/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 0.8.5 ] */ /* [wxMaxima: section start ] Refutation of Einstein General Relativity orbits [wxMaxima: section end ] */ /* [wxMaxima: comment start ] define radius function r(theta) of a precessing ellipse [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ r = alpha/(1+epsilon*cos(x*theta)); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] multiply by (epsilon*cos(x*theta)+1) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ %*(epsilon*cos(x*theta)+1); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] divide by r [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ %/r; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] subtract 1 [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ %-1; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] divide by epsilon [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ %/epsilon; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] simplify [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ expand(ratsimp(%)); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] transform cos to sin by using theorem sin(x)^2 + cos(x)^2 = 1 [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ sin(x*theta)^2 = 1 - cos(x*theta)^2; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] insert result above for cos(x*theta) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ sin(x*theta)^2 = 1 - (alpha/(epsilon*r)-1/epsilon)^2; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] work out square of sum and take common denominator [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ radcan(%); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] simplify [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ expand(%); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] This expression has to be eqated with the result of EGR [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ 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); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] multiply by epsilon^2*x^2 [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ E*epsilon^2*x^2; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] 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. [wxMaxima: comment end ] */ /* [wxMaxima: comment start ] Plot of precessing ellipses [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ r: alpha/(1+epsilon*cos(x*theta)); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ r1: ev(r, [alpha=1, epsilon=0.2, x=1]); r2: ev(r, [alpha=1, epsilon=0.2, x=1.1]); /* [wxMaxima: input end ] */ /* [wxMaxima: section start ] Orbital Plots [wxMaxima: section end ] */ /* [wxMaxima: input start ] */ 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))\$ /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ 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))\$ /* [wxMaxima: input end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"\$