OK I created the following Matlab code: The G term was a polynomial best fit to the gravity as a function of depth. The initial angular velocity is at the equator.
[t,y]=ode45(@orbit_ode,[0 200],[6500 0 0 2*pi/(24*3600)]);
polar(y(:,3),y(:,1))
function dx=orbit_ode(t,x);
dx=zeros(4,1);
%x(1) = r position
%x(2) = r velocity
%x(3) = theta position
%x(4) = theta velocity
dx(1)= x(2); %Velocity
dx(2)= x(1)*x(4)^2-(.0037*x(1)-3e-7*x(1)^2);
dx(3)= x(4);
dx(4)= (-2*x(2)*x(4))/x(1);
end
The plot isn't very impressive. It looks like a line straight through the center. The min radius is 114m so basically over 6500m drop the center moves about 114 m.