### Geodetic Precession

Â Precession in Curved Space
"The Geodetic Effect"

If you ever had a spinning top, you know that its axis tends to stay lined up in the same direction--usually, vertically, though in space any direction qualifies.

Give it a nudge, however, and the axis will start to gyrate wildly around the vertical, its motion tracing a cone (drawing). The spinning Earth moves like that, too, though the time scale is much slower--each spin lasts a year, and each gyration around the cone takes 26 000 years. The axis of the cone is perpendicular to the plane of the ecliptic.

The cause of the precession is the equatorial bulge of the Earth, caused by the centrifugal force of the Earth's rotation (the centrifugal force is discussed in a later section). That rotation changes the Earth from a perfect sphere to a slightly flattened one, thicker across the equator. The attraction of the Moon and Sun on the bulge is then the "nudge" which makes the Earth precess.

Right: Precession of a spinning top: the spin axis traces the surface of a cone.

Through each 26 000-year cycle, the direction in the sky to which the axis points goes around a big circle, the radius of which covers an angle of about 23.50. The pole star to which the axis points now (within about one degree) used to be distant from the pole, and will be so again in a few thousand years (for your information, the closest approach is in 2017). Indeed, the "pole star" used by ancient Greek sailors was a different one, not nearly as close to the pole.

Our early theoretical understanding of spinning tops assumed that space was flat (i.e., that gravity was Newtonian in character), but thanks to Einstein's theory of general relativity we now know that the Earth is a top spinning in curved space. The curvature of space changes the way that our planet's spin axis precesses -- these changes are very small and hard to measure. In 1916, W. de Sitter predicted a minute relativistic correction to the complicated motions of the Earth-Moon system around the Sun -- an effect finally detected in 1988 through an elaborate combination of lunar ranging and radio interferometry data. For a gyroscope like the ones on Gravity Probe B, the predicted effect is a rotation in the orbit-plane of 6,600 milliarc-seconds per year -- quite a large angle by relativistic standards. For more information please visit "Directionality in Space and Time," a web site at Stanford University.

Much of this explanation was drawn from "Precession," a web site at the Goddard Space Flight Center.