The beginning formula is wrong.
xp = 760 and xe = 500 produces a delay: dt = 206us;
and for exactly the same transmission but reversed only, produces result:
xe = 760 and xp = 500: dt = 215us
This is a nonsense!
Author of this fallacy should correct this immediately, or delete completely this erroneous formula - if he is unable to do math.
additional note:
![{\displaystyle \Delta t\approx {\frac {4GM}{c^{3}}}\left\{\ln \left[{\frac {x_{p}+(x_{p}^{2}+d^{2})^{1/2}}{-x_{e}+(x_{e}^{2}+d^{2})^{1/2}}}\right]-{\frac {1}{2}}\left[{\frac {x_{p}}{(x_{p}^{2}+d^{2})^{1/2}}}+{\frac {2x_{e}+x_{p}}{(x_{e}^{2}+d^{2})^{1/2}}}\right]\right\}+O\left({\frac {G^{2}M^{2}}{c^{6}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81186559c7c7e9ef16f717bd5570380b86448299)
hence an approximated form - up to second order is:
![{\displaystyle \Delta t\approx {\frac {4GM}{c^{3}}}\left\{\ln \left[{\frac {x_{p}+x_{p}(1+d^{2}/2x_{p}^{2})}{-x_{e}+x_{e}(1+d^{2}/2x_{e}^{2})}}\right]-{\frac {1}{2}}\left[3+{\frac {x_{p}}{x_{e}}}\right]\right\}={\frac {4GM}{c^{3}}}\left\{\ln \left[{\frac {4x_{p}\cdot x_{e}}{d^{2}}}\right]-1/2\left[3+{\frac {x_{p}}{x_{e}}}\right]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/553c1a06c648977009eb14b568e9962439e3828e)
so, this is inconsistent with the next equation.
You lost this: :
, what is a quite big number.
