scholarly journals On the Desirableness of a Re-investigation of the Problems growing out of the Mean Motion of the Moon

1903 ◽  
Vol 63 (5) ◽  
pp. 316-324 ◽  
Author(s):  
S. Newcomb
Keyword(s):  
The Moon ◽  
Mean Motion ◽  
The Mean

scholarly journals On The lunar Secular Acceleration: A Possible Approach

1990 ◽  
Vol 141 ◽  
pp. 201-202
Author(s):  
V. Protitch-Benishek
Keyword(s):  
Celestial Mechanics ◽  
Numerical Evaluation ◽  
Quadratic Term ◽  
The Moon ◽  
Moon System ◽  
Secular Acceleration ◽  
Mean Motion ◽  
The Earth ◽  
Exact Agreement ◽  
The Mean

The secular quadratic term in the expression of the Moon's longitude has been introduced empirically after the conclusion that its mean motion is not constant (Halley, 1695).But, the explanation of this term and also of its numerical evaluation presented and still presents in our time great difficulties. All efforts, namely, to obtain an exact agreement between observed and theoretical value of Moon's secular acceleration were unsuccessful: the first of these two values exceeds always the second one by a very large amount. This discordance and unexplained residuals (O – C) in the mean longitude of the Moon gave rise finally to the statement that these are due to a retardation and irregularity in the Earth's rotation. But, after hardly a fifty years, this hypothesis revealed even more new difficulties and questions concerning also the problem of stability of the Earth-Moon system. It seems that there is a true reason for which this problem occurs as one of the unsolved problems of Celestial Mechanics (Brumberg and Kovalevsky, 1986; Seidelmann, 1986).

scholarly journals A first analysis of the mean motion of CHAMP

2003 ◽  
Vol 1 ◽  
pp. 95-101
Author(s):  
F. Deleflie ◽  
P. Exertier ◽  
P. Berio ◽  
G. Metris ◽  
O. Laurain ◽  
...  
Keyword(s):  
Orbital Motion ◽  
Surface Forces ◽  
The Moon ◽  
Orbital Elements ◽  
Champ Satellite ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
Low Altitude

Abstract. The present study consists in studying the mean orbital motion of the CHAMP satellite, through a single long arc on a period of time of 200 days in 2001. We actually investigate the sensibility of its mean motion to its accelerometric data, as measures of the surface forces, over that period. In order to accurately determine the mean motion of CHAMP, we use “observed" mean orbital elements computed, by filtering, from 1-day GPS orbits. On the other hand, we use a semi-analytical model to compute the arc. It consists in numerically integrating the effects of the mean potentials (due to the Earth and the Moon and Sun), and the effects of mean surfaces forces acting on the satellite. These later are, in case of CHAMP, provided by an averaging of the Gauss system of equations. Results of the fit of the long arc give a relative sensibility of about 10-3, although our gravitational mean model is not well suited to describe very low altitude orbits. This technique, which is purely dynamical, enables us to control the decreasing of the trajectory altitude, as a possibility to validate accelerometric data on a long term basis.Key words. Mean orbital motion, accelerometric data

On the mean motion of the Moon

1877 ◽  
Vol s3-14 (83) ◽  
pp. 401-410
Author(s):  
S. Newcomb
Keyword(s):  
The Moon ◽  
Mean Motion ◽  
The Mean

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

scholarly journals On tho proportions of the prevailing winds, the mean temperature, and depth of rain in the climate of London, computed through a cycle of Eighteen Years, or periods of the Moon’s declination

1843 ◽  
Vol 4 ◽  
pp. 300-300
Keyword(s):  
The Moon ◽  
Fair Weather ◽  
North West ◽  
West Wind ◽  
North East ◽  
East Wind ◽  
The North ◽  
The Common ◽  
The Mean ◽  
Solar Influence

In this paper the author investigates the periodical variations of the winds, rain and temperature, corresponding to the conditions of the moon’s declination, in a manner similar to that he has already followed in the case of the barometrical variations, on a period of years extending from 1815 to 1832 inclusive. In each case he gives tables of the average quantities for each week, at the middle of which the moon is in the equator, or else has either attained its maximum north or south declination. He thus finds that a north-east wind is most promoted by the constant solar influence which causes it, when the moon is about the equator, going from north to south; that a south-east wind, in like manner, prevails most when the moon is proceeding to acquire a southern declination ; that winds from the south and west blow more when the moon is in her mean degrees of declination, going either way, than with a full north or south declination ; and that a north-west wind, the common summer and fair weather wind of the climate, affects, in like manner, the mean declination, in either direction, in preference to the north or south, and most when the moon is coming north. He finds the average annual depth of rain, falling in the neighbourhood of London, is 25’17 inches.

scholarly journals Precise Reduction to the Apparent Places of Stars

1974 ◽  
Vol 61 ◽  
pp. 319-319
Author(s):  
S. Yumi ◽  
K. Hurukawa ◽  
Th. Hirayama
Keyword(s):  
The Sun ◽  
Maximum Difference ◽  
The Moon ◽  
Uniform System ◽  
Outer Planets ◽  
The Mean ◽  
Astronomical Constants

For a precise reduction to the apparent places of the stars in a uniform system during the 19th and 20th centuries, the ‘Solar Coordinates 1800–2000’ by Herget (Astron. Papers14, 1953) may conveniently be used, because no coordinates of the Sun, referred to the mean equinox of 1950.0, are given in the Astronomical Ephemeris before 1930.A maximum difference of 0″.0003 was found between the aberrations calculated from both the Astronomical Ephemeris and Herget's Tables for the period 1960–1969, taking into consideration the effect of the outer planets, which amounted to 0″.0109.The effect of the inner planets on the aberration is estimated to be of the order of 0″.0001 at the most and the correction for the lunar term due to the change in astronomical constants is 0″.00002. It is recommended that the solar coordinates be calculated directly from Newcomb's formulae taking the effects of all the planets into consideration, but the effect concerned with the Moon can be neglected.

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