scholarly journals The yielding of the earth to disturbing forces

1909 ◽  
Vol 82 (551) ◽  
pp. 73-88 ◽  
Keyword(s):  
Spherical Surface ◽  
The State ◽  
Equilibrium Theory ◽  
Uniform Density ◽  
The Sun ◽  
Additional Hypothesis ◽  
Long Period ◽  
The Earth ◽  
Additional Qualification

1. Any estimate of the rigidity of the Earth must be based partly on some observations from which a deformation of the Earth’s surface can be inferred, and partly on some hypothesis as to the internal constitution of the Earth. The observations may be concerned with tides of long period, variations of the vertical, variations of latitude, and so on. The hypothesis must relate to the arrangement of the matter as regards density in different parts, and to the state of the parts in respect of solidity, compressibility, and so on. In the simplest hypothesis, the one on which Lord Kelvin’s well-known, estimate was based, the Earth is treated as absolutely incompressible and of uniform density and rigidity. This hypothesis was adopted to simplify the problem, not because it is a true one. No matter is absolutely incompressible, and, the Earth is not a body of uniform density. It cannot be held to be probable that it is a body of uniform rigidity. But when any part of the hypothesis, e. g ., the assumption of uniform density, is discarded, the estimate of rigidity is affected. Different estimates are obtained when different laws of density are assumed. Again, whatever hypothesis we adopt as regards the arrangement of the matter, so long as we consider the Earth to be absolutely incompressible and of uniform rigidity, different estimates of this rigidity are obtained by using observations of different phenomena. Variations of the vertical may give one value, variations of latitude a notably different value. It follows that “the rigidity of the Earth” is not a definite physical constant. But there are two determinate constant numbers related to the methods that have been used for obtaining estimates of the rigidity of the Earth. One of these numbers specifies the amount by which the surface of the Earth yields to forces of the type of the tide-generating attractions of the Sun and Moon. The other number specifies the amount by which the potential of the Earth is altered through the rearrangement of the matter within it when this matter is displaced by the deforming influence of the Sun and Moon. If we adopt the ordinarily-accepted theory of the Figure of the Earth, the so-called theory of “fluid equilibrium,” and if we make the very probable assumption that the physical constants of the matter within the Earth, such as the density or the incompressibility, are nearly uniform over any spherical surface having its centre at the Earth’s centre, we can determine both these numbers without introducing any additional hypothesis as to the law of density or the state of the matter. We shall find, in fact, that observations of variations of latitude lead to a determination of the number related to the inequality of potential, and that, when this number is known, observations of variations of the vertical lead to a determination of the number related to the inequality of figure. [ Note added , December 15, 1908.—This statement needs, perhaps, some additional qualification. It is assumed that, in calculating the two numbers from the two kinds of observations, we may adopt an equilibrium theory of the deformations produced in the Earth by the corresponding forces. If the constitution of the Earth is really such that an equilibrium theory of the effects produced in it by these forces is inadequate, we should expect a marked discordance of phase between the inequality of figure produced and the force producing it. Now Hecker’s observations, cited in § 6 below, show that, in the case of the semidiurnal term in the variation of the vertical due to the lunar deflexion of gravity, the agreement of phase is close. If, however, an equilibrium theory is adequate, as it appears to be, for the semidiurnal corporeal tide, a similar theory must be adequate for the corporeal tides of long period and for the variations of latitude.]

scholarly journals The Lunar orbit paradox

2013 ◽  
Vol 40 (1) ◽  
pp. 135-146
Author(s):  
Aleksandar Tomic
Keyword(s):  
Inertial Mass ◽  
Lunar Orbit ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Three Body ◽  
Origin Of The Moon ◽  
Force Intensity ◽  
Critical Consideration

Newton's formula for gravity force gives greather force intensity for atraction of the Moon by the Sun than atraction by the Earth. However, central body in lunar (primary) orbit is the Earth. So appeared paradox which were ignored from competent specialist, because the most important problem, determination of lunar orbit, was inmediately solved sufficiently by mathematical ingeniosity - introducing the Sun as dominant body in the three body system by Delaunay, 1860. On this way the lunar orbit paradox were not canceled. Vujicic made a owerview of principles of mechanics in year 1998, in critical consideration. As an example for application of corrected procedure he was obtained gravity law in some different form, which gave possibility to cancel paradox of lunar orbit. The formula of Vujicic, with our small adaptation, content two type of acceleration - related to inertial mass and related to gravity mass. So appears carried information on the origin of the Moon, and paradox cancels.

Addendum 2020 to ‘Measurement of the Earth’s rotation: 720 BC to AD 2015’

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200776
Author(s):  
L. V. Morrison ◽  
F. R. Stephenson ◽  
C. Y. Hohenkerk ◽  
M. Zawilski
Keyword(s):  
Angular Momentum ◽  
Earth’S Rotation ◽  
The Sun ◽  
Earth's Rotation ◽  
Moon System ◽  
Link Type ◽  
The Earth ◽  
Solar Eclipses ◽  
Rotation Of The Earth

Historical reports of solar eclipses are added to our previous dataset (Stephenson et al. 2016 Proc. R. Soc. A 472 , 20160404 ( doi:10.1098/rspa.2016.0404 )) in order to refine our determination of centennial and longer-term changes since 720 BC in the rate of rotation of the Earth. The revised observed deceleration is −4.59 ± 0.08 × 10 −22  rad s −2 . By comparison the predicted tidal deceleration based on the conservation of angular momentum in the Sun–Earth–Moon system is −6.39 ± 0.03 × 10 −22  rad s −2 . These signify a mean accelerative component of +1.8 ± 0.1 × 10 −22  rad s −2 . There is also evidence of an oscillatory variation in the rate with a period of about 14 centuries.

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.

scholarly journals XXXII. On the precession of the equinoxes produced by the sun's attraction

1779 ◽  
Vol 69 ◽  
pp. 505-526
Keyword(s):  
Uniform Density ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Different Parts

If the actions of the Sun and the Moon upon the different parts of the earth were equal; of if the earth itself were perfectly spherical, and of an uniform density from the center to the surface; in either case the attractions of those remote bodies would have no effect on the position of the terrestrial equator, and the equinoctial points would constantly be the same in the heavens.

Mathematical Recreations

1952 ◽  
Vol 45 (7) ◽  
pp. 553-555
Author(s):  
Aaron Bakst
Keyword(s):  
The Sun ◽  
The Earth

Calendar problems have fascinated many a mathematician. Every now and then a formula for the determination of the days of the week or of the Easter date is published. Such formulas are valid for a certain number of years. The reason for such limitations is associated with the fact that the length of the year, that is, the length of the period of the year is not the same. The earth completes one cycle on its orbit around the sun in approximately 365.24220 days.

scholarly journals ‘The Earth but a Satellite of the Sun’

1958 ◽  
Vol 11 (4) ◽  
pp. 409-410
Author(s):  
R. d'E. Atkinson ◽  
E. G. R. Taylor
Keyword(s):  
High Rank ◽  
The Sun ◽  
Experimental Proof ◽  
Main Thesis ◽  
The Earth ◽  
The Absolute ◽  
Made In

I Have read Professor Taylor's article with great enjoyment. There are, however, two matters of fact on which, though they do not affect her main thesis, the record should, I think, be set right, (a) The earliest experimental proof of the Earth's revolution round the Sun was neither Bessel's detection of the relative parallax of 61 Cygni, nor Henderson's determination of the absolute parallax of α Centauri (both of which occurred in 1838) but Bradley's very beautiful discovery of aberration in 1725, together with his slightly later explanation. The discovery was made in a deliberate search for parallaxes; and although that particular proof of the Earth's movement was not then achieved, it was at once recognized that aberration provided a different and equally cogent one. Bradley's work was indeed resisted, in some quarters and for a short while, for reasons which Professor Taylor will by no means find unexpected. His later discovery of one term in the nutation was also a discovery of something which would have embarrassed Ptolemy, and delighted Newton; it certainly tended to confirm the picture, if that were needed. By the time parallaxes actually were discovered, though there still were individuals, sometimes of high rank, whose prejudices were stronger than their intellects, the only point of genuine doubt was the question how far away the nearest stars really were.

scholarly journals Changes in Rainfall and Climate Classification in South Sulawesi

2021 ◽  
Vol 2 (5) ◽  
pp. 37-50
Author(s):  
Ridahwati Ridahwati
Keyword(s):  
Rainfall Intensity ◽  
Geographical Location ◽  
Subtropical Climate ◽  
The Sun ◽  
Q Value ◽  
Climate Classification ◽  
Climate Type ◽  
South Sulawesi ◽  
The Earth

The study discuss about Changes in Rainfall and Climate Classification in South Sulawesi. The climate of the Earth is determined by the location of the sun in relation to the earth's surface. Geographical location influences the categorization of climate on our planet. The results of the study (1) Rainfall in Bone Regency has been classified as high rainfall intensity for the last 10 years; (2) Determination of climate classification can be done by processing rainfall data obtained from data before weighting, after weighting, ranking, and opportunity; (3) The climate classification according to Schmidt-Ferguson for Bone Regency has a B climate type, which is a humid subtropical climate; and (4) The climate classification according This is based on a comparison of the number of dry months (BK) and wet months (BB), from which the Q value is obtained, which is then used to determine the type of climate according to Schmidt-Ferguson; (4) Oldeman's climate classification for Bone Regency has a C1 climate type, which has the characteristics of planting lowland rice once a year and secondary crops twice a year; (5) Oldeman's climate classification for Bone Regency has a This is based on the number of Wet Months (BB) and Dry Months (BK) in a given year

scholarly journals Passive Remote Study of the Aerosol in the Upper Atmosphere of the Earth

2019 ◽  
pp. 1-6
Author(s):  
Oleksandr Zbrutskyi ◽  
◽  
Nevodovskyi P ◽  
Anatoliy Vid’machenko ◽  
◽  
...  
Keyword(s):  
Global Warming ◽  
Energy Balance ◽  
Climate Changes ◽  
Upper Atmosphere ◽  
Anthropogenic Factors ◽  
The Sun ◽  
Earth System ◽  
Relative Contribution ◽  
The Earth

Climate changes on planet Earth are mainly caused by disturbances in the energy balance of the Sun-Earth system. This process is the result of both natural changes in nature and the influence of anthropogenic factors. The combined effect of these factors can lead to threatening phenomena for mankind - a decrease in the power of the ozone layer, the formation of “ozone holes” and global warming on the planet and other disasters. The study of the causes of these factors and the determination of their relative contribution is one of the pressing problems of our time.

scholarly journals The Restricted 2+2 Body Problem: Parametric Variation of the Equilibrium States of the Minor Bodies and Their Attracting Regions

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Maria N. Croustalloudi ◽  
Tilemahos J. Kalvouridis
Keyword(s):  
Body Problem ◽  
Type Structure ◽  
Artificial Satellites ◽  
Test Problems ◽  
The Sun ◽  
Numerical Determination ◽  
Binary Asteroids ◽  
Parametric Variation ◽  
The Earth

The restricted 2+2 body problem was stated by Whipple (1984) as a particular case of the general n + v problem described by Whipple and Szebehely (1984). In this work we reconsider the problem by studying some aspects of the dynamics of the minor bodies, such as the parametric variation of their equilibrium positions, as well as the attracting regions formed by the initial approximations used for the numerical determination of these positions. In the latter case we describe the process to form these regions, and we numerically investigate their dependence on the parameters of the system. The results in many cases show a fractal-type structure of these regions. As test problems, we use the Sun-Jupiter-binary asteroids and the Earth-Moon-dual artificial satellites systems.

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