Dynamics of a vertical flight in the stationary gravitational field of a celestial body: Post-newtonian corrections and gravitational redshift
- Institute of Theoretical and Experimental Physics (Russian Federation)
The standard problem of a radial motion of test particles in the stationary gravitational field of a spherically symmetric celestial body is solved and is used to determine the time features of this motion. The problem is solved for the equations of motion of general relativity (GR), and the time features are obtained in the post-Newtonian approximation, with linear GR corrections proportional to r{sub g}/r and {beta}{sup 2} (in the solution being considered, they are of the same order of smallness) being taken rigorously into account. Total times obtained by integrating the time differentials along the trajectories of motion are considered as the time features in question. It is shown that, for any parameters of the motion, the proper time (which corresponds to watches comoving with a test particle) exceeds the time of watches at rest (watches at the surface of the celestial body being considered). The mass and the radius of the celestial body, as well as the initial velocity of the test particle, serve as arbitrary parameters of the motion. The time difference indicated above implies a leading role of the gravitational redshift, which decreases somewhat because of the opposite effect of the Doppler shift. The results are estimated quantitatively for the important (from the experimental point of view) case of vertical flights of rockets starting from the Earth's surface. In this case, the GR corrections, albeit being extremely small (a few microseconds for several hours of the flight), aremeasurable with atomic (quantum) watches.
- OSTI ID:
- 21439613
- Journal Information:
- Physics of Atomic Nuclei, Vol. 73, Issue 4; Other Information: DOI: 10.1134/S1063778810040071; Copyright (c) 2010 Pleiades Publishing, Ltd.; ISSN 1063-7788
- Country of Publication:
- United States
- Language:
- English
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COSMOLOGY AND ASTRONOMY
APPROXIMATIONS
ATOMIC CLOCKS
CORRECTIONS
DOPPLER EFFECT
EQUATIONS OF MOTION
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
MASS
MATHEMATICAL SOLUTIONS
RED SHIFT
SPHERICAL CONFIGURATION
STARS
TEST PARTICLES
TRAJECTORIES
CALCULATION METHODS
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVITY THEORY