scholarly journals On the effect of ocean tides and tesseral harmonics on spacecraft flybys of the Earth

2016 ◽  
Vol 463 (2) ◽  
pp. 2119-2124 ◽  
Author(s):  
L. Acedo
Keyword(s):  
Ocean Tides ◽  
The Earth ◽  
Tesseral Harmonics

scholarly journals Evaluation of global ocean tide models based on tidal gravity observations in China

2020 ◽  
Author(s):  
Hongbo Tan ◽  
Chongyong Shen ◽  
Guiju Wu
Keyword(s):  
High Precision ◽  
Earth Tide ◽  
Global Ocean ◽  
Ocean Tide ◽  
Ocean Tides ◽  
Ocean Tide Model ◽  
Tidal Forces ◽  
The Earth ◽  
Gravity Observation ◽  
Ocean Tide Models

<p>Solid Earth is affected by tidal cycles triggered by the gravity attraction of the celestial bodies. However, about 70% the Earth is covered with seawater which is also affected by the tidal forces. In the coastal areas, the ocean tide loading (OTL) can reach up to 10% of the earth tide, 90% for tilt, and 25% for strain (Farrell, 1972). Since 2007, a high-precision continuous gravity observation network in China has been established with 78 stations. The long-term high-precision tidal data of the network can be used to validate, verifying and even improve the ocean tide model (OTM).</p><p>In this paper, tidal parameters of each station were extracted using the harmonic analysis method after a careful editing of the data. 8 OTMs were used for calculating the OTL. The results show that the Root-Mean-Square of the tidal residuals (M<sub>0</sub>) vary between 0.078-1.77 μgal, and the average errors as function of the distance from the sea for near(0-60km), middle(60-1000km) and far(>1000km) stations are 0.76, 0.30 and 0.21 μgal. The total final gravity residuals (Tx) of the 8 major constituents (M<sub>2</sub>, S<sub>2</sub>, N<sub>2</sub>, K<sub>2</sub>, K<sub>1</sub>, O<sub>1</sub>, P<sub>1</sub>, Q<sub>1</sub>) for the best OTM has amplitude ranging from 0.14 to 3.45 μgal. The average efficiency for O<sub>1</sub> is 77.0%, while 73.1%, 59.6% and 62.6% for K<sub>1</sub>, M<sub>2</sub> and Tx. FES2014b provides the best corrections for O<sub>1</sub> at 12 stations, while SCHW provides the best for K<sub>1 </sub><sub>,</sub>M<sub>2</sub>and Tx at 12,8and 9 stations. For the 11 costal stations, there is not an obvious best OTM. The models of DTU10, EOT11a and TPXO8 look a litter better than FES2014b, HAMTIDE and SCHW. For the 17 middle distance stations, SCHW is the best OTM obviously. For the 7 far distance stations, FES2014b and SCHW model are the best models. But the correction efficiency is worse than the near and middle stations’.</p><p>The outcome is mixed: none of the recent OTMs performs the best for all tidal waves at all stations. Surprisingly, the Schwiderski’s model although is 40 years old with a coarse resolution of 1° x 1° is performing relative well with respect to the more recent OTM. Similar results are obtained in Southeast Asia (Francis and van Dam, 2014). It could be due to systematic errors in the surroundings seas affecting all the ocean tides models. It's difficult to detect, but invert the gravity attraction and loading effect to map the ocean tides in the vicinity of China would be one way.</p>

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.

scholarly journals Rotational Accelerations

1972 ◽  
Vol 48 ◽  
pp. 162-164 ◽  
Author(s):  
Wm. Markowitz
Keyword(s):  
Earth Tides ◽  
Ocean Tides ◽  
Maximum Acceleration ◽  
Secular Changes ◽  
The Core ◽  
The Earth

Rotational accelerations of the Earth arise from changes in speed of rotation: periodic, irregular, and secular. Changes are caused by winds, Earth tides, ocean tides, and motions of the core. The semimonthly lunar body tide produces the maximum acceleration.

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.

V. On the bodily tides of viscous and semi-elastic spheroids, and on the ocean tides on a yielding nucleus

1878 ◽  
Vol 27 (185-189) ◽  
pp. 419-424
Keyword(s):  
Viscous Fluid ◽  
Thin Shell ◽  
Elastic Solid ◽  
The State ◽  
Internal Strain ◽  
Incompressible Viscous Fluid ◽  
Elastic Sphere ◽  
Ocean Tides ◽  
The Earth ◽  
Bodily Tides

Sir W. Thomson’s investigation of the bodily tides of an elastic sphere has gone far to overthrow the idea of a semi-fluid interior to the earth, yet geologists are so strongly impressed by the fact that enormous masses of rock have been poured out of volcanic vents in the earth’s surface, that the belief is not yet extinct that we live on a thin shell over a sea of molten lava. It appeared to me, therefore, to be of interest to investigate the consequences which would arise from the supposition that the matter constituting the earth is of a viscous or imperfectly elastic nature. In this paper I follow out these hypo-theses, and it will be seen that the results are fully as hostile to the idea of any great mobility of the interior of the earth as are those of Sir W. Thomson. I begin by showing that the equations of flow of an incompressible viscous fluid have precisely the same form as those of strain of an incompressible elastic solid, at least when inertia is neglected. Hence, every problem about the strains of the latter has its analogue touching the flow of the former. This being so, the solution of Sir W. Thomson’s problem of the bodily tides of an elastic sphere may be adapted to give the bodily tides of a viscous spheroid. Sir W. Thomson, however, introduces the effects of the mutual gravitation of the parts of the sphere, by a synthetical method, after he has found the state of internal strain of an elastic sphere devoid of gravitational power The parallel synthetical method becomes, in the case of the viscous spheroid, somewhat complex, and I have preferred to adapt the solution analytically so as to include gravitation.

Lunar ranging experiment ephemerides and the reduction of observations (summary only)

1977 ◽  
Vol 284 (1326) ◽  
pp. 467-467
Keyword(s):  
Solid Body ◽  
Equations Of Motion ◽  
The Body ◽  
Lunar Orbit ◽  
Earth Tides ◽  
Lunar Laser Ranging ◽  
Fitting Procedure ◽  
The Earth ◽  
Starting Conditions ◽  
Tesseral Harmonics

The generation of a lunar laser ranging ephemeris uses numerical integrations of the lunar orbit and physical librations and a data fitting procedure. The relativistic equations of motion for the nine planets and the Moon are simultaneously integrated with perturbations on the lunar orbit from zonal harmonics of the Earth through degree four, lunar tesseral harmonics through degree and order three, and a tidal bulge on the Earth. The integration of the lunar rotation follows from the torques of the Earth and Sun on a solid body Moon with gravitational harmonics through degree and order three. The fitting program utilizes the integrations of the orbit and physical librations, nominal values of U.T. 1 and polar motion from the Bureau International de l’Heure, and includes corrections for atmospheric delays, nutations of the Earth’s pole taken to the body axis, solid body Earth tides, monthly and bimonthly tidal corrections in U. T. 1, and relativistic clock transformations. Not only do the fits give new starting conditions for the orbit and libration integrations but improved observatory and retroreflector coordinates, the mass ratio Sun/(Earth + Moon), and harmonics of the lunar gravity field.

scholarly journals Constants related to the Earth and Moon

1965 ◽  
Vol 21 ◽  
pp. 67-79
Author(s):  
Harold Jeffreys
Keyword(s):  
Gravitational Field ◽  
The Moon ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Tesseral Harmonics

The author discusses various determinations of zonal and tesseral harmonics of the Earth's gravitational field, the values of the solar parallax, and the constants related to the figure of the Moon and its motion.

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