Show LECTURES ON ASTRON ASTRONOMY OBIT BY PROF bason PRATT LECTURE FIFTH all that we have stated in our former lee lectures bires gives us no inform information ution in regard to the mode of oata obtaining 1 itina the true distance of the earth from the sun we have heretofore merely merel y assumed tiie the mean distance to be equal to unity and pointed out the method of determining ter fer the proportional distances in different parts of re its orbit as well as the law of its proportional velocities lo but these proportional distances and velocities lo cities do not inform us whether the sun is ten miles off or ten thousand millions of miles TO persons unacquainted with the principles of trigonometry it may nayse seem ern impossible to measure the distance to an inaccessible object like the sun stin but it must be admitted thattie that the results derived from calculations do with the greatest accuracy corres pond with actual measurements where the objects are accessible and there therefore foreit it cannot be doubted but that the same rules when applied to inaccessible ob give just as accurate results if a person wished asbed to know the exact distance from this council house to some visible object on an island in the salt lake laie let him accurately measure a base line in some convenient direction dai action not directly towards or from the object let this line be some 2 or 3 miles in length from each extremity of this line take the angle which it makes with the object and if the measurements of these angles and base line be correct he can in a few minutes calculate the exact distance to the object it is exactly upon this principle that we calculate the distance honi h oni the earth to the sun the semi diameter of the earth is chosen as the bise base line 1 observations upon the suns apparent place in i a tho the ke heavens avens as seen from the extremities of this base line pre are accurately accurate lv taken the amount of angular displacement arising from foro the difference of the positions from which the observations were taken is called the suns suna horizontal parallax this displacement pr parallax maybe may be more clearly understood by supposing three observers to be stationed u upon pon the same saffie ropi idian about the time when the sun sim crosses the equinoctial let one of these observers he be stationed at this city another be stationed on the equator due south and the third as far south of the e equator 01 wr as we are re north at noon the observer at agi the equator will see the chesun sun directly over head or in the zenith it will appear to him in the same position as it would to an observer placed at the centre of the earth abis his may may be termed its true position but the oleaver at tw this I 1 city would woold behold the sun displaced W jo 10 the south of its true place while tiie e 0 observer tn inthe ahe southern hemi bemi phere would see th esuna little north of its true place the distance lit lat it deviates either north or south of its true place is called its parallax 1 the creater the distance of the stations either north coriou er the greater will be the parallax chispa this pa allax may be inea measured by astronomy astro nom norn cal instruments I 1 at any two stations 0 on the same meridian in the northern and southern hem hemispheres land and the distance between the stations beina being equal to the sum slim of the signs of the latitude is known ana therefore the afore it is easy from these data to compute the suns real distance the s suns great a t distance compared with the semi of the earth arth renders the honz horizontal parallax very mall and alid consequently a very small error in the observed parallax will make many m lyions of miles error in the computed distance of the sun towards the last of the seventeenth seventeen ih century dr di hauey halley pointed out ont a method of obtaining the sons horizontal parallax with far greater accuracy than what was ever before known his method depended tipon tillon the observations of i the he transits transita tran sits of venus across the suns dise disc this happens gappens only once or twice ii ia a century dr halley in 1691 predicted a transit ahvenus 41 Tenus that happ enedin in 1761 he showed how astronomers by being stationed in different parts of the earth andy and y observing the exact time of the beginning and end of the transit might calculate with a grat at degree of accuracy the suns hor horizontal montal parallax accordingly when the time drew draw near several nations sited out expeditions to various quarters of the earth this disi desirable rable object the results of their combined observations and calculations give a horizontal parallax at the sun sundean mean distance eq equal bial to sec by a simple calculation this parallax gives the suns mean mead distance equal to 2419 times the mean radius of the eaith HIP mean semi gemi diameter of the earth is equal to mi miles 1 es this multiplied into the be above gives miles this distance can be relied upon it exact within a very y small fraction of the whole amount by multiplying the mean distance bythe by the pro proportional poll distances of the extremes and which as we have already shown are deduced from the observed apparent diameters of the sun stin when in apogee POE ee and pongee perigee we obtain his gi cicat eaf est and least nf dist distances nees from the earth ex expressed presed in in miles which are respect respectively ivOy equal to and the eccentricity of the orbit is obtained by taking the diffie difference rence between the mem distance and either extremes extreme whiz which is val to 1 miles about the of Di december cember when the eat eaith th is in that pont of its orbit called the perihelion the sun is miles nearer the earth than on the alst 1st ownly when it is in its aphelion the circumference of 4 a circle whose semi diameter is equal to the earths mean distance from the sun would be miles mile but the earths orbit being t elliptical its circumference is about miles less than this or about equal to miles which is the of a circle whose diameter is half the sum of the major and minor axes of the orbit over this vast distance i es every year the average velocity odthe of the earth berday is 1635 miles the average per hour is wiles miles during the time that this audience have been listening to my lecture they have been caffea wafted with an average velocity of 11 1136 36 miles antes every minute little do we team realize ze that during every second of time we are I 1 transported 19 rn miles iles in in space we are startled at the a annon baU ball flying 8 miles per minute I 1 and wonder tp w x it is possible pbs sible for it to dart with such P great mt rapidity but how inconceivably more hron on i g afis it ia tt tc this vast globe with all it I 1 conla contains inq flying through h space with a velocity I 1 44 tames sw fler than 1 li 1 t of a cannon ball if ff we wei e to travel both day and night on oil a railroad car wua with a velocity i of 30 miles an lion it would require over 2271 years to pass over a space equal to the earths orbit obit we have al aheady eady staled staged that the velocity of the earth in its obit o bit is 6 not m at its mean ilaf d sl ance i its velocity in 24 mean solar hours is 1635 miles mile at the perihelion its daily dail v velocity is mile at the aphelion it is miles the difference between the extremes of the daily velocities is miles about the of december we are carried about 38 miles per minute swifter than on the let of july for the benefit of those who may desire to know the process of obtaining the velocity of the earth at any point of its elliptic orbit we ve will here give the formula formilia expressed in cods instead I 1 of symbols let twice the distance ft aiom om the upper focus of the ellipse be multiplied ino inlo the square of the velocity which the earth would have if it revolved in a circle whose radius is i equal to its di d stance from the sun and the product be divided by tile the maor insor axis of the orbit and the square root of the quotient will be e equal to the velocity of the earl earth h at any point ot oits its orbit in consequence of the unequal velo velocity cily of the earth it describes one half of its angular distance ai aund around the sun much sooner than the other half if we vve conceive a right 1 lie ne drawn through the sun at right angles to the major mai or axis as and extended expended on each side to the bartlit eart lit orbit that portion of the orbit on oil tile the pei ahel on side of this line will contain an equal Il number limber of degrees that the other portion contains but the portion poi tion of the orbit on the meribel pe peri ribel heln on side is much shorter ahoi ter and alo alio is described wilh wih greater velocity than the othe the difference of tune in the description of tin si se two portions of the debit is about 7 days davs and 17 houis bows cons q ici aly oui ou s trainer immer is about 8 days davs longer than our winte i that thai is is the still is is about 8 days longer ion 1 in the six signs on the northern side of afie th e eai eqi equator I 1 a than he is in tile 0 ther other six on oil the southern side during the time that the earth performs one annual revolution the inhabitants experience a variety of seasons those who live in the southern hemisphere have their seasons in the reverse order of those in the northern norl hem november december and january Jani iary are their monas mont ls while here they are our winter months their spring I 1 corre corresponds ponds to our autumn their winter to our their autumn to our spring when the lays days in the northern hemisphere are aie the longest in the southern th they ey are the shortest and vice verse versa when am ae the sh shortest ort e st here are the longest there from the of to the of september tile the sun shines without any intermission antei mission on our north pole while the south pole d tiring during that time is enveloped in darkness from the of september to the of march 1 the south pole is constantly enlightened by the sun while our north pole is left in darkness the whole order of the seasons in the northern hemisphere is is repeated in in the he southern but during daring the opposite time or of year if the earth revolved around tile the sun directly f om west to east that is if the plane of the earths orbit coincided with hie die pline plane of the equator there would be no variel variety y of seasons and ako aho I 1 the he days and nights over the whole earth would be of equal length if the earth revolved around the sun from south to north and back again to the south then our seasons would have the greatest possible change that could be given to them tile tiie df difference ference between the benl length th of days and nights would increase with much greater rapidity and the extremes of temperature between summer and winter would also be far greater on the of march the days and nights would be equal from that time until about the of may the days davs would in our latitude ro nc crease rease from 12 hours to 24 while the nights would decrease from 12 hows to nothing from the of aly ito to the ad of A agust the sun sim would not set to us hilt but he would be seen among our circumpolar stars exhibiting the same apparent phenomena man manifested bested by those stars about abom the ad of august au night would again set in the length of which would now nov increase until the of september when the days and nights would again be equal fi aiom orn the of september the length of the nights would increase until about the I 1 alth lill of november when the sun would set and remain below the southern horizon about 80 days or until about the of january when the day would set et in being behig only a few minute long at first but increasing rapidly in ill length until the of march when dagand day and night would again be equal thus if the earth revolved in an orbit whose plane was pern perpendicular end cular to the plane of the equator the vicissitudes of the seasons and the variations of day and night would be such as to render our globe unfit for the habitation of man at one season of the year he would be scorched not only with a vertical sun but with an accumulation of heat beat ar arising izing from the great ten th of the day wh le ie at another seison lie would be exposed to all the severity of cold experienced in the polar regions if the earth should revolve around the sun gun in in any other direction except the two that we have already mentioned the di difference ferenee of the seasons and of day and night would be proportional to the inclination of the ecliptic to the plane of the equator as the allie angle of inclination increases so would the differences in in the severity of the seasons increase title inclination of the two planes is called the olia of the ecliptic amich is about 23 de deg m 27 mm min see sec for the beginning of the present year from the of december to the 21 qt it of june the earth pursues a d not due east but beai neaily ly east south basti bvm om the of june jano to the of december its direction is nearly east cast northeast north east in december the earth is in cancer while the sun appears in capricorn it is evident that while the earth goes east southeast from cancer to capricorn it must pass from the north through the equinoctial plane to the e south the earth crosses the equinoctial about the of march it is then in the first point of abi L hi a while the sun sim appears in the first fira po pd nt of arie when the earth goes east northeast north ea east t from capricorn to cancer it re ic crosses the equinoctial from south to north about the of september when it is in the first point of aries and the sun appears in the fist point of lara As the ine earth goes round its annual circuit it nun man taina its axis axi i s parallel piral lel to 10 itself that is the angle of its inclination to the plane of its orbit obit o bit remains rem uns the same an entire revolution consequents the llie axis will be directed towards one particular point poat in the infinite sphere of the heaven in other words woi ds if the parallel parallel lines represented by the parallel position of the it axis in every point of its ife orbit were ere produced to the immense distance of the starry sphere they would seem to coalesce in in one point therefore Tiie Tae the stars because of their gi gibat eat distance would not exhibit Aliv fan v appreciable parallax or displacement by the earths annual motion that is the whole orbit of the earth if seen from the d stance of ohp th fixed stars appear like a mere pont po nt subtending sub tending no apparent angle now if a line be drawn from the sun sim to the earth it will be perpendicular to the axis of rotation when the earth is in the venal and autumnal equinoxes equinox es hence the days and nights will he equal at ill all other seasons of the year the angle which the radius vector makes w th the file axis of rotation deviates from the perpendicular this deviation on either side of the perpendicular is equal to th the e suns north or south deel matios when the sun is in either of the trop tropics cs the deviation is is at its maximum and is then to the obliquity of the ecliptic aalthe all the variety of the seasons lo together grether with the differ differences entes of the length of day and night are the results of the continual variation of this angle and the variation of the anode angle which the radius vector makes make with the earths ax axis ali s is the result of the ubiquity of w sm of the axis in different points of the abit the ecliptic is divided di into twelve equal parts called signs each sign therefore contains 30 degrees these signs are reckoned f om the vernal vei nil equinox and are called aries taurus gemini gem ini cancer leo virgol bra scorpio 0 o S 8 Capric Capri comus omu 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