Geodetic precession

The geodetic precession is the name given to the phenomenon of Précession which the kinetic Moment undergoes of an object, or the Spin of a Elementary particle when it has an accelerated trajectory, subjected or not to the force S nelles Gravitation. The geodetic precession is in fact the combination of two effects, the Précession of Thomas who relates to the forces nongravitational, and discovered within the framework of the spin of the electron of a Atome of Hydrogène, and the Effet of Sitter, which relates to the gravitational forces of origin. The precession of Thomas is explainable within the framework of the restricted Relativité, the effect Sitter within the framework of the General relativity. It is necessary to uncouple the nongravitational part of the gravitational part, because in this last case, it is necessary to take account of the deformations of space generated by the gravitational Champ. These deformation being non-existent in the case of forces nongravitational, the effect of the gravitational field on the geodetic precession differs from that which would be caused by a nongravitational force of intensity and equivalent direction.

Formulate precession

The clean kinetic moment $\ mathbf {S}$ of an object undergoing a Accélération $\ mathbf {has}$ origin nongravitational and plunged in a well of potential U , and animated from a speed $\ mathbf {v}$ in a Référentiel given goes précesser according to the usual formula

\ frac = {\ mathbf {\ Omega}} \ wedge {\ mathbf {S}}

with

{\ mathbf {\ Omega}} = \ frac {1} {2} \ frac {\ left ({\ mathbf {has}} - 3 {\ mathbf {\ nabla}} U \ right) \ wedge {\ mathbf {v}}} {c^2}

where C is the Speed of light. The first term of the member of left of the vector Product (

{\ mathbf {has}}

) corresponds to the precession of Thomas, the second

3 {\ mathbf {\ nabla}} U

with the effect Sitter.

In practice, three potentially interesting cases occur:

If the object is in freefall, then the acceleration of nongravitational origin is null, and only the effect Sitter is present.
If the gravitational forces are negligible (as for an electron in an atom), only the precession of Thomas is present.
If the object is located at the surface of a body, it undergoes an acceleration opposed to the gravitational field (the reaction of the support, opposed to the gravitational field, is ${\ mathbf {has}} = + {\ mathbf {\ nabla}} U$ ). One has then, by not taking account of other nongravitational forces,

{\ mathbf {has}} - 3 {\ mathbf {\ nabla}} U = - 2 {\ mathbf {\ nabla}} U

. To note that factor 3 front the gravitational field shows that the gravitational and nongravitational forces do not play the same part here. If such were case, acceleration of gravity

- {\ mathbf {\ nabla}} U

would appear in the same way that nongravitational acceleration

{\ mathbf {has}}

, which is not the case here, because of factor 3.

For the physical interpretation of these two effects (precession of Thomas and effect Sitter), to see the corresponding articles.

See too

Reference

, page 1118 and 1119.

Note

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