Mercury & Suns

The small "half circle" represents the Newtonian orbit of Mercury. The larger "half ellipse" is a Newtonian orbit with more eccentricity and with a new sun 1,000,000 times more massive than our sun, but with unchanged perihelion. The points show the results of a MathCad worksheet calculation for the orbit as a geodesic in a three dimensional curved space. This calculation is an application of the principle of least action.


The solid line in the plot below is an enlarged representation of Mercury's Newtonian orbit with our sun. The points are from a calculation for the orbit as a geodesic in Einstein's four dimensional space-time continuum. Schwarzschild's metric was used.



The points below show six revolutions of Mercury about its new sun, according to the same calculation which was done for the points in the previous image. The advance of perihelion is significant even from one revolution to the next. The solid blue line is Mercury's Newtonian orbit with our sun. The solid red line is the Newtonian orbit around the heavy sun. Since the Newtonian theory predicts one revolution in the new orbit every 7 hours, this is clearly a relativistic problem.


Mathematical Details