# Parallax Sentence Examples

For the relation of this inequality to the solar

**parallax**see Moon.Brown the value of the solar

**parallax**derived by this method is about 8.773".To obtain the true

**parallax**, the mean**parallax**of the comparison stars must be added to this relative**parallax**.Annual

**parallax**is the angle between the direction in which a star appears from the earth and the direction in which it appears from the centre of the sun.It is, the orbit and periodic time is known, and also the

**parallax**, the masses of the stars can be found.AdvertisementThe stars selected to be examined for

**parallax**are usually either the brightest stars or those with an especially large proper motion.He now resolved to try the experiment of applying photography to the determination of stellar

**parallax**.He was elected a fellow of the Royal Society in 1840, and in 1892 was awarded one of the royal medals for his work on photometry and stellar

**parallax**.Doubt was first thrown on the accuracy of this number by an announcement from Hansen in 1862 that the observed parallactic inequality of the moon was irreconcilable with the accepted value of the solar

**parallax**, and indicated the much larger value 8.97".By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the

**parallax**derived from each.AdvertisementHad the internal contacts alone been used, which many astronomers would have considered the proper course, the result would have been 8.776" In 1877 Sir David Gill organized an expedition to the island of Ascension to observe the

**parallax**of Mars with the heliometer.The failure of the method based on transits of Venus led to an international effort carried out on the initiative of Sir David Gill to measure the

**parallax**by observations on those minor planets which approach nearest the earth.On these occasions the actual

**parallax**would be six times greater than that of the sun, and could therefore be measured with much greater precision than in the case of any other planet.So exact is the latter determination that, were there no weak point in the subsequent parts of the process, this method would give far the most certain result for the solar

**parallax**.The theoretical element is the ratio of the parallactic inequality to the solar

**parallax**.AdvertisementProbably no general agreement could now be reached on a statement more definite than this; the last result may be left out of consideration, and the value of the solar

**parallax**is probably contained between the limits 8.77" and 8.80."These pairs of observations have shown a

**parallax**from which the elevation of the objects above the earth, the lengths and directions of their courses, &c. could be computed.The instrument so altered was in use at the Cape Observatory from March 1881 till 1887 in determining the

**parallax**of some of the more interesting southern stars.Examples of this mode of procedure will be found, in the case of stellar

**parallax**in the Mem.He also reduced the solar

**parallax**to 14" (less than a quarter of Kepler's estimate), corrected the sun's semi-diameter to 15' 45", recommended decimal notation, and was the first to make tidal observations.AdvertisementIn 1680 Jean Picard, in his Voyage d'Uranibourg, stated, as a result of ten years' observations, that Polaris, or the Pole Star, exhibited variations in its position amounting to 40" annually; some astronomers endeavoured to explain this by

**parallax**, but these attempts were futile, for the motion was at variance with that which**parallax**would occasion.Most of the mechanical contrivances which made Tycho Brahe's instruments so superior to those of his contemporaries were adopted at Cassel about 1584, and from that time the observations made there seem to have been about as accurate as Tycho's; but the resulting longitudes were 6' too great in consequence of the adopted solar

**parallax**of 3'.The greatest displacement of the star from its mean position (the semi-axis major of the ellipse) is called its

**parallax**.He found for it a

**parallax**of o 35" a value which agrees well with more modern determinations.Henderson at the Cape of Good Hope measured the

**parallax**of a Centauri, but his resulting value 1" was considerably too high.AdvertisementMore accurate determinations have shown that this star, which is the third brightest star in the heavens, has a

**parallax**of 0.75", this indicates that its distance is 25,000,000,000,000 m.The quantity determined by these methods is the relative

**parallax**between the star measured and the stars with which it is compared.It is, however, fair to assume that the comparison stars will rarely have a

**parallax**as great as o oi "; for it must be remembered that it is quite the exception for a star taken at random to have an appreciable**parallax**; particularly if a star has an ordinarily small proper motion, it is likely to be very distant.A

**parallax**of 0.01" denotes a distance a hundred times as great, and so on, the distance and**parallax**being inversely proportional.Neither criterion is a guarantee that the star shall have a measurable

**parallax**.These two stars must have an intrinsic brilliancy enormously greater than that of the sun, for if the sun were removed to such a distance (

**parallax**o oi"), it would appear to be of about the tenth magnitude.It is greatly to be desired that a general survey of the heavens, or cf typical regions of the heavens, should be made with a view to determining all the stars which have an appreciable

**parallax**.We should learn perhaps the distribution and luminosities of the stars within a sphere of radius sixty light years (corresponding to a

**parallax**of about 0.05"), but of the structure of the million-fold greater system of stars, lying be y ond this limit, yet visible in our telescopes, we should learn nothing except by analogy.When the

**parallax**of a star is known, we are able to infer from its proper motion its actual linear speed in miles per hour, in so far as the motion is transverse to the line of sight.This result, while it does not afford any means of determining the parallaxes of individual stars, enables us to determine the mean

**parallax**of a group of stars, if we may assume their peculiar motions practically to cancel one another.Estimates of this distance vary, but it may probably be put at more than three thousand light years (

**parallax**less than o ooi ").As has been explained the mean distance of a group of stars can be readily determined from the parallactic motion, which, when not foreshortened, is approximately four times the

**parallax**; but to obtain a complete knowledge of the distribution of stars it is necessary to know, not merely the mean**parallax**of the group, but also the frequency law, i.e.It was at Ascension that Mr, afterwards Sir, David Gill determined, in 1877, the solar

**parallax**.The first really adequate determinations of solar

**parallax**were those of Sir David Gill, measured by inference from the apparent diurnal shift of Mars among the stars as the earth turned diurnally upon its axis; the observations were made at the island of Ascension in 1878.The equation of light is the time taken by light to traverse the sun's mean distance from the earth; it can be found by the acceleration or retardation of the eclipses of Jupiter's satellites according as Jupiter is approaching opposition or conjunction with the sun; a recent analysis shows that its value is 498.6", which leads to the same value of the

**parallax**as above, but the internal discrepancies of the material put its authority upon a much lower level.C. Chandler considers the value 20.52" is well established; this would give a

**parallax**of 8.78".Brown's lunar theory would imply a

**parallax**8.778".Using the

**parallax**8.80", the resulting diameter of the sun is 864,000 m.No certain guide has been found to tell which stars are nearest to us; both brightness and large proper motion, though of course increased by proximity, are apparently without systematic average relation to

**parallax**.Several 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.P. Langley's Researches on Solar Heat are published by the War Department (Signal Service, xv.) (Washington, 1884), and Gill's

**parallax**researches in Cape Annals, vols.Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the

**parallax**, or the inclination of the lunar orbit.Oscil., a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in Philosophy, and added out of my aforesaid paper an instance of their usefulness, in comparing the forces of the moon from the earth, and earth from the sun; in determining a problem about the moon's phase, and putting a limit to the sun's

**parallax**, which shews that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it; so that a while after, when Mr Hooke propounded the problem solemnly, in the end of his attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now.The volume of the gas in the measuring tube is determined by bringing the water in both tubes to the same level, and reading the graduation on the tube, avoiding

**parallax**and the other errors associated with recording the coincidence of a graduation with a (By permission of Messrs Baird & Tatlock.) FIG.His discussion of the effects of

**parallax**in the transit of a planet over the sun's disc excited great interest, having appeared (in 1764) between the dates of the two transits of Venus that took place in the 18th century.Thus a reduction for

**parallax**is required.Among the fruits of the strenuous career of Nicolas Louis de Lacaille were tables of the sun, in which terms depending upon planetary perturbations were, for the first time, introduced (1758); an extended acquaintance with the southern heavens; and a determination of the moon's

**parallax**from observations made at opposite extremities of an arc of the meridian 85' in length.Leverrier, in 1858, calculated a value of 8.95" for the solar

**parallax**(equivalent to a distance of 91,000,000 m.) from the " parallactic inequality " of the moon; Professor Newcomb, using other forms of the gravitational method, derived in 1895 a**parallax**of 8.76".The rate of light-transmission was accordingly made the subject of an elaborate set of experiments by Professor Newcomb in 1880-1882; and the result, taken in connexion with the aberration-constant as determined at Pulkowa, yielded a solar

**parallax**of 8.79", or a distance (in round numbers) of 93,000,000 m.The opposition of November 1900, though only moderately favourable, could not be neglected; an international photographic campaign was organized at Paris with the aid of 58 observatories; and the voluminous collected data imply, so far as they have been discussed, a

**parallax**for the sun a little greater than 8.8".C. Kapteyn and Simon Newcomb, to estimate, through the analysis of their proper motions, the " mean

**parallax**" of stars assorted by magnitude.The

**parallax**of the moon is determined by observation from two widely separated points; the most accurate measures are those made at Greenwich and at the Cape of Good Hope.The measures of

**parallax**agree perfectly with the computed distance in showing a mean**parallax**of 57' 2.8", and a mean distance of 238,800 miles.The expressions for the longitude, latitude `and

**parallax**appear as an infinite trigonometric series, in which the coefficients of the sines and cosines are themselves infinite series proceeding according to the powers of the above small numbers.Among its results were determinations of the lunar and of the solar

**parallax**(Mars serving as an intermediary), the first measurement of a South African arc of the meridian, and the observation of io,000 southern stars.More valid instances of the anticipation of modern discoveries may be found in his prevision that a small annual

**parallax**would eventually be found for some of the fixed stars, and that extra-Saturnian planets would at some future time be ascertained to exist, and in his conviction that light travels with a measurable, although, in relation to terrestrial distances, infinite velocity.That he had carefully studied the comet of 1577 as an astronomer, we may gather from his adducing the very small

**parallax**of this comet as disproving the assertion of the Aristotelians that a solid sphere enveloped the heavens.He found that as the observer moved to the north or south the axis of the light appeared to be displaced in the direction of the motion, which is the opposite of the effect due to

**parallax**, but in the same sense as the effect of the greater atmospheric absorption of the light on the side nearest the horizon.They took advantage of this fact to explain to them that this distance was obtained by measuring the

**parallax**of the moon.Seeing the two stars allowed astronomers to calculate the foreground star's distance from Earth, using a method called

**parallax**.However, even with the most powerful modern telescopes, there is only so far you can go with using

**parallax**.A transit of Venus, as it is called, was once of great practical observational importance for determining the solar

**parallax**.Trigonometric

**parallax**is used to measure the distances of the nearby stars.His reasoning was correct, but even Tycho's marvelous instruments were not accurate enough to register stellar

**parallax**given the vast distances involved.From their data the first accurate value of the solar

**parallax**was found, giving the distance from the Earth to the sun.What is its true declination, after correcting for geocentric

**parallax**?The isolated the motion

**parallax**cue by constructing a random dot display that was yoked to the movement of the head.The unit allows focusing of the specimen and camera image through the

**parallax**focus periscope.If the

**parallax**angle of a star is known then its distance can be calculated by trigonometry.It consisted essentially in the adoption of Delauny's final numerical expressions for longitude, latitude and

**parallax**, with a symbolic term attached to each number, the value of which was to be determined by substitution in the equations of motion.Geocentric

**parallax**is the angle between the direction of the body as seen from the surface of the earth and the direction in which it appears from the centre of the earth.Hipparchus fixed the chief data of astronomy - the lengths of the tropical and sidereal years, of the various months, and of the synodic periods of the five planets; determined the obliquity of the ecliptic and of the moon's path, the place of the sun's apogee, the eccentricity of his orbit, and the moon's horizontal

**parallax**; all with approximate accuracy.From the mode-7 rotating landscapes,

**parallax**scrolling and more, it's a treat for squinting eyes.From a fresh discussion of the transits of Venus in 1761 and 1769 he deduced (1822-1824) a solar

**parallax**of 8" 57, long accepted as authoritative.The most brilliant star of this constellation, a-Aquilae or Altair, has a

**parallax**of 0.23", and consequently is about eight times as bright as the sun; q-Aquilae is a short-period variable, while Nova Aquilae is a " temporary " or " new " star, discovered by Mrs Fleming of Harvard in 1899.For stellar parallaxes see Star; the solar

**parallax**is discussed below.The

**parallax**8.5776" found by Encke was therefore accepted without question, and was employed in the Nautical Almanac from 1834 to 1869.Advantage was taken of the occasion to make photographic measures for

**parallax**at various points of the earth on a very large scale.The corresponding value of the solar

**parallax**is 8.782".The determination of the solar

**parallax**through the parallactic inequality of the moon's motion also involves two elements - one of observation, the other of purely mathematical theory.In determinations of stellar or solar

**parallax**, comparison stars, symmetrically situated with respect to the object whose**parallax**is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results.This motion is evidently not due to

**parallax**, for, in this case, the maximum range should be between the June and December positions; neither was it due to observational errors.Assured that his explanation was true, Bradley corrected his observations for aberration, but he found that there still remained a residuum which was evidently not a

**parallax**, for it did not exhibit an annual cycle.The most important of these, the sun's mean

**parallax**, was at that time subject to considerable uncertainty.If 7r be the

**parallax**, and R the radius of the earth's orbit, the distance of the star is R/sin ir.The determination of stellar parallaxes is a matter of great difficulty on account of the minuteness of the angle to be measured, for in no case does the

**parallax**amount to I"; moreover, there is always an added difficulty in determining an annual change of position, for seasonal instrumental changes are liable to give rise to a spurious effect which will also have an annual period.In the table are collected the parallaxes and other data of all stars for which the most probable value of the

**parallax**exceeds 0.20".To convert parallaxes into distance we may remember that a

**parallax**of i" denotes a distance of 182 billion miles, or 206,000 times the distance of the sun from the earth.Brightness is particularly deceptive; thus Canopus, the second brightest star in the heavens, has probably a

**parallax**of less than 0.01 ", and so also has Rigel.If three plates (or three sets of exposures on one plate) are taken at intervals of six months, when the stars in the region have their maximum parallactic displacements, the first and third plates serve to eliminate the proper motion of the star, and the detection of a

**parallax**is easy.