**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