The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.
In the diagram shown here, the amount of the advance is greatly exaggerated. The actual advance is only 43 seconds of arc per century.
The same phenomenon is more dramatically seen in the binary pulsar PSR 1913+16 where the periastron advances by about 4.2 degrees per year.
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