Geodesic line is also calledBig ground wireorGeodesic, which can be defined as the local shortest or longest path of two points in space.The name Geodesic comes fromearthSize and shapeGeodesy(Geodesy)。
It's a man with Riemann connectionsRiemannian manifold。If a parametric curve
stay
There are
, the curve is said to be at point
Geodesic survey at.If for
If every point is geodesic, the curve is called geodesic.[5]
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Objects like the earth are notgravitationThe force ofCurved spaceThe track motion of the geodesic is the closest to the straight line in the.For example, the surface of the earth is curved2D space。The geodesic on the earth is called the great circle, which is the nearest path between two points.Since the geodesic line is the shortest distance between two airports, this is the route that the pilot asks the pilot to fly.stayGeneral relativityThe object always followsFour-dimensional space-timeThe geodesic line of.Nevertheless, in ourthree-dimensional spaceIt seems that it follows a curved path (it is just like watching an airplane flying over the ground with many mountainsthree-dimensional spaceIts shadow follows a curved path on the two-dimensional ground.[1]
Geodesic
Geodesic
If two surfaces are tangent along a curve, and this curve is the geodesic line of one surface, it is also the geodesic line of the other surface.At any point on the surface, given the tangent direction of a surface, there is a unique geodesic tangent in this direction.The geodesic line connecting any two points in an appropriate small range is the shortest line, so the geodesic line is also called geodesic line.[2]
Geodetic effect
The light passes through aMassive celestial bodyIn the vicinitygravitationUnder the action (or entering the curved space near the object), the route will deflect, which is called "geodesic effect".[3]
The professional term of the curve with the shortest distance in relativity is geodesic. In fact, the three kinds of geodesics corresponding to the speed less than C, equal to C, and greater than C are respectively called time-like geodesics, quasi optical geodesics, and quasi aerial geodesics.Therefore, if it is not affected by other forces other than gravity, the object will move on the timelike or optical geodesic line (because no object's speed can exceedlight speed）
For example, an object like the earth does not move along a curved orbit under the action of a force called gravity;On the contrary, the reason why they move along a curved track is that they follow a path closest to a straight line in curved space, which is called geodesic.In technical terms, a geodesic is defined as the shortest (or longest) path between two adjacent points.
From the point of view of gravitation and magnetism, the geodesic effect first comes from the orbit-Spin couplingeffect.In the observation of gravitational detector B, this isGravity detector BIngyroscopeAnd the mass flow of the earth at the center of the orbitInteraction。In essence, this can be completely compatible withElectromagnetic theoryThomas precession in.The precession caused by this interaction accounts for one third of the total geodesic precession.
The other two-thirds of the contribution cannot be explained by gravitational magnetism, but can only be attributed to the curvature of space-time.In short,Flat spacetimeOrbitingspinangular momentumThe direction will followgravitational fieldResultingSpace-time curvatureAnd tilt.This is not difficult to understand: the vector perpendicular to a plane will certainly change direction after the plane bends.According to calculation,gravitationThe perimeter of detector B's earth orbit is due toGravity of the earthThe influence of the field will be 1.1 inches shorter than the perimeter without considering the gravitational field. This example is often referred to as the "lost inch" in the research of Gravity Detector B.stayGravity detector BAt an altitude of 642 kilometersPolar orbitOn,General relativityThe theory predicts that due to spin orbitcouplingandSpatiotemporal curvatureResulting fromTrack planeOnGeodetic effect Sum is per yearPrecessionsix point six zero sixAngular second(about 0.0018 degrees).This is important for the weak gravitational fieldrelativityAs for the effect, it has already been a quite significant influence (as one of the observation tasks of Gravity Detector BReference System Drag170 times weaker than the geodesic effect).The observation results of Gravity Probe B were first held in April 2007American Physical SocietyA quick report was made at the annual meeting in April, and its observation results are consistent withTheoretical errorLess than 1%.
