Perturbations of the orbit of a satellite near to the earth

1958 ◽  
Vol 248 (1252) ◽  
pp. 55-62 ◽  
Keyword(s):  
Satellite Orbit ◽  
The Sun ◽  
The Earth ◽  
First Approximation ◽  
Different Types ◽  
Electromagnetic Effects ◽  
The Subject ◽  
The Cross ◽  
Earth’S Oblateness

The main perturbations of a satellite orbit near the earth are those caused by the earth’s oblateness and the atmosphere. Fortunately these two sources produce perturbations of quite different types, and as a first approximation they can be treated separately, though the cross-couplings would have to be evaluated in a thorough analysis of the subject. There are other perturbations to the orbit, caused by the attractions of the sun, moon and planets, by relativity effects, by the fact that the earth is not symmetrical about its axis and by electromagnetic effects; but these perturbations are expected to be small and will not be discussed here.

III—Interplanetary Navigation

1955 ◽  
Vol 8 (1) ◽  
pp. 35-40
Author(s):  
J. G. Porter
Keyword(s):  
Dead Reckoning ◽  
Difficult Problem ◽  
Base Line ◽  
The Sun ◽  
Space Navigation ◽  
Simple Matter ◽  
The Earth ◽  
The Subject ◽  
The One ◽  
Interplanetary Navigation

Most people know something about space ships nowadays, and probably think that navigation in space is quite a simple matter; at any rate, it is a subject that is glossed over very briefly in most books on the subject. In my view, space navigation is not a simple matter, and it has certainly not received the attention it deserves. Navigation on the Earth is easy, because of the one important fact that you are on the surface of the Earth. A couple of sights, measuring the angles from two stars down to the horizon, together with the azimuths of the stars and the distance from the centre of the Earth, will give an exact statement of position. But out in space there is no Earth, no horizon—in fact nothing whatever to use as a basis of measurement. Clearly then, two angles are not enough; a third one is needed, to give a sort of tripod of sights—two of the legs being anchored to two planets (or the Sun and a planet) because their positions in space at any time are known, and the distance between them can be used as a base-line. The solution of all the triangles involved is indeed a difficult problem, but there is also the impossibility of making three simultaneous observations. It might be thought that one could do as at sea and take one sight followed later by others, making allowance for the motion of the ship in the intervals. However, this involves the idea of dead reckoning, which, although a useful concept at sea, is quite impossible to apply in space, as the following example shows.

scholarly journals XIII. On the precession of a viscous spheroid, and on the remote history of the Earth

1879 ◽  
Vol 170 ◽  
pp. 447-538 ◽  
Keyword(s):  
Relative Motion ◽  
Mass Motion ◽  
The Sun ◽  
The Earth ◽  
Bodily Tides ◽  
History Of ◽  
The Subject ◽  
Theoretical Dynamics

The following paper contains the investigation of the mass-motion of viscous and imperfectly elastic spheroids, as modified by a relative motion of their parts, produced in them by the attraction of external disturbing bodies; it must be regarded as the continuation of my previous paper, where the theory of the bodily tides of such spheroids was given. The problem is one of theoretical dynamics, but the subject is so large and complex, th at I thought it best, in the first instance, to guide the direction of the speculation by considerations of applicability to the case of the earth, as disturbed by the sun and moon.

scholarly journals THE FORGOTTEN GEOGRAPHIC AND PHYSICAL – OCEANOGRAPHIC KNOWLEDGE OF THE PREHISTORIC GREEKS

2017 ◽  
Vol 43 (1) ◽  
pp. 92 ◽  
Author(s):  
I.D Mariolakos
Keyword(s):  
Atlantic Ocean ◽  
Relative Position ◽  
British Isle ◽  
The Sun ◽  
Greek Mythology ◽  
The West ◽  
The Earth ◽  
The Subject ◽  
Greek Myths

Many believe that the Greek Mythology is a figment of the vivid imagination of the ancient Greeks. Consequently, the Greek Myths are all fantastic stories. In my opinion, this view is erroneous, at least on the subject concerning the geographic and physical-oceanographic characteristics of the Atlantic Ocean, as these were described mainly by Homer, Hesiod, the Orphics and Plutarch. In the present paper (i) some of the references made by the above mentioned authors are selectively reported, and (ii) the physical and geological validation is given, based on the present-day scientific views and knowledge. Namely, the prehistoric Greeks knew about the Hyperboreans, the island of Ierne (Ireland), the British isle etc., by the Orphics. From the writings of Plutarch, they knew (i) the relative position of the present-day Iceland (Ogygia) and its distance from Britain, (ii) that to the west of Iceland, three other islands are located, where the sun sets for only an hour a day, (iii) that further to the west there is a “great continent”, which surrounds the Ocean and more. Homer and Hesiod wrote that (i) the Ocean is a “river” that flows continuously, (ii) that this river encircles the Earth and (iii) that its flow is turbulent not only on the surface, but in depth as well. Unfortunately, all this knowledge was gradually forgotten by all. This is the reason why Odyssey is considered just an entertaining poem and Ulysses’ nostos a fantastic story, with no trace of historic reality.

VI. The Sun as a Star

1988 ◽  
Vol 20 (1) ◽  
pp. 102-106
Author(s):  
L.E. Cram
Keyword(s):  
Time Scales ◽  
Spatial Extent ◽  
The Sun ◽  
Distinguishing Characteristic ◽  
X Ray ◽  
Spatially Resolved ◽  
Solar Observations ◽  
The Earth ◽  
The Subject

Studies of the global (spatially unresolved) output from the sun are important for two main reasons: (1) the global solar output directed towards the earth plays a central role in solar-terrestrial relations, and (2) global solar observations form a link between (neccessarily) global observations of stars and the more refined spatially resolved observations which are available for the sun. This report covers both aspects (insofar as they concern the sun), using the time-scales of various phenomena as a basic distinguishing characteristic. Note that certain studies of spatially unresolved solar output have not been discussed, since they are actually directed toward the investigation of phenomena of strictly limited spatial extent [e.g. radiospectrograph observations (e.g. Wiehl et al. 1985) and studies of X-ray bursts (e.g. Thomas et al. 1985)]. Collections of relevant papers may be found in De Jager and Svestka (1985) and Labonte et al. (1984), while a review of germane stellar work is available in Baliunas and Vaughan (1985) and solar-terrestrial work in Donnelly and Heath (1985). A comprehensive summary of the subject by Hudson will appear soon in Review of Geophysics and Planetary Physics.

scholarly journals On the precession of the equinoxes

1832 ◽  
Vol 1 ◽  
pp. 253-254
Keyword(s):  
The Sun ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
The Third ◽  
The Earth ◽  
Figure Of The Earth ◽  
The Subject

The Professor observes, that Sir Isaac Newton was the first mathematician who endeavoured to estimate the quantity of the precession from the attractive influence of the sun and moon on the spheroidal figure of the earth. His investigations relating to this subject evince the same transcendent abilities that are displayed in other parts of his Principia; but it is admitted, that, from a mistake in his process, his conclusion is erroneous. The investigations of other mathematicians in attempting the solu­tion of the same problem are arranged by the author under three general heads. The first arrive at wrong conclusions, in consequence of mistake in some part of their proceedings; the second obtain just conclusions, but rendered so by balance of opposite errors; the third approach as near the truth as the nature of the subject will admit, but, in the author’s estimation, are liable to the charge of obscurity and perplexity.

scholarly journals Essay towards a first approximation to a map of cotidal lines

1837 ◽  
Vol 3 ◽  
pp. 188-190 ◽  
Keyword(s):  
High Water ◽  
The Earth ◽  
First Approximation ◽  
Open Sea ◽  
The World ◽  
Extensive Range ◽  
The Subject ◽  
Real Forms ◽  
General Explanation ◽  
Different Parts

The general explanation of the phenomena of the tides originally given by Newton, although assented to by all subsequent philosophers, has never been pursued in all the details of which its results are susceptible, so as to show its bearing on the more special and local phenomena, to connect the actual tides of all the different parts of the world, and to account for their varieties and seeming anomalies. The first scientific attempt that was made to compare the developed theory with any extensive range of observations, was that of Daniel Bernouilli in 1740: the subject has since been pursued by Laplace and Bouvard, and still more recently by Mr. Lubbock. But the comparison of contemporaneous tides has hitherto been unaccountably neglected: and to this particular branch of the subject the researches of the author are in this paper especially directed the principal object of his inquiry being to ascertain the position of what may be called cotidal lines , that is, lines drawn through all the adjacent parts of the ocean where it is high water at the same time; as, for instance, at a particular hour on a given day. These lines may be considered as representing the summit or ridge of the tide wave existing at that time, and which advances progressively along the sea, bringing high water to every place where it passes. Hence the cotidal lines for successive hours represent the successive positions of the summit of the tide wave, which in the open sea travels round the earth once in twenty-four hours, accompanied by another at twelve hours’ distance from it, and both sending branches into the narrower seas. Thus a map of cotidal lines may be constructed, at once exhibiting to the eye the manner and the velocity of all these motions. Although the observations on the periods of the tides at different places on the coast and different parts of the ocean, which have been at various times recorded, are exceedingly numerous, yet they are unfortunately for the most part too deficient in point of accuracy, or possess too little uniformity of connexion to afford very satisfactory results, or to admit of any extended comparison with theory. With a view to arrive at more correct conclusions, the author begins his inquiry by endeavouring to determine what may be expected to be the forms of the cotidal lines, as deduced from the laws which regulate the motions of water: and he proceeds afterwards to examine what are their real forms, as shown by the comparison of all the tide observations which we at present possess.

scholarly journals XXXIII. On the figure of the earth

1826 ◽  
Vol 116 ◽  
pp. 548-578 ◽  
Keyword(s):  
Present State ◽  
Royal Society ◽  
Mathematical Theory ◽  
Second Order ◽  
The Earth ◽  
First Approximation ◽  
Figure Of The Earth ◽  
The Subject ◽  
The Difference

The ellipticity of the earth, deduced by Captain Sabine from a series of pendulum experiments the most extensive, and apparently the most deserving of confidence, that has ever been made, differs considerably from that which, as is generally believed, is indicated by geodetic measures. The difference can only be explained by errors of observation, by peculiarities of local circumstances, or by some defect in the theory which connects the figure of the earth with the variation of gravity on its surface: under the last head may be placed defects in the mathematical part of the theory, and errors in the assumptions of the original constitution and present state of the earth. It was with a view to ascertain the sufficiency of the mathematical theory, that I undertook the investigations contained in this paper. The celebrated proposition called Clairaut's theorem, by which the earth's ellipticity is inferred from the variation of gravity on its surface, is obtained only by the rejection of the squares and higher powers of the ellipticity. It is by the same rejection that the figure of the earth, supposed a heterogeneous fluid, is proved to be an elliptic spheroid. It appeared therefore probable, that a more accurate theory might introduce some modification into Clairaut's theorem, and might also show he figure of the earth to differ from an ellipsoid ; and there was no reason to think that the first approximation to that figure was more accurate, than the first approximation to the motion of the moon’s perigee. The result of my investigation does not at all serve to reconcile the pendulum observations made by Captain Sabine with the measures of degrees : and with respect to one object, which I hoped to obtain, I am therefore completely unsuccessful. The theory shows, however, that the earth’s figure, on the usual suppositions as to its constitution, is not an elliptic spheroid; and the formulæ which I have obtained will give the means of determining very exactly the figure of the earth, when the experiments on the variation of gravity, or the measures of arcs on the earth’s surface, shall be thought sufficiently accurate. As the subject is one whose interest is not confined to the present time, I have ventured to offer my investigations to the Royal Society. The first part of the following sheets contains the theory of the heterogeneous earth, pushed so far as to include all the terms of the second order: it is succeeded by a comparison of this theory with Captain Sabine’s results, and with the best arcs of the meridian that have been measured and in the conclusion, I have offered some suggestions on the propriety of repeating some of these measures.

scholarly journals IX. On the tidal friction of a planet attended by several satellites, and on the evolution of the solar system

1881 ◽  
Vol 172 ◽  
pp. 491-535 ◽  
Keyword(s):  
Solar System ◽  
Central Body ◽  
The Sun ◽  
Tidal Friction ◽  
The Earth ◽  
History Of ◽  
The Subject ◽  
Complete Investigation

In previous papers on the subject of tidal friction I have confined my attention principally to the case of a planet attended by a single satellite. But in order to make the investigation applicable to the history of the earth and moon it was necessary to take notice of the perturbation of the sun. In consequence of the largeness of the sun’s mass it was not there requisite to make a complete investigation of the theory of a planet attended by a pair of satellites. In the first part of this paper the theory of the tidal friction of a central body attended by any number of satellites is considered.

scholarly journals Exeter Book Riddle 95: ‘The Sun’, a New Solution

2019 ◽  
Vol 137 (4) ◽  
pp. 612-638
Author(s):  
Dieter Bitterli
Keyword(s):  
Tenth Century ◽  
Exeter Book ◽  
The Sun ◽  
Anglo Saxon ◽  
The Past ◽  
The Earth ◽  
English Verse ◽  
Isidore Of Seville ◽  
The Subject ◽  
The One

Abstract Elusive and fraught with textual difficulties, Riddle 95, the ‘last’ of the Old English verse riddles preserved in the tenth-century Exeter Book, has long baffled modern readers as one of a handful of thorny items in the collection that have so far defied solution. ‘Book’ is the answer that has found most acceptance with critics in the past, yet the speaking subject of Riddle 95 is unlike anything described in those items of the collection that actually deal with writing and the tools of the monastic scriptorium. Rather, the linguistic and thematic parallels between Riddle 95 on the one hand, and the cosmological riddles and poems in the Exeter Book on the other, strongly suggest that the subject of Riddle 95 is the sun, a frequent topic of early medieval enigmatography. The poem obliquely relates how the rising sun installs itself in the sky to shed its welcome light upon the earth before it sets and vanishes from sight, completing its daily orbit along unknown paths. The main clues helping to secure the solution ‘sun’ are based upon what was known in Anglo-Saxon England about the solar course and the planetary motions, especially from the astronomical writings of Isidore of Seville and Bede. Further evidence is provided by several analogues in the Anglo-Latin riddle tradition, including the Enigmata of Aldhelm and his followers.

scholarly journals Orbital Perigee Deviation under Inclination Window for Sun Synchronized Low Earth Orbits

2019 ◽  
Vol 4 (10) ◽  
pp. 127-130
Author(s):  
Shkelzen Cakaj ◽  
Bexhet Kamo
Keyword(s):  
Orbital Plane ◽  
Earth Observation ◽  
Gas Content ◽  
The Sun ◽  
Orbital Inclination ◽  
The Earth ◽  
Low Earth Orbits ◽  
Earth Observation Satellites ◽  
Earth Orbits ◽  
Earth’S Oblateness

Data processing related to the Earth’s changes, gathered from different platforms and sensors implemented worldwide and monitoring the environment and structure represents Earth observation (EO). Environmental monitoring includes changes in Earth’s vegetation, atmospheric gas content, ocean state, melting level in the ice fields, etc. This process is mainly performed by satellites. The Earth observation satellites use Low Earth Orbits (LEO) for their missions. These missions are accomplished mainly based on photo imagery. Thus, the relative Sun’s position related to the observed area, it is very important for the photo imagery, in order the observed area from the satellite to be treated under the same lighting (illumination) conditions. This could be achieved by keeping a constant Sun position related to the orbital plane due to the Earth’s motion around the Sun. This is called Sun synchronization for low Earth orbits, the feature which is applied for satellites dedicated for the Earth observation. Nodal regression is the phenomenon which is utilized for low circular orbits providing to them the Sun synchronization. Nodal regression refers to the shift of the orbit’s line of nodes over time as Earth revolves around the Sun,  caused due to the Earth’s oblateness. Nodal regression depends on orbital altitude and orbital inclination angle. For the in advance defined range of altitudes stems the inclination window for the satellite low Earth orbits to be Sun synchronized. For analytical and simulation purposes, the altitudes from 600km to 1200km are considered. Further for the determined inclination window of the Sun synchronization it is simulated the orbital perigee deviation for the above considered altitudes and the eventual impact on the satellite’s mission.

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