11/14/2023 0 Comments Precise astrometryNowadays a major breakthrough is on the way due to astrometric sky surveys from space. Over the centuries astrometry has greatly contributed to the advance of the knowledge of the Universe. This contribution focuses on the importance of astrometry and on its future developments. Astronomical Observatory of Padova, National Institute for Astrophysics (INAF), Padova, Italy.the metric, \(g_ time derivatives of the metric tensor both in the gravity field equations and in the equations of motion of test particles and massive bodies and parametrizes the post-Newtonian expansion of these equations in the form of a slow-motion parameter ( Kopeikin 2004).The most important tensors of the spacetime manifold are: This leads to introduction of more complicated mathematical objects on the manifold - functions, curves, vectors and tensors. The goal of the differential geometry is to establish the geometric relationships between the points of the manifold. The manifold has four dimensions but no rigidly-defined relationships between the points, like the distance. A continuous set of points forms a mathematical structure known as spacetime manifold. The most primitive physical object can be modeled as a point occupying no volume in spacetime. Hence, we shall ignore the hypothetical but still unobservable, relativistic effects associated with extra-dimensions. The world may have more dimensions at microscopic level as predicted by advanced unified field theories but those dimensions are irrelevant for interpretation of modern astrometric observations and for constructing the fundamental inertial frame in the sky. We all live in four-dimensional world called spacetime. Theoretical Foundations Spacetime manifold
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