6. Mercury: a battered world
Einstein and Mercury's anomalous orbital motion
Instead of returning to its starting point to form a closed ellipse in one orbital period, Mercury moves slightly ahead in a winding path that can be described as a rotating ellipse. As a result, the point of Mercury's closest approach to the Sun, the perihelion, advances by a small amount, 43 seconds of arc per century, beyond that which can be accounted for by planetary perturbations using Newton's law of gravitation. This unexpected effect is known as the anomalous precession of Mercury's perihelion.
According to Einstein's theory, known as the General Theory of Relativity, space is distorted and curved in the neighborhood of matter, and the distortion is the cause of gravity. In the absence of matter, space is not distorted and is described by the geometry developed by the ancient mathematician, Euclid (around 300 BC). In the presence of matter, space becomes curved and it must be described by non-Euclidean geometry.
The result is a gravitational effect that departs slightly from Newton's expression near a very massive object, and the planetary orbits are not exactly elliptical. This produces an advance of perihelion, and the amount predicted by Einstein for Mercury was 43 seconds of arc per century - exactly the observed amount. Because the amount of space curvature produced by the Sun falls off with increasing distance, the perihelion advances for the other planets are much smaller than Mercury's.
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Copyright 2010, Professor Kenneth R. Lang, Tufts University