scholarly journals On the value of the secular acceleration of the mean longitude of the moon

1919 ◽  
Vol 95 (669) ◽  
pp. 300-302
Keyword(s):  
Present Note ◽  
Theoretical Development ◽  
The Moon ◽  
Secular Acceleration ◽  
The Mean ◽  
Solar Eclipses

It is known that Hansen employed 12·8" for the value of the secular acceleration of the mean longitude of the Moon, instead of the value 6·18" deduced from theory, for the reason that the results of his theoretical development could not be brought by any smaller value into accord with the observations of the early solar eclipses and the later Greenwich observations. Later research has shown that these early solar eclipses can be as well represented by the theoretical value of the secular acceleration as by the empirical value employed by Hansen in his tables, and the present note will suffice to show that the more modern observations can also be represented by the theoretical value of the secular acceleration, thus serving to reconcile theory and observation.

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).

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.

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 The Role of Occultations in the Improvement of the Lunar Ephemeris

1972 ◽  
Vol 47 ◽  
pp. 395-401
Author(s):  
L. V. Morrison
Keyword(s):  
Time Scale ◽  
The Moon ◽  
Secular Acceleration ◽  
Lunar Ephemeris ◽  
Occultation Data ◽  
Correction Terms ◽  
Empirical Constants ◽  
Atomic Time

Analyses of occultation timings show that periodic correction terms with semi-amplitude as great as 0.″18 arise from corrections required to the empirical constants of the Brown/Eckert theory. Using the atomic time-scale, some of the occultation data have been used to determine a correction of – 30 ± 16″/cy2 to Spencer Jones' value for the secular acceleration of the Moon. In the light of this correction, and previous determinations, attention is drawn to the possible weakness of Spencer Jones' value, which is not reflected in his quoted error of ± 1″/cy2. Further analyses of 50000 occultations observed since 1943 promise to reveal more accurately-determined corrections.

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 IV. Further particulars of the transit of Venus across the Sun, December 9, 1874; observed on the Himalaya Mountains, Mussoorie, at Mary-Villa station, Lat. 30° 28' N., Long. 78° 3' E., height above sea 6,765 feet, with the Royal Society’s 5-inch equatoreal. Note III

1879 ◽  
Vol 29 (196-199) ◽  
pp. 297-302
Keyword(s):  
Present Note ◽  
The Sun ◽  
The Mean ◽  
The Himalaya ◽  
Himalaya Mountains

1. The object of the present note is to add to Notes I and II some particulars of the transit not detailed in those notes. The latter contained only sufficient extracts from my observatory notes in connexion chiefly with the three contacts which I observed; as, however, various other facts, besides the contacts, were developed in course of the transit, and elicited remarks from me at the time, it seems desirable that a complete transcript of these observatory notes should also be put on record; both in connexion with what hereafter follows, and also to meet any possible future requirements of details, such as expressed by Captain Tupman in his discussion of the mean solar parallax.

scholarly journals The mean distance to the Moon as determined by radar

1965 ◽  
Vol 21 ◽  
pp. 81-93 ◽  
Author(s):  
B. S. Yaplee ◽  
S. H. Knowles ◽  
A. Shapiro ◽  
K. J. Craig ◽  
D. Brouwer
Keyword(s):  
The Moon ◽  
The Earth ◽  
Lunar Topography ◽  
Radar Measurements ◽  
The Mean

The results of 1959-1960 radar measurements of the distance of the Moon are given. The method of reduction of the data is described The possible effects of lunar topography and errors of other origins are discussed, as well as the effects of different constants such as the radii of the Earth and of the Moon.

scholarly journals Effects of Solar Invasion on Earth Observation Sensors at a Moon-Based Platform

2019 ◽  
Vol 11 (23) ◽  
pp. 2775
Author(s):  
Hanlin Ye ◽  
Wei Zheng ◽  
Huadong Guo ◽  
Guang Liu ◽  
Jinsong Ping
Keyword(s):  
Mean Value ◽  
Earth Observation ◽  
The Sun ◽  
The Moon ◽  
Entrance Pupil ◽  
Evaluation Approach ◽  
The Mean ◽  
Potential Damage ◽  
Geometrical Relationship ◽  
Key Parameter

The solar invasion to an Earth observation sensor will cause potential damage to the sensor and reduce the accuracy of the measurements. This paper investigates the effects of solar invasion on the Moon-based Earth observation sensors. Different from the space-borne platform, a Moon-based sensor can be equipped anywhere on the near-side of the Moon, and this makes it possible to reduce solar invasion effects by selecting suitable regions to equip sensors. In this paper, methods for calculating the duration of the Sun entering of the sensor’s field of view (FOV) and the solar invasion radiation at the entrance pupil of the sensor are proposed. By deducing the expressions of the proposed geometrical relationship between the Sun, Earth, and Moon-based platform, it has been found that the key parameter to the effects of solar invasion is the angle between the Sun direction and the line-of-sight vector. Based on this parameter, both the duration and radiation can be calculated. In addition, an evaluation approach based on the mean value and standard deviation has been established to compare the variation of solar invasion radiation at different positions on the lunar surface. The results show that the duration is almost the same wherever the sensor is placed in the permanent Earth-observation region. Further, by comparing the variation of solar invasion radiation at different positions on the near-side of the Moon, we suggest that equipping sensors on the mid–high latitude regions within the permanent Earth-observation region will result in less solar invasion affects.

Sign in / Sign up

Export Citation Format

Share Document