Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

scholarly journals IV. On the dynamical theory of the tides of long period

1887 ◽  
Vol 41 (246-250) ◽  
pp. 337-342 ◽  
Keyword(s):  
Angular Velocity ◽  
Dynamical Theory ◽  
Equilibrium Theory ◽  
Earth’S Rotation ◽  
Laplace’S Method ◽  
Earth's Rotation ◽  
Long Period ◽  
Laplace's Method ◽  
William Thomson

In the following note an objection is raised against Laplace’s method of treating these tides, and a dynamical solution of the problem, founded on a paper by Sir William Thomson, is offered. Let θ , Φ be the colatitude and longitude of a point in the ocean, let ξ and η sin θ be the displacements from its mean position of the water occupying that point at the time t , let h be the height of the tide, and let ℓ be the height of the tide according to the equilibrium theory; let n be the angular velocity of the earth’s rotation, g gravity, a the earth’s radius, and γ the depth of the ocean at the point θ , Φ .

scholarly journals On the Effect of Ocean Tides on the Secular Retardation of the Earth's Rotation

1972 ◽  
Vol 48 ◽  
pp. 240-240 ◽  
Author(s):  
N. N. Pariisky ◽  
M. V. Kuznetsov ◽  
L. V. Kuznetsova
Keyword(s):  
World Ocean ◽  
Classical Problem ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Tidal Waves ◽  
Tidal Forces ◽  
The Earth ◽  
Secular Variations ◽  
Bodily Tides ◽  
Frictional Forces

The classical problem of determining the secular retardation of the Earth's rotation due to the effect of tides (oceanic and bodily) has an important geophysical value in determining the possible existence of processes inside the Earth, which lead to secular variations of rotation of the whole Earth or its external layers.Using new cotidal charts of the world ocean calculated by Bogdanov for the main tidal waves M2, S2, K1 and O1 and using the method of moments of tidal forces the retarding moment was found to be 8.3 × 1023 dyn cm. This is twice the amount of previous evaluations. (This method is superior to the method of calculating the dissipation of energy or the moments of frictional forces). This amount corresponds to a retardation of 3.8 μs/century in the speed of the Earth's rotation. But the observations of the Sun give only 1.9 μs/century for the retardation. Thus, there seem to be nontidal and probably internal processes, which accelerate the Earth's rotation by about 2 μs/century. And this is without taking account of additional smaller effects of bodily tides. The search for these processes is an important problem.The full text of the paper will be published in the magazine Physics of the Earth, No. 2, 1972.

On Some Problems of BIH and IPMS Services

1975 ◽  
Vol 26 ◽  
pp. 409-413
Author(s):  
P. Melchior
Keyword(s):  
Polar Motion ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
General Opinion

The ideas I shall try to develop are probably not original but I hope they reflect a general opinion of those who have looked into the problem of the Earth’s rotation.We must examine here related points:1. The polar motion and the variation of UT1.2. The system of reference with respect to which these periodic or secular variations are described.

scholarly journals Earth rotation from a simultaneous reduction of LLR and LAGEOS laser ranging data

1981 ◽  
Vol 63 ◽  
pp. 31-40
Author(s):  
Peter J. Shelus ◽  
Nelson R. Zarate ◽  
Richard J. Eanes
Keyword(s):  
Earth Rotation ◽  
Artificial Satellite ◽  
Laser Ranging ◽  
Earth’S Rotation ◽  
Lunar Laser Ranging ◽  
Earth's Rotation ◽  
Accuracy And Precision ◽  
Lunar Laser ◽  
Single Station ◽  
Three Components

As the techniques of lunar and artificial satellite laser ranging mature, emphasis is being placed upon the use of these observations to monitor the Earth’s rotation. It is important to note, however, that at the present time neither technique alone can furnish all three components of this rotation to an accuracy which surpasses those results obtained from classical techniques. In the case of LAGEOS laser ranging, unmodeled secular orbital effects couple with axial Earth rotation in such a way that these effects are not separable in the analysis of those observations. In the case of lunar laser ranging, observations have been regularly available only from a single station for the past ten years or so with the result that a change in latitude along the McDonald Observatory meridian is not separable into the ordinary (x,y) components of polar motion. The main purpose of this paper is to present the first stages of an investigation to combine LAGEOS and lunar laser ranging observations. It is hoped that the proper implementation of such a process might eliminate the shortcomings inherent in each technique, while accentuating the advantages of each. This has the potential of producing all three components of the Earth’s rotation to an accuracy and precision which is compatible with the present observational uncertainties.

scholarly journals The relationship between global volcanic activity and variations in the velocity of Earth's rotation

2019 ◽  
Vol 484 (6) ◽  
pp. 729-733
Author(s):  
B. W. Levin ◽  
E. V. Sasorova ◽  
V. B. Gurianov ◽  
V. V. Yarmolyuk
Keyword(s):  
United States ◽  
Angular Velocity ◽  
Volcanic Activity ◽  
Rotational Velocity ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Deceleration Phase ◽  
The Earth ◽  
Smithsonian Institute ◽  
The Relationship

Analysis of observations of the Earth's rotational velocity and volcanic activity of the planet from 1720 until 2015 suggests that higher volcanic activity temporally coincided with periods of decreased angular velocity of Earth's rotation (deceleration), and, vice versa, lower volcanic activity coincided with the periods of increased velocity of the Earth's rotation (acceleration). Our analysis employed the data from the catalog by the Smithsonian Institute, United States, in which each volcanic explosion had its own determined value of the Volcanic Explosivity Index (VEI). The total number of selected intensive eruptions with VEI > 4 was 160, including 25 eruptions with VEI > 5. At present (beginning from 2006), the Earth was entry in a deceleration phase and series of catastrophic eruptions reveals the tendency toward intensifying volcanic activity.

Effect of the Change in the Geomagnetic Dipole Moment on the Rate of the Earth's Rotation

1972 ◽  
Vol 48 ◽  
pp. 229-230
Author(s):  
Takesi Yukutake
Keyword(s):  
Dipole Moment ◽  
Angular Velocity ◽  
Electromagnetic Coupling ◽  
Dipole Field ◽  
Earth’S Rotation ◽  
Present Moment ◽  
Earth’S Core ◽  
Earth's Rotation ◽  
Earth's Core ◽  
Geomagnetic Dipole

The electromagnetic coupling between the Earth's core and the mantle is studied when the geomagnetic dipole field varies periodically. The oscillation of the geomagnetic dipole moment with a period of 8000 years, its amplitude being 50% of the present moment, is capable of causing a fluctuation of 10−11 rad/s in the angular velocity of the mantle. The angular velocity increases with a decrease in the dipole moment.

Sign in / Sign up

Export Citation Format

Share Document