scholarly journals New Approach to the Earth’s Rotation Problem Consistent with the General Planetary Theory

1997 ◽  
Vol 165 ◽  
pp. 301-306 ◽  
Author(s):  
V.A. Brumberg ◽  
T. V. Ivanova
Keyword(s):  
Earth’S Rotation ◽  
Planetary Theory ◽  
The Moon ◽  
Euler Parameters ◽  
Earth's Rotation ◽  
New Approach ◽  
Poisson Equations ◽  
Translatory Motion ◽  
Lunar Evolution ◽  
General Planetary Theory

AbstractThe equations of the translatory motion of the major planets and the Moon and the Poisson equations of the Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution).

scholarly journals A supplementary note on constructing the general Earth's rotation theory

2014 ◽  
Vol 9 (S310) ◽  
pp. 13-16
Author(s):  
Victor A. Brumberg ◽  
Tamara V. Ivanova
Keyword(s):  
Equations Of Motion ◽  
Combined Treatment ◽  
Earth’S Rotation ◽  
Combined System ◽  
Euler Parameters ◽  
Earth's Rotation ◽  
The Earth ◽  
Practical Development ◽  
The Mean ◽  
General Planetary Theory

AbstractRepresenting a post-scriptum supplementary to a previous paper of the authors Brumberg & Ivanova (2011) this note aims to simplify the practical development of the Earth's rotation theory, in the framework of the general planetary theory, avoiding the non–physical secular terms and involving the separation of the fast and slow angular variables, both for planetary–lunar motion and Earth's rotation. In this combined treatment of motion and rotation, the fast angular terms are related to the mean orbital longitudes of the bodies, the diurnal and Euler rotations of the Earth. The slow angular terms are due to the motions of pericenters and nodes, as well as the precession of the Earth. The combined system of the equations of motion for the principal planets and the Moon and the equations of the Earth's rotation is reduced to the autonomous secular system with theoretically possible solution in a trigonometric form. In the above–mentioned paper, the Earth's rotation has been treated in Euler parameters. The trivial change of the Euler parameters to their small declinations from some nominal values may improve the practical efficiency of the normalization of the Earth's rotation equations. This technique may be applied to any three-axial rigid planet. The initial terms of the corresponding expansions are given in the Appendix.

scholarly journals Commission 19: Rotation of the Earth

1985 ◽  
Vol 19 (1) ◽  
pp. 193-205 ◽  
Author(s):  
Ya. S. Yatskiv ◽  
W. J. Klepczynski ◽  
F. Barlier ◽  
H. Enslin ◽  
C. Kakuta ◽  
...  
Keyword(s):  
Time Frame ◽  
Laser Ranging ◽  
Earth’S Rotation ◽  
The Moon ◽  
Earth's Rotation ◽  
The Earth ◽  
Long Time ◽  
Terrestrial Reference System ◽  
Rotation Of The Earth

During the period, work on the problem of the Earth’s rotation has continued to expand and increase its scope. The total number of institutions engaged in the determination of the Earth’s rotation parameters (ERP) by different techniques has been increased significantly. The rotation of the Earth is currently measured by classical astrometry, Doppler and laser satellite tracking, laser ranging of the Moon, and radio interferometry. Several long time series of the ERP are available from most of these techniques, in particular, those made during the Main Campaign of the MERIT project. The various series have been intercompared and their stability, in the time frame of years to days, has been estimated for the purposes of establishing a new conventional terrestrial reference system (COTES). On the other hand, the difficulties of maintaining a regular operation for laser ranging to the Moon (LLR) have been recognized. It resulted in the proposal to organize an one-month campaign of observations in 1985 in order to complement the COTES collocation program and to allow additional intercomparisons with other techniques.

scholarly journals On the Eclipse of Hipparchus

2019 ◽  
Vol 50 (1) ◽  
pp. 3-15
Author(s):  
Leslie V. Morrison ◽  
F. Richard Stephenson ◽  
Catherine Y. Hohenkerk
Keyword(s):  
Earth’S Rotation ◽  
The Moon ◽  
Earth's Rotation

We investigate the date of observation of the Hipparchus eclipse using our latest measurement of historical variations in the Earth’s rotation to plot the tracks of the potential eclipses. We conclude that Hipparchus most probably analysed the eclipse of −189 in deriving the distance to the Moon, as concluded by Toomer in 1974.

scholarly journals The oceans and the Earth's rotation

1988 ◽  
Vol 128 ◽  
pp. 349-352
Author(s):  
P. Brosche
Keyword(s):  
Solid Earth ◽  
Earth’S Rotation ◽  
The Moon ◽  
Tidal Effects ◽  
Earth's Rotation ◽  
Tidal Friction ◽  
Long Run ◽  
Short Time ◽  
Tidal Variations ◽  
Observational Techniques

In the long run, the tidal interaction between the Moon and the solid Earth is mediated by the oceans. It produces the retardation of the Earth's rotation known as ‘tidal friction’. Due to the changing configuration of the continents, it is a non-monotonic function of time. Tides of the solid Earth dominate the short-periodic tidal effects while the exchange with the atmosphere is preponderant in climatic changes, especially with an annual signature. It is shown that the influences of the oceans within such short time-scales must be taken into account for tidal and for non-tidal variations as well if one wants to model the Earth's rotation at the cm-level corresponding to the most advanced observational techniques.

scholarly journals Historic Variations in the Rotation of the Earth

1972 ◽  
Vol 48 ◽  
pp. 160-161
Author(s):  
R. R. Newton
Keyword(s):  
Earth’S Rotation ◽  
The Moon ◽  
Earth's Rotation ◽  
Tidal Friction ◽  
The Past ◽  
The Earth ◽  
Rotation Of The Earth

The purpose of this work is to investigate changes in the rotation of the Earth in the past few thousand years. Since most available observations involve the Moon, study of the Earth's rotation is inseparable from study of the Moon's motion. Since it is doubtful that present theories of tidal friction account for the present acceleration (Spencer Jones, 1939; Van Flandern, 1970; Pariisky et al., 1972) of the Moon, we cannot safely assume that consequence of the theories which says that tidal friction has been almost constant.

scholarly journals On Construction of a Long-Term Moon’s Theory

1999 ◽  
Vol 172 ◽  
pp. 415-416
Author(s):  
T.V. Ivanova
Keyword(s):  
Lunar Theory ◽  
Planetary Theory ◽  
The Moon ◽  
Planetary Orbits ◽  
Small Parameters ◽  
The One ◽  
General Planetary Theory ◽  
Laplace Type

An analytical long-term theory of the motion of the Moon is constructed within the framework of the general planetary theory (Brumberg, 1995). A method, different from the one of (Ivanova, 1997) designated below as (*), for the determination of the perturbations depending on the eccentricities and inclinations of lunar and planetary orbits is used which allows to obtain the solution of the problem in the purely trigonometric form up to any order with respect to the small parameters.The aim of this paper is to construct the long-term Lunar theory in the form consistent with the general planetary theory (Brumberg, 1995). For this purpose the Moon is considered as an additional planet in the field of eight major planets (Pluto being excluded). In the result the coordinates of the Moon may be represented by means of the power series in the evolutionary eccentric and oblique variables with trigonometric coefficients in mean longitudes of the Moon and the planets. The long-period perturbations are determined by solving a secular system in Laplace-type variables describing the secular motions of the lunar perigee and node and taking into account the secular planetary inequalities.

Sign in / Sign up

Export Citation Format

Share Document