3,1.7],
             title         = "Precessing Ellipse, 12 orbits",
key           = "r(theta), x=1.0",
color         = red,
polar(r1, theta, 0, 24.*%pi),
key           = "r(theta), x=1.1",
color         = blue,
polar(r2, theta, 0, 24.*%pi))$