XV. — Researches in physical astronomy

1831 ◽  
Vol 121 ◽  
pp. 231-282
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Lunar Theory ◽  
System Of Equations ◽  
Planetary Theory ◽  
The Moon ◽  
Celestial Bodies ◽  
Independent Variable ◽  
The Mean ◽  
The One

The method pursued by Clairaut in the solution of this important problem of Physical Astronomy, consists in the integration of the differential equations furnished by the principles of dynamics, upon the hypothesis that in the gravitation of the celestial bodies the force varies inversely as the square of the distance, and in which the true longitude of the moon is the independent variable ; the time is thus obtained in terms of the true longitude, and by the reversion of series the longitude is afterwards obtained in terms of the time, which is necessary for the purpose of forming astronomical tables. But while on the one hand this method possesses the advantage, that the disturbing func­tion can be developed with somewhat greater facility in terms of the true lon­gitude of the moon than in terms of the mean longitude, yet on the other hand, the differential equations in which the true longitude is the independent variable are far more complicated than those in which the time is the inde­pendent variable. The latter equations are used in the planetary theory ; so that the method of Clairaut has the additional inconvenience, that while the lunar theory is a particular case of the problem of the three bodies, one system of equations is used in this case, and another in the case of the planets. The method of Clairaut has been adopted, however, by Mayer, by Laplace, and by M. Damoiseau. The last-mentioned author has arranged his results with remarkable clearness, so that any part of his processes may be easily verified by any one who does not shrink from this gigantic undertaking; and the immense labour which this method requires, when all sensible quantities are retained, may be seen in his invaluable memoir. Mr. Brice Bronwin has recently communicated to the Society a lunar theory, in which the same method is adopted.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 128-129
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Disturbing Function ◽  
Direct Integration ◽  
Planetary Theory ◽  
The Moon ◽  
Disturbing Force ◽  
Other Hand ◽  
The Stability ◽  
The One

The present paper contains some further developments of the theory of the moon, which are given at length, in order to save the trouble of the calculator, and to avoid the danger of mistake. The author remarks, that while it seems desirable, on the one hand, to introduce into the science of physical astronomy a greater degree of uniformity, by bringing to perfection a theory of the moon founded on the integration of the equations employed in the planetary theory, it is also no less important, on the other hand, to complete, in the latter, the method hitherto applied solely to the periodic inequalities. Hi­therto those terms in the disturbing function which give rise to the secular inequalities, have been detached, and the stability of the system has been inferred by means of the integration of certain equations, which are linear when the higher powers of the eccentri­cities are neglected and from considerations founded on the varia­tion of the elliptic constants. But the author thinks that the stability of the system may be inferred also from the expressions which result at once from the direct integration of the differential equations. The theory, he states, may be extended, without any analytical difficulty, to any power of the disturbing force, or of the eccentricities, ad­mitting the convergence of the series; nor does it seem to be limited by the circumstance of the planet’s moving in the same direction.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 51-52
Keyword(s):  
Differential Equations ◽  
Great Distance ◽  
Original Position ◽  
Lunar Theory ◽  
Great Length ◽  
The Moon ◽  
The Earth ◽  
Method Of Solution ◽  
Independent Variable ◽  
The One

The first part of this paper relates to the theory of the moon. The method of solution pursued by Clairaut consisted in the inte­gration of differential equations, in which the true longitude of the moon is the independent variable: the time is then obtained in terms of the true longitude; and by the reversion of series, the lon­gitude afterwards obtained in terms of the time. This method is the one adopted by Mayer, Laplace, and Damoiseau. The au­thor has been led, by reflecting on the difficulties of this problem, to believe that the integration of the differential equations in which the time is the independent variable would be at least as easy as the former process; and it would possess the advantage of employing the same system of equations for the moon as for the planets. The lunar theory proposed by the author, and developed in this paper, is an extension of the equations given in his former Researches in Physical Astronomy, already published in the Philosophical Trans­actions; by including those terms, which, in consequence of the great eccentricity of the moon’s orbit, are sensible; and by sup­pressing those which are insensible from the great distance of the sun, the disturbing body. He has not yet attempted to obtain numerical results, but proposes at some future time to engage in their computation. In the second part of the paper, he investigates the precession of the equinoxes, on the supposition that the earth revolves in a re­sisting medium; an investigation which may also be considered as a sequel to the author’s last paper on Physical Astronomy. The effects of the resistance of such a medium is to increase the latitude of the axis of rotation (reckoned from the equator of the figure) till it reaches 90°. Such is now the condition of the axis of the earth: but as the chances are infinitely great against this having been its original position, may not its attainment of this position be ascribed to the resistance of a medium of small density acting for a great length of time, —a supposition which may account for many geological indications of changes having taken place in the climates of the earth ? The operation of such a cause would be also sen­sible in the case of comets: and the accuracy with which the ec­centricity of the Halleian comet of 1759 is known, would appear to afford a favourable opportunity of verifying this hypothesis.

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.

scholarly journals VIII. On the theory of the moon

1834 ◽  
Vol 124 ◽  
pp. 127-141
Keyword(s):  
Differential Equations ◽  
Great Increase ◽  
Direct Method ◽  
Sufficient Accuracy ◽  
The Moon ◽  
Great Precision ◽  
Similar Series ◽  
Independent Variable ◽  
The Subject ◽  
The Mean

When I commenced the investigations relating to the theory of the moon which I have had the honour to communicate to the Society, I proposed to show how, by a different but more direct method, the numerical results given by M. Damoiseau might be obtained. The approximations were in fact carried much further by M. Damoiseau than had been done before, and the details which accompany M. Damoiseau's work evince at once the immense labour of the undertaking, and inspire confidence in the accuracy of the results offered. But the state of the question is now changed by the appearance of M. Plana’s admirable work, entitled “Théorie du Mouvement de la Lune,” in which, although M. Plana's employs the same differential equations as those used by M. Damoiseau, and obtains in the same manner finally the expressions for the coordinates of the moon, in terms of the mean longitude by the reversion of series, yet M. Plana’s expressions have a very different analytical character and im­portance, from the circumstance that the author develops all the quantities intro­duced by integration, according to powers of the quantity called m , which expresses the ratio of the sun’s mean motion to that of the moon. In this form of the expression the coefficients of the different powers of m , of the eccentricity, &c., are determinate, as are, for example, the numerical coefficients in the expression for the sine in terms of the arc, and other similar series. An inestimable advantage results from this pro­cedure, which more than compensates for the great increase of labour it occasions, by diminishing the danger of neglecting any terms of the same order as those taken into account, and by affording the means of verifying many terms long before final and complete results shall have been obtained independently by myself or any other person. By treating the differential equations in which the time is the independent variable, as I have proposed, similar results to those of M. Plana may be obtained directly; but the calculations which are required in either method are so prodigiously irksome and laborious, that until identical expressions have actually been obtained independently, to the extent of every sensible term, the theory of the moon cannot, I think, be considered complete. It might, indeed, be supposed that already, through the labours of mathematicians, from Clairaut to the present time, the numerical values of the coefficients of the different inequalities were ascertained with sufficient accuracy for practical purposes, and that any further researches connected with the subject would be more likely to gratify curiosity than to lead to any useful result. Astronomical observations are now made with so great precision, that the numerical values of the coefficients are wanted to at least the tenth of a second of space: very few, however, of the coefficients of MM. Damoiseau and Plana agree so nearly, and some differ much more, as may be seen in the following comparison of the numerical values of the coefficients of some of the arguments in the expression for the true longitude of the moon in terms of her mean longitude, being indeed those which differ the most.

scholarly journals Figures and Mirrors in Demetrios Triklinios's 'Selenography'

2021 ◽  
pp. 54-73
Author(s):  
Divna Manolova
Keyword(s):  
Fourteenth Century ◽  
Visual Cognition ◽  
The Other ◽  
Lunar Theory ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Mediterranean World ◽  
The One

This article is about the interplay between diagrammatic representation, the mediation of mirrors, and visual cognition. It centres on Demetrios Triklinios (fl. ca. 1308–25/30) and his treatise on lunar theory. The latter includes, first, a discussion of the lunar phases and of the Moon's position in relation to the Sun, and second, a narrative and a pictorial description of the lunar surface. Demetrios Triklinios's Selenography is little-known (though edited in 1967 by Wasserstein) and not available in translation into a modern scholarly language. Therefore, one of the main goals of the present article is to introduce its context and contents and to lay down the foundations for their detailed study at a later stage. When discussing the Selenography, I refer to a bricolage consisting of the two earliest versions of the work preserved in Bayerische Staatsbibliothek, graecus 482, ff. 92r–95v (third quarter of the fourteenth century) and Paris, Bibliothèque nationale de France, graecus 2381, ff. 78r–79v (last quarter of the fourteenth century). I survey the available evidence concerning the role of Demetrios Triklinios (the author), John Astrapas (?) (the grapheus or scribe-painter), and Neophytos Prodromenos and Anonymus (the scribes-editors) in the production of the two manuscript copies. Next, I discuss the diagrams included in the Selenography and their functioning in relation to Triklinios's theory concerning the Moon as a mirror reflecting the geography of the Earth, on the one hand, and to the mirror experiment described by Triklinios, on the other. Finally, I demonstrate how, even though the Selenography is a work on lunar astronomy, it can also be read as a discussion focusing on the Mediterranean world and aiming at elevating its centrality and importance on a cosmic scale.

scholarly journals Lunar

JOGED ◽  
2017 ◽  
Vol 7 (2) ◽  
Author(s):  
Dewi Sinta Fajawati
Keyword(s):  
Full Moon ◽  
Big Bang ◽  
The Other ◽  
The Sun ◽  
The Moon ◽  
Big Bang Theory ◽  
Essential Idea ◽  
Visual Reaction ◽  
Night Sky ◽  
The One

Bulan merupakan sumber inspiratif dalam penggarapan karya tari ini. Secara ilmu pengetahuan, Bulan adalah benda langit yang disebut satelit, satelit satu-satunya yang dimiliki Bumi dan tercipta secara alami. Banyak teori yang mengatakan tentang terbentuknya Bulan, salah satunya adalah teori Big bang atau dentuman besar. Pada dasarnya Bulan hanyalah sebuah Benda besar berbentuk bulat yang tidak bisa bercahaya, cahaya yang kita lihat pada malam hari merupakan refleksi dari cahaya matahari. Akan tetapi keindahannya memang tidak bisa dipungkiri, karena dia paling bercahaya diantara hamparan langit yang gelap. Cahayanya tidak selalu terang, bahkan tidak selalu bulat, terkadang hanya terlihat setengah atau terlihat seperti sabit..            Penata tari memetaforakan objek bulan yang berada di tempat yang sangat tinggi sebagai sebuah cita-cita yang ingin dicapai. Seringkali lagu anak-anak yang menjadi pengalaman auditif penata tari, menjadikan bulan sebagai objek yang ingin digapai, misal lagu ‘Ambilkan Bulan Bu’. Namun intisari yang akan dipakai dalam penggarapan koregrafinya adalah tentang fase bulan yang tercipta. Bersumber dari rangsang awal melihat bulan atau rangsang visual, penata tari menginterpretasikan fase-fase bulan yang terjadi sebagai fase kehidupan yang dijalani untuk menggapai sebuah cita-cita tersebut.            Koreografi diwujudkan dalam bentuk kelompok dengan membagi dua karate penari. Delapan penari merupakan simbolisasi Bulan, dan satu penari sebagai manusia yang bercita-cita. Dengan bentuk tari dramatik, penyajiannya dibagi menjadi 5 adegan, yaitu Introduksi Big bang, Adegan 1 Moon happen, Adegan 2 Mengejar Impian, Adegan 3 Dancing with Moon, dan Ending ‘Catch Your Dream’. The moon is the essential inspirations of this choreograph. Theoretically, the moon is a sky object which is called as satellite. The one and only naturally created satellite belongs to the planet Earth. There are many theories that explain how the moon was created. One of those theories is Big Bang theory or massive crash. Basically, the moon is just a huge circle thing which is unable to shine its glow. The light that we experience in the evening is the reflection of the sun. However, thebeauty of the moonlight is undeniable as it has the significant light within the darkest night sky. Its light is not always the strongest, even it’s not always circle (full), every so often it is seemed only the half part of it or crescent moon.            The choreographer interpreted the moon that belongs in the highest as the goals that she wants to reach. Most of the time, the children songs (lullaby) that pick the moon as the main object that is desired to be reached, for example the song “Ambilkan Bulan, Bu”. The essential idea that is explored in this choreograph is the creational phase of the moon itself. It was started by way of visual reaction when the choreographer observed the moon, she interpret the moon’s phases as the phases in human’s life which are gone through to reaching their goals. Fall and recovery, passionate, and even sometimes they give it in, are interpreted from the moonlight. The full moon which has the brightest and the most perfect light is likened as the strong spirit. The crescent moon with its soft light is interpreted as low spirit and unconfident.             This in-group-choreograph is separated into two characters with 8 female dancers that are the symbolization of the moon and the other one female dancer symbolizes a human with aspire. With dramatic dance form, this choreograph is presented into five parts, including introduction part of Big Bang, Moon Happen in part one, Chasing Dream is part two, Dancing With The Moon in part three, Catch Your Dream in the ending part.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

A search for ‘frozen optical messages’ from extraterrestrial civilizations

2002 ◽  
Vol 1 (1) ◽  
pp. 71-73 ◽  
Author(s):  
R. Weinberger ◽  
H. Hartl
Keyword(s):  
Solar System ◽  
The Other ◽  
Physical Processes ◽  
High Quality ◽  
Sky Surveys ◽  
Systematic Examination ◽  
Other Hand ◽  
Celestial Bodies ◽  
The One

For a quarter of a century we have been engaged in a systematic examination of high-quality photographic (optical) sky surveys in the search for new celestial bodies of various kinds. It took about 5000 hours to cover the whole northern celestial hemisphere and half of the southern one. In total, about 12000 new objects were discovered. From the very beginning of our programme we also searched for objects (or groupings of them) of rather peculiar morphology. The motivation was to detect objects revealing exceptional physical processes, on the one hand, but also to discover constructions possibly created by advanced extraterrestrial civilizations (ETCs), on the other hand. A number of very peculiar objects were indeed found (these were mostly studied in detail later), but none of these appeared likely to be the product of alien masterminds. We may conclude that at least within about 10000–20000 light-years around the Solar system no highly advanced ETCs intend to reveal themselves through such objects.

The Effect of Waking Suggestion on Post-Hypnotic Amnesia

1981 ◽  
Vol 11 (1) ◽  
pp. 44-46 ◽  
Author(s):  
D.P. Fourie
Keyword(s):  
Point Of View ◽  
The Other ◽  
Hypnotic Susceptibility ◽  
The Subject ◽  
The Mean ◽  
The Difference ◽  
The One ◽  
The Relationship ◽  
Female Subjects

It is increasingly realized that hypnosis may be seen from an interpersonal point of view, meaning that it forms part of the relationship between the hypnotist and the subject. From this premise it follows that what goes on in the relationship prior to hypnosis probably has an influence on the hypnosis. Certain of these prior occurences can then be seen as waking suggestionns (however implicitly given) that the subject should behave in a certain way with regard to the subsequent hypnosis. A study was conducted to test the hypothesis that waking suggestions regarding post-hypnotic amnesia are effective. Eighteen female subjects were randomly divided into two groups. The groups listened to a tape-recorded talk on hypnosis in which for the one group amnesia for the subsequent hypnotic experience and for the other group no such amnesia was suggested. Thereafter the Stanford Hypnotic Susceptibility Scale was administered to all subjects. Only the interrogation part of the amnesia item of the scale was administered. The subjects to whom post-hypnotic amnesia was suggested tended to score lower on the amnesia item than the other subjects, as was expected, but the difference between the mean amnesia scores of the two groups was not significant.

scholarly journals A TWO-STRAIN EPIDEMIC MODEL WITH UNCERTAINTY IN THE INTERACTION

2012 ◽  
Vol 54 (1-2) ◽  
pp. 108-115 ◽  
Author(s):  
M. G. ROBERTS
Keyword(s):  
Differential Equations ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Influenza A ◽  
Reproduction Number ◽  
The Other ◽  
Orthogonal Functions ◽  
Dependent Variables ◽  
Independent Variable ◽  
Cross Immunity

AbstractAnnual epidemics of influenza A typically involve two subtypes, with a degree of cross-immunity. We present a model of an epidemic of two interacting viruses, where the degree of cross-immunity may be unknown. We treat the unknown as a second independent variable, and expand the dependent variables in orthogonal functions of this variable. The resulting set of differential equations is solved numerically. We show that if the population is initially more susceptible to one variant, if that variant invades earlier, or if it has a higher basic reproduction number than the other variant, then its dynamics are largely unaffected by cross-immunity. In contrast, the dynamics of the other variant may be considerably restricted.

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