The long period term in the mean longitude of the moon with the argument, 3J - 8 M + 4 E

1911 ◽  
Vol 27 ◽  
pp. 26
Author(s):  
William T. Carrigan
Keyword(s):  
The Moon ◽  
Long Period ◽  
Period Term ◽  
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.

On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

1966 ◽  
Vol 25 ◽  
pp. 197-222 ◽  
Author(s):  
P. J. Message
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Large Amplitude ◽  
Restricted Problem ◽  
Small Amplitude ◽  
Minor Planets ◽  
Long Period ◽  
Numerical Integrations ◽  
Period Variations ◽  
The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

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.

Slow variability and circumstellar shells of red variable stars

1987 ◽  
Vol 122 ◽  
pp. 541-542
Author(s):  
T. Lloyd Evans
Keyword(s):  
Variable Stars ◽  
Circumstellar Dust ◽  
Infrared Photometry ◽  
Constant Ratio ◽  
Giant Stars ◽  
Long Period ◽  
Period Variations ◽  
Cyclic Variations ◽  
Circumstellar Shells ◽  
The Mean

Infrared photometry shows that while all RV Tauri stars have circumstellar dust shells, the RVb stars with slow cyclic variations in mean light as well as the 30–100 day variations common to all RV stars have more hot dust close to the star (Lloyd Evans 1985). Many M giant stars which are variables of semiregular type also show long-period variations in the mean light (O'Connell 1933; Payne-Gaposchkin 1954), with a roughly constant ratio between the two periods. Payne-Gaposchkin (1954) found P2/P1 ~9.4 for red variables of type M and P2/P1 ~19.4 for stars of type F-K, most of which are FV Tauri stars. Re-analysis using the more extensive data available now indicates P2/P1 ~10 for the M giants and P2/P1 ~15 for the FV Tauri stars. The nature of the long-period variability is unknown (Wood 1975).

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.

scholarly journals North-south asynchrony and long-term variations of sunspot latitudes

2008 ◽  
Vol 4 (S259) ◽  
pp. 237-238 ◽  
Author(s):  
Nadezhda V. Zolotova ◽  
D. I. Ponyavin
Keyword(s):  
Sunspot Area ◽  
Magnetic Equator ◽  
Phase Component ◽  
Long Period ◽  
The North ◽  
Sign Change ◽  
The Mean ◽  
South Asymmetry ◽  
Northern And Southern Hemispheres

AbstractThe long-term records of sunspot area available separately for Northern and Southern Hemispheres have been investigated by means of cross-recurrence technique. Phase component of the north-south asymmetry was extracted. This measure demonstrates long-period systematic variations with the sign change of hemispheric leading in 1930s and 1960s. Moreover phase north-south asynchrony anticorrelates with the so called magnetic equator, which was defined as difference of the mean sunspot latitudes between two hemispheres. Relationships of the phase north-south asynchrony, magnetic equator and butterfly diagrams are presented and discussed.

On an inequality of long period in the motions of the Earth and Venus

1837 ◽  
Vol 3 ◽  
pp. 77-78
Keyword(s):  
Principal Term ◽  
The Sun ◽  
Method Of Calculation ◽  
The Third ◽  
Long Period ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
The Difference

The author had pointed out, in a paper published in the Philosophical Transactions for 1828, on the corrections of the elements of Delambre’s Solar Tables, that the comparison of the corrections of the epochs of the sun and the sun’s perigee, given by the late observations, with the corrections given by the observations of the last century, appears to indicate the existence of some inequality not included in the arguments of those tables. As it was necessary, therefore, to seek for some inequality of long period, he commenced an examination of the mean motions of the planets, with the view of discovering one whose ratio to the mean motion of the earth could be expressed very nearly by a proportion of which the terms are small. The appearances of Venus are found to recur in very nearly the same order every eight years; some multiple, therefore, of the periodic time of Venus is nearly equal to eight years. It is easily seen that this multiple must be thirteen; and consequently eight times the mean motion of Venus is nearly equal to thirteen times the mean motion of the earth. The difference is about one 240th of the mean annual motion of the earth; and it implies the existence of an inequality of which the period is about 240 years. No term has yet been calculated whose period is so long with respect to the periodic time of the planets disturbed. The value of the principal term, calculated from the theory, was given by the author in a postscript to the paper above referred to. In the present memoir he gives an account of the method of calculation, and includes also other terms which are necessarily connected with the principal inequality. The first part treats of the perturbation of the earth’s longitude and radius victor; the second of the perturbation of the earth in latitude; and the third of the perturbations of Venus depending upon the same arguments.

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