Tesseral harmonics of the gravitational potential of the earth as derived from satellite motions

1961 ◽  
Vol 66 ◽  
pp. 355 ◽  
Author(s):  
Yoshihide Kozai
Keyword(s):  
Gravitational Potential ◽  
The Earth ◽  
Tesseral Harmonics

INVESTIGATION OF THE ABSOLUTENESS OF TIME

2021 ◽  
pp. 51-54
Author(s):  
S. Tiguntsev
Keyword(s):  
High Precision ◽  
Gravitational Potential ◽  
High Speed ◽  
Relativistic Effect ◽  
Theoretical Research ◽  
Clock Frequency ◽  
Positioning Systems ◽  
The Earth ◽  
Flow Of Time ◽  
The Difference

In classical physics, time is considered absolute. It is believed that all processes, regardless of their complexity, do not affect the flow of time The theory of relativity determines that the flow of time for bodies depends both on the speed of movement of bodies and on the magnitude of the gravitational potential. It is believed that time in space orbit passes slower due to the high speed of the spacecraft, and faster due to the lower gravitational potential than on the surface of the Earth. Currently, the dependence of time on the magnitude of the gravitational potential and velocity (relativistic effect) is taken into account in global positioning systems. However, studying the relativistic effect, scientists have made a wrong interpretation of the difference between the clock frequency of an orbiting satellite and the clock frequency on the Earth's surface. All further studies to explain the relativistic effect were carried out according to a similar scenario, that is, only the difference in clock frequencies under conditions of different gravitational potentials was investigated. While conducting theoretical research, I found that the frequency of the signal changes along the way from the satellite to the receiver due to the influence of Earth's gravity. It was found that the readings of two high-precision clocks located at different heights will not differ after any period of time, that is, it is shown that the flow of time does not depend on the gravitational potential. It is proposed to conduct full-scale experiments, during which some high-precision clocks are sent aboard the space station, while others remain in the laboratory on the surface of the earth. It is expected that the readings of the satellite clock will be absolutely identical to the readings of the clock in the Earth laboratory.

scholarly journals The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Jarbas Cordeiro Sampaio ◽  
Rodolpho Vilhena de Moraes ◽  
Sandro da Silva Fernandes
Keyword(s):  
Dynamical System ◽  
Numerical Integration ◽  
Lyapunov Exponents ◽  
Orbital Dynamics ◽  
Zonal Harmonics ◽  
Chaotic Orbits ◽  
The Earth ◽  
Tesseral Harmonics ◽  
Final System

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonicsJ20andJ40and the tesseral harmonicsJ22andJ42are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.

scholarly journals Rotation of the Rigid Earth

1997 ◽  
Vol 165 ◽  
pp. 295-300
Author(s):  
P. Bretagnon
Keyword(s):  
Time Domain ◽  
Time Span ◽  
Euler Angles ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Rigid Earth ◽  
The Time Domain ◽  
Tesseral Harmonics ◽  
External Forces

AbstractWe present the results of a solution of the Earth’s rotation built with analytical solutions of the planets and of the Moon’s motion. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth for the zonal harmonics Cj,0 for j from 2 to 5, and also for the tesseral harmonics C2,2, S2,2C3,k, S3,k for k from 1 to 3 and C4,1, S4,1. We determine three Euler angles ψ, ω, and φ by calculating the components of the torque of the external forces with respect to the geocenter in the case of the rigid Earth. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900–2050. The differences do not exceed 16 μas for ψ and 8 μas for ω whereas the contribution of the tesseral harmonics reaches 150 μas in the time domain.

On the motion of nearly synchronous satellites

1965 ◽  
Vol 288 (1412) ◽  
pp. 60-68 ◽  
Keyword(s):  
Disturbing Function ◽  
One Dimensional ◽  
The Earth ◽  
Tesseral Harmonics ◽  
Correction Terms

The longitudinal forces due to the very slight asymmetry of the Earth about its axis can have considerable effects on nearly synchronous satellites. For orbits of general inclination and eccentricity the disturbing function for the combination of all tesseral harmonics is developed in terms of the usual elliptic elements and the resonant terms retained. Provided the eccentricity is small and the satellite nearly synchronous, the motion in mean longitude relative to the Earth is approximately equivalent to a particle moving in a one-dimensional potential. The analysis is carried to the stage where it could be used to determine the even tesseral harmonic coefficients from observations on existing synchronous satellites, giving due consideration to lunisolar effects and other correction terms.

Sign in / Sign up

Export Citation Format

Share Document