What Is Geodesic?

Geodesics, also called geodesics or geodesics, can be defined as the local shortest or longest path at two points in space. The name Geodesic comes from Geodesy for the size and shape of the earth.

Geodesic Overview

Also called Geodesic Effect or Geodetic Precession refers to the influence of the space-time curvature of the gravitational field on the motion state of the test mass with spin angular momentum in the general relativity prediction. This caused the precession of the spin angular momentum of the test mass along the geodesic in the gravitational field. This effect is today an experimental verification method for general relativity and has been confirmed in observations by the scientific detection satellite "Gravity Detector B" launched by NASA in 2004.

Geodesic effect diagram

Geodesic interpretation

Since general relativity itself is a geometric theory, all gravitational effects can be explained by the curvature of space-time, and the geodesic effect is no exception. However, the precession of spin angular momentum can also be understood in part from one of the alternative theories of general relativity, gravity magnetism. ^[4]

From the perspective of gravitational magnetism, the geodesic effect originates first from the orbital-spin coupling effect. In the observation of Gravity Probe B, this is the interaction of the gyroscope's spin and the Earth's mass flow in the center of the orbit. Essentially, this is analogous to Thomas Precession in electromagnetic theory. The precession caused by this interaction contributes a third of all geodesic precessions.

The other two-thirds contribution cannot be explained by gravitational magnetism, but can only be considered to come from the curvature of space-time. In simple terms, the direction of the spin angular momentum of orbital motion in flat spacetime will tilt as the spacetime curve caused by the gravitational field. This is actually not difficult to understand: a vector perpendicular to a plane will definitely change direction when the plane is bent. According to the calculation, the circumference of the orbit around the gravitational prober B will be 1.1 inches (about 2.8 cm) shorter than the perimeter due to the gravitational field of the earth. This example is often used in the research of gravitational prober B. Known as the "lost inch". In gravitational prober B's polar orbit at an altitude of 642 kilometers, the theory of general relativity predicts that the sum of the geodesic effects on the orbital plane due to the spin-orbit coupling and the space-time curvature is 6.606 arc seconds per year ( (About 0.0018 degrees). This is already a significant effect on the relativistic effect in the weak gravitational field (the reference frame drag of the earth's gravitational field, which is also one of the observation tasks of the gravitational detector B, is 170 times weaker than the geodesic effect) . The observation results of Gravitational Detector B were first reported at the April Annual Meeting of the American Physical Society in April 2007, and their observations and theoretical errors were less than 1%.