Geodetic effect

The geodetic effect is a curious thing that happens because of the shape of space and time, as described by general relativity. It makes the direction of something like the spin of a spinning object, such as a gyroscope, change a little as it moves around a planet or star. This idea was first predicted in 1916 by the scientist Willem de Sitter, who studied how the Earth and Moon move.

Experiments, like the Gravity Probe B mission, have tested this idea by measuring how a gyroscope’s spin changes when it orbits the Earth. The geodetic effect shows us how Einstein’s ideas about the universe work in real life. It helps scientists learn more about how things move in space and how mass affects their paths.

There are two ways to think about the geodetic effect, depending on whether the object is spinning or not. Objects that are not spinning follow the straightest possible path in space, called a geodesic. But spinning objects, like a gyroscope, follow paths that are just a little different because of their spin.

This effect is different from another phenomenon called Lense–Thirring precession, which happens because of the rotation of a big object, like a spinning planet. The geodetic effect happens just because there is a mass, like the Earth, even if that mass isn’t spinning. By studying both effects together, scientists can learn even more about how gravity works in our universe.

Experimental confirmation

The geodetic effect was tested by an experiment called Gravity Probe B. It looked at how the spin of tiny objects called gyroscopes changed when they moved around Earth. In 2007, the results showed that the effect was real. These results were shared at a meeting of the American Physical Society.

Formulae

This section explains how scientists work out the geodetic effect with special math ideas. It starts with a description of space and time around a big object, like Earth, using something called the Schwarzschild metric. By adding rotation to this idea, scientists can guess how a spinning object, like a gyroscope, will move in space because of the shape of space.

These calculations help us learn how gravity and turning together change how things move in space. One big idea is that the geodetic effect looks like old rules of motion, but with more details from Einstein’s theory of relativity.

Derivation using parallel transport about a circular orbit

Parallel transport explains how the direction of a free-falling object changes in space. Think of it like moving a pencil along a curved path while keeping it pointed the same way relative to the space around it.

When an object orbits a large body like Earth in a circle, its direction changes because of the shape of space around the body. This change is called the geodetic effect. Scientists measured this effect using tools like the Gravity Probe B satellite. This satellite carried gyroscopes to detect very small changes in direction during its orbit.

Thomas precession

The geodetic effect has two parts. One part is called Thomas precession. The other part is due to the shape of space and time. Some experts think Thomas precession applies to things on Earth’s surface but not to things moving freely in space. The Fermi-Walker transport equation helps explain both the geodetic effect and Thomas precession. It shows how the direction of spin changes for objects moving in curved space and time. When there is no pushing or pulling, this equation shows the spin change from the geodetic effect. For steady circular motion in flat space, it shows the Thomas precession.

Main article: Thomas precession
Further information: Fermi-Walker transport equation