The first, for a memoir on the construction of a clepsydra for measuring time exactly at sea, he gained at the age of twenty-four; the second, for one on the physical cause of the inclination of the planetary orbits, he divided with his father; and the third, for a communication on the tides, he shared with Euler, Colin Maclaurin and another competitor.

95The orbits are always open behind, never being surrounded by bone.

95The orbits of earth and moon are elliptical, so that the earth is sometimes nearer, sometimes farther away from the sun, and the same is the case with the moon in relation to the earth.

33The squamosals form the posterior outer margin of the orbits and are frequently continued into two lateral downward processes across the temporal fossa.

22Below are set forth the methods of determining and dealing with such orbits.

10No post-orbital processes or any separation between orbits and temporal fossae.

10The same statements are true of the orbits of the satellites around their primaries.

10Elliptic orbits, and a parabolic orbit considered as the special case when the eccentricity of the ellipse is 1, are almost the only ones the astronomer has to consider, and our attention will therefore be confined to them in the present article.

11It has been supposed that certain electrons revolve like satellites in orbits around the atoms with which they are associated, a view which receives strong support from the phenomena of the Zeeman effect, and on this assumption a theory has been worked out by P. Langevin, 2 which accounts for many, of the observed facts of magnetism.

11As a consequence of the structure of the molecule, which is an aggregation of atoms, the planes of the orbits around the latter may be oriented in various positions, and the direction of revolution may be right-handed or left-handed with respect to the direction of any applied magnetic field.

11Such unstable orbits can be stabilized by tiny control forces.

11Orbits the zodiac in four years plus two to four months.

11It is also remarkable that all the great planets and many of the small ones have their orbits very nearly in the same plane, and nearly circular in form.

13Nasal apertures very large, and extending high on the face between the orbits; nasal bones short, elevated, triangular and pointed in front.

15In all the cases which have yet arisen in astronomy the extraneous forces are so small compared with the gravitation of the central body that the orbit is approximately an ellipse, and the preliminary computations, as well as all determinations in which a high degree of precision is not necessary, are made on the hypothesis of elliptic orbits.

00In the Berlin Memoirs for 1778 and 1783 Lagrange gave the first direct and theoretically perfect method of determining cometary orbits.

00It was followed by a series of profound investigations, in which Lagrange and Laplace alternately surpassed and supplemented each other in assigning limits of variation to the several elements of the planetary orbits.

00The long-sought cause of the "great inequality" of Jupiter and Saturn was found in the near approach to commensurability of their mean motions; it was demonstrated in two elegant theorems, independently of any except the most general considerations as to mass, that the mutual action of the planets could never largely affect the eccentricities and inclinations of their orbits; and the singular peculiarities detected by him in the Jovian system were expressed in the so-called "laws of Laplace."

00John Kepler inferred that the planets move in their orbits under some influence or force exerted by the sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to admit of a precise statement of the nature of the force.

00From an investigation of all the observations upon Mercury and the other three interior planets, Simon Newcomb found it almost out of the question that any such mass of matter could exist without changing either the figure of the sun itself or the motion of the planes of the orbits of either Mercury or Venus.

00The attention devoted to the matter soon elucidated the phenomena of meteors, and proved them to be small planetary bodies, practically infinite in numbers and illimitable in the extent and variety of their orbits.

00The great variety in the apparent motions of meteors proves that they are not directed from the plane of the ecliptic; hence their orbits are not like the orbits of planets and short-period comets, which are little inclined, but like the orbits of parabolic comets, which often have great inclinations.

00- The postfrontal bones are restricted to the posterior border of the orbits.

00ELLIPTICITY, in astronomy, deviation from a circular or spherical form; applied to the elliptic orbits of heavenly bodies, or the spheroidal form of such bodies.

00He was several times a successful competitor for the prizes given by the Academy of Sciences of Paris; the subjects of his essays being: - the laws of motion (Discours sur les lois de la communication du mouvement, 1727), the elliptical orbits of the planets, and the inclinations of the planetary orbits (Essai d'une nouvelle physique celeste, 1735).

00orbits so nearly circular in form that the unaided eye would not notice the deviation from that form.

00But as the orbits are not centred on the sun, which is in a focus of each, the displacement of the seeming circle would be readily seen in the case of Mercury and of Mars.

00The major planets all move around the sun in the same direction, from west to east, in orbits but little inclined to each other.

00All the known minor planets have the same common direction, but their orbits generally have a greater eccentricity and mutual inclination.

00The general rule is that the satellites also move round in the same direction, and in orbits of moderate inclination.

00For the elements of the orbits, and the general character of the several planets see PLANET.

00He studied medicine at GÃ¶ttingen, 1 7771 7 80, attending at the same time Kaestner's mathematical course; and in 1779, while watching by the sick-bed of a fellow-student, he devised a method of calculating cometary orbits which made an epoch in the treatment of the subject, and is still extensively used.

00A table of eighty-seven calculated orbits was appended, enlarged by Encke in the second edition (1847) to 178, and by Galle in the third (1864) to 242.

00His demonstration that the planes of all the planetary orbits pass through the centre of the sun, coupled with his clear recognition of the sun as the moving power of the system, entitles him to rank as the founder of physical astronomy.

00Aberration Of Light This astronomical phenomenon may be defined as an apparent motion of the heavenly bodies; the stars describing annually orbits more or less elliptical, according to the latitude of the star; consequently at any moment the star appears to be displaced from its true position.

00Pursuing the investigations of Laplace, he demonstrated with greater rigour the stability of the solar system, and calculated the limits within which the eccentricities and inclinations of the planetary orbits vary.

00The skull is elongated, with an overhanging occiput, complete bony rims to the orbits, and the premaxillae separated from the arched and rather long nasals.

00The skull generally resembles that of Camelus, the relatively larger brain-cavity and orbits and less developed cranial ridges being due to its smaller size.

00Before leaving it for Queen's College, Oxford, in 1673, he had observed the change in the variation of the compass, and at the age of nineteen, he supplied a new and improved method of determining the elements of the planetary orbits (Phil.

00But, as has been remarked by Dr Robert Grant (History of Physical Astronomy, p. 515), we are no more warranted in drawing so important a conclusion from casual remarks, however sagacious, than we should be justified in stating that Seneca was in possession of the discoveries of Newton because he predicted that comets would one day be found to revolve in periodic orbits.

00When the orbits are eccentric, the tidal disturbance varying with the distance between the two components will probably cause changes in their absolute brilliancy; the variation due to change in the aspect of the system presented to us may thus be supplemented by a real intrinsic variation, both, however, being regulated by the orbital motion.

00Albrecht has shown that, of the 10 members of the S Cephei class for which both the orbits and the light-variations are thoroughly known, the maximum light always occurs approximately at the time when the brighter component is approaching us most rapidly; this relation, which seems to be well established, is a most perplexing one.

00From the very few orbits that have as yet been determined one interesting result has been arrived at.

00Most of the orbits are remarkably eccentric ellipses, the average eccentricity being about 0.5.

00Tidal action also accounts for the progressively increasing eccentricities of the orbits, already referred to.

00The mutual gravitation of a large number of stars crowded in a comparatively small space must be considerable, and the individual stars must move in irregular orbits under their mutual attractions.

00lvi.; the orbits of the principal binaries are discussed in T.

00His great contribution to astronomy dates from 1866, when he showed that meteors or shooting stars traverse space in cometary orbits, and, in particular, that the orbits of the Perseids and Comet III., 1862, and of the Leonids and Comet I., 1866, were practically the same.

00If in this we put r= I/u, and eliminate t by means of (15), we obtain the general differential equation of central orbits, viz.

00The orbits may be divided into two classes according as h2>

00The question presents itself whether ther then is any other law of force, giving a finite velocity from infinity, under which all finite orbits are necessarily closed curves.

00The n formulae of this type represent a normal mode of free vibration; the individual particles revolve as a rule in elliptic orbits which gradually contract according to the law indicated by the exponential factor.

00If the friction be relatively small, all the normal modes are of this character, and unless two or more values of ~ are nearly equal the elliptic orbits are very elongated.

00The results of these skilfully conducted observations were published in a memoir on The Uranian and Neptunian Systems. 3 From this research it appears that the orbits of all four satellites of Uranus are sensibly circular, and although no special search was made, he concludes that none of Sir William Herschel's supposed outer satellites can have any real existence.

00Thus the " Celtic " ox (Bos longifrons), from remote ages the common type in the Alpine regions, is characterized by the height of its forehead above the orbits, by its highly-developed occipital region, and its small horns.

00In 1809 he published at Hamburg his Theoria motus corporum coelestium, a work which gave a powerful impulse to the true methods of astronomical observation; and his astronomical workings, observations, calculations of orbits of planets and comets, &c., are very numerous and valuable.

00In man the surface of the skull is comparatively smooth, and the brow-ridges project but little, while in the gorilla these ridges overhang the cavernous orbits like penthouse roofs.

00Several estimates have been made which agree well together; whether direct use is made of known parallaxes, or comparison is made with binaries of well-determined orbits of the same spectral type as the sun, in which therefore it may be assumed there is the same relation between mass and brilliancy (Gore), the result is found that the sun's magnitude is - 26.5, or the sun is Io n times as brilliant as a first magnitude star; it would follow that the sun viewed from a Centauri would appear as of magnitude 0.7, and from a star of average distance which has a parallax certainly less than o 1 ", it would be at least fainter than the fifth magnitude, or, say, upon the border-line for naked-eye visibility.

00Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

00In the other letters written in 1685 and 1686 he applies to Flamsteed for information respecting the orbits of the satellites of Jupiter and Saturn, respecting the rise and fall of the spring and neap tides at the solstices and the equinoxes, respecting the flattening of Jupiter at the poles (which, if certain, he says, would conduce much to the stating the reasons of the precession of the equinoxes), and respecting the difference between the observed places of Saturn and those computed from Kepler's tables about the time of his conjunction with Jupiter.

00It would add to my satisfaction if you would be pleased to let me know the long diameters of the orbits of Jupiter and Saturn, assigned by yourself and Mr Halley in your new tables, that I may see how the sesquialteral proportion fills the heavens, together with another small proportion which must be allowed for."

00At the other extreme we know that innumerable swarms of minute bodies, probably little more than particles, move round the sun in orbits of every degree of eccentricity, making themselves known to us only in the exceptional cases when they strike the earth's atmosphere.

00Even in the case of the planets, the variations in the form and position of the orbits are so slow that long periods of observation are required for their correct determination.

00Among the problems of theoretical astronomy we may assign the first place to the determination of orbits, which is auxiliary to the prediction of the apparent motions of a planet, satellite or star.

00But when definitive results as to the orbits are required, it is necessary to compute the perturbations produced by such of the major planets as have affected the motions of the body.

00The precision with which the path of an eclipse is laid down years in advance cannot but imbue the minds of men with a high sense of the perfection reached by astronomical theories; and the discovery, by purely mathematical processes, of the changes which the orbits and motions of the planets are to undergo through future ages is more impressive the more fully one apprehends the nature of the problem.

00(4) If a number of bodies are projected from any point in space with the same velocity, but in various directions, and subjected only to the attraction of the sun, they will all return to the point of projection at the same moment, although the orbits in which they move may be ever so different.

00These conditions are: - (I) The smallness of the masses of the planets in comparison with that of the sun, in consequence of which the orbit of each planet deviates but slightly from an ellipse during any one revolution; (2) the fact that the orbits of the planets are nearly circular, and the planes of their orbits but slightly inclined to each other.

00The result of these conditions is that all the quantities required admit of development in series proceeding according to the powers of the eccentricities and inclinations of the orbits, and the ratio of the masses of the several planets to the mass of the sun.

00We first conceive of the planets as moving in invariable elliptic orbits, and thus obtain approximate expressions for their positions at any moment.

00But the variations thus determined will not be rigorously exact, because the pull from which they arise has been determined on the supposition that the planets are moving in unvarying orbits, whereas the actual pull depends on the actual position of the planets.

00The first depend on the mean longitudes of the planets, and always tend back to their original values when the planets return to their original positions in their orbits.

00The orbits thus present themselves to us in the words of a distinguished writer as " Great clocks of eternity which beat ages as ours beat seconds."

00In the problems of celestial mechanics the angles within the parentheses are represented by sums or differences of multiples of the mean longitudes of the planets as they move round their orbits.

003 represent the two orbits, the sun being at C. We know that the period of Jupiter is nearly twelve years, and that of Saturn a little less than thirty years.

00The result of these repetitions is that, during a number of revolutions, the special mutual actions of the two planets at these three points of their orbits repeat themselves, while the actions corresponding to the three intermediate arcs are wanting.

00Thus it happens that if the mutual actions are balanced through a period of a few revolutions only there is a small residuum of forces corresponding to the three regions in question, which repeats itself in the same way, and which, if it continued indefinitely, would entirely change the forms of the two orbits.

00If we conceive a pole to each of these orbits, determined by the points in which lines perpendicular to their planes intersect the celestial sphere, the pole of the satellite orbit will revolve around the pole of the planetary orbit precisely as the pole of the earth does around the pole of the ecliptic, the inclination of the two orbits remaining unchanged.

00The orbits of these bodies have a large inclination, nearly 27°, to the plane of the planet's orbit.

00Nor was it feasible, on this showing, to place the sun at the true centre of any of the planetary orbits; so that his ruling position in the midst of them was illusory.

00The proper share of each in bringing about this memorable result is not easy to apportion, since they freely imparted and profited by one another's advances and improvements; it need only be said that the fundamental proposition of the invariability of the planetary major axes laid down with restrictions by Laplace in 1773, was finally established by Lagrange in 1776; while Laplace in 1784 proved the subsistence of such a relation between the eccentricities of the planetary orbits on the one hand, and their inclinations on the other, that an increase of either element could, in any single case, proceed only to a very small extent.

00He, moreover, threw out the suggestion (in his Cometographia, 1668) that comets move round the sun in orbits of a parabolic form.

00MUSIC OF THE SPHERES, in Pythagorean philosophy, the harmony produced by the heavenly bodies in their orbits, inaudible to human ears.

00When all the bodies of the system are taken into account, the invariable plane is a certain mean among the planes of all the orbits.

00He shows that, supposing the cloud of particles to move around the sun in nearly circular orbits immediately outside the earth, the perturbations by the earth in the motion of the particles will result in their retardation in that part of the orbit nearest the earth, and therefore in their always being more numerous in a given space in this part of the orbit Ethan in any other.

00Of supreme importance is the fertile conception of the planets revolving about the sun in elliptic orbits.

00This image is made up from the many pictures received from the NEAR Shoemaker spacecraft as it orbits the asteroid Eros.

00bifurcation parameter, yielding to chaos and unstable periodic orbits.

00comet orbits.

00conic section orbits is sketched in Cor.

00changing the eccentricity enables orbits of planets and comets to be compared.

00The lower two frames show eccentricity, or how elliptical their orbits are.

00These are on very elliptical orbits, and almost all approach within 38 AU of the Sun.

00Interactions with Neptune and Uranus have made their orbits so elliptical.

00elliptical orbits into spiral arms.

00The orbits are tilted to the earth's equator by 55 degrees to ensure coverage of polar regions.

00hap hazard orbits, eternally falling into the night.

00heliocentric orbits, forming a triangle of 5 million km sides.

00Tan Lei (Warwick) Orbits correspondence in parabolic implosion.

00The Moon orbits the spinning earth that is itself in orbits the spinning earth that is itself in orbit round the Sun.

00These density waves are twisted by the elliptical orbits into spiral arms.

00We study the homoclinic orbits of the completely integrable discrete sine-Gordon.

00Geosynchronous orbits are ones where an artificial satellite in orbit around the Earth has a period of exactly one day.

00In addition the mechanism of control for periodic orbits is now quite well understood [2] .

00In Vienna, Professor Edmond Weiss was busy calculating probable close encounters between Earth and comet orbits.

00orbits of comets.

00periodic orbits is now quite well understood [2] .

00perturb orbits.

00planets in tight, circular orbits.

00Players can fly much closer to planetary bodies; where space stations can hang in low planetary orbits.

00The extrasolar planet is five times as massive as Earth and orbits a red dwarf, a relatively cool star, every 10 years.

00semiclassical theory of scarring of quantum eigenfunctions by classical periodic orbits to include situations where these orbits undergo generic bifurcations.

00These objects are generally thought to have been scattered out to their present orbits by a gravitational slingshot with Neptune.

00spin around their stars at great speed, often in highly elliptical orbits.

00synchronous orbits, up to eight at a time, by Titan 3 rockets.

00unstable orbits can be stabilized by tiny control forces.

00The Newtonian theory is an analysis of the elementary movements which in their combination determine the planetary orbits, and gives the formula of the proportions according to which they act.

00In any case the orbits of comets are exposed to such tremendous perturbations from the planets that it is unsafe from the present orbit of a comet to conjecture what that orbit may have been in remote antiquity.

00von Oppolzer's Lehrbuch zur Bahnbestimmung der Kometen and Planeten (2 vols.), which contains voluminous tables, formulae, and instructions for the computation of orbits in the many special cases that arise.

00More recent and better adapted to study is Bauschinger's Bahnbestimmung der Himmelskorper (1 vol., Leipzig, 1906), which, alone of the three, treats orbits of satellites and double stars.

00Let PP1P2 be the path of the moving point, and let OT, OT 1, OT2, be drawn from the fixed point 0 parallel and equal to the velocities at P, P 1, respectively, then the locus of T is the hodograph of the orbits described by P (see figure).

00The distances separating the individual orbits in each group seem to approximate to a certain order of progression, expressed in Bode's law (see Bode).

00In other cases, such as the measurement of the mutual distances and position angles of the satellites of Jupiter, for derivation of the elements of the orbits of the satellites and the mass of Jupiter, reference must also be made to measures of standard stars whose relative distance and position angle is accurately determined by independent methods (see Annals of the Cape Observatory, vol.

00He studied medicine at GÃƒ¶ttingen, 1 7771 7 80, attending at the same time Kaestner's mathematical course; and in 1779, while watching by the sick-bed of a fellow-student, he devised a method of calculating cometary orbits which made an epoch in the treatment of the subject, and is still extensively used.

00In this, the most memorable of Kepler's multifarious writings, two of the cardinal principles of modern astronomy - the laws of elliptical orbits and of equal areas - were established (see Astronomy: History); important truths relating to gravity were enunciated, and the tides ascribed to the influence of lunar attraction; while an attempt to explain the planetary revolutions in the then backward condition of mechanical knowledge produced a theory of vortices closely resembling that afterwards adopted by Descartes.

00But popular phraseology did not conform to this canon, and comitia, which gained in current Latin the sense of "elections" was sometimes used of the assemblies of the Halley concluded that all the three orbits belonged to the same comet, of which the periodic time was about 76 years.

00Generalized features are also displayed by the Oligocene Hypisodus, which in its short skull and large orbits presents a curious approximation to the African dik-dik antelopes of the genus Madoqua (see Antelope).

00(1827), &c. In the first of these memoirs Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces.

00Details of the calculated orbits of 63 spectroscopic binaries are given in Publications of the Alleghany Observatory, vol.

00As early as 1860 Newcomb communicated an important memoir to the American Academy, 4 On the Secular Variations and Mutual Relation of the Orbits of the Asteroids, in which he discussed the two principal hypotheses to account for the origin of these bodies - one, that they are the shattered fragments of a single planet (Olbers' hypothesis), the other, that they have been formed by the breaking up of a revolving ring of nebulous matter.

00The orbits of these bodies have a large inclination, nearly 27Ã‚°, to the plane of the planet's orbit.

00The curve has important mechanical relations, in particular it is the orbit of a particle moving under the influence of a central force which varies inversely as the square of the distance of the particle; this is the gravitational law of force, and the curve consequently represents the orbits of the planets if only an individual planet and the sun be considered; the other planets, however, disturb this orbit (see Mechanics).

00We extend the semiclassical theory of scarring of quantum eigenfunctions by classical periodic orbits to include situations where these orbits undergo generic bifurcations.

00Some of these giant worlds spin around their stars at great speed, often in highly elliptical orbits.

00The 100lb satellites were launched into near synchronous orbits, up to eight at a time, by Titan 3 rockets.

00Kepler's discoveries on celestial bodies and their orbits were revolutionary in his time.

00Turbine blades turn in several parts of the country, generating power from the wind currents that flow across the Earth as a direct result of the uneven heating of the planet as it orbits the sun.

00Maxilla-The bone of the upper jaw which serves as a foundation of the face and supports the orbits.

00In the early 1600's Johannes Kepler discovered that the elliptical orbits of the planets as they circled the sun and referred to the Divine Proportion in his explanation.

00No one likes to deal with a chronically autocratic, pain-in the-butt twit who thinks he orbits in a more rarefied atmosphere far above any of the sub-par creatures he's forced deal with, crawling thru the slime way down below.

00Discarding those of Uranus, in which the orbits of the satellites are highly inclined to the ecliptic, and in which manifestly some exceptional influences have been at work, we find that the satellites revolve around the primaries also in the same direction (Exceptions are Saturn ix.

01In this way we account most simply for the uniformity in the direction in which the planets revolve, and for the mutual proximity of the planes in which their orbits are contained.

01The modern method of determining orbits from three or four observations was first developed by C. F.

01- Among recent works on the determination of orbits, J.

01For those orbits whose projection upon a plane perpendicular to the field is righthanded, the period of revolution will be accelerated by the field (since the electron current is negative), and the magnetic moment consequently increased; for those which are left-handed, the period will be retarded and the moment diminished.

01The main anatomical justification of this sub-family is given by the postfrontal bones, which, besides bordering the orbits posteriorly, are extended forwards so as to form the upper border of the orbits, separating the latter from the frontals.

01We have seen that under the law of the inverse square all finit orbits are elliptical.

01

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