Geodetic effect

The geodetic effect is a fascinating phenomenon that happens because of the shape of space and time, as described by general relativity. It causes a slight change in the direction of something like the spin of a spinning object, such as a gyroscope, as it moves around a planet or star. This effect 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 theories about the universe work in real life. It helps scientists understand more about the motion of objects in space and how mass shapes the paths they follow.

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 massive 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 measured how the spin axis of tiny spinning objects called gyroscopes changed when they orbited the Earth. The results showed that the effect was real, and they were announced in 2007 at a meeting of the American Physical Society.

Formulae

The formulae section explains how scientists calculate the geodetic effect using special mathematical ideas. It starts with a description of space and time around a massive object, like Earth, using something called the Schwarzschild metric. By adding rotation to this description, scientists can predict how a spinning object, such as a gyroscope, will change its direction over time due to the curvature of space.

These calculations help us understand how gravity and rotation together affect the motion of objects in space. One key result shows that the geodetic effect follows patterns similar to those predicted by older laws of motion, but with extra details from Einstein’s theory of relativity.

Derivation using parallel transport about a circular orbit

Parallel transport describes how a free-falling object’s direction changes in space. In simple terms, it’s like moving a pencil point along a curved path while keeping it pointing the same way relative to the space around it.

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

Thomas precession

The geodetic effect can be thought of as having two parts: one is called Thomas precession, and the other is due to the shape of space and time. Some experts say 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 just 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