Show A S T R 0 IN 0 M Y I 1 I 1 I 1 I 1 I 1 plain I 1 and easy rules por fay jinking the periodic C time T inte of a planet qi or I 1 its mean distance also to find its ais distance from Us its period I 1 I 1 r BY ORSON aratt sivi SEN 1 r I 1 I 1 I 1 TO TIM EDITOR E OF TRY NEWS 1 sm SIR I 1 saw an article in your paper or of the ilia irth mat insl handed ended hr samuel elliot cover core his bis theo rv of astronomy coph copied d from the U united states magazine it is with no small degree of pleasure that I 1 learn for the first time odthe laudable exertions ot of mr cues in ill endeavoring to trace put i iid and id tile laws that govern tile workings odthe Uld universe veree I 1 am hoppy also to learn tit it he hat has cist cast away the vague and foolish idea of attracting and projectile forces and adopted in iii some measure mearill re my iny t theory be rv or of the self moving for oes 14 of ahe which I 1 published 1 in Jati uary I 1 8 I 1 I 1 1 altho aldio he has endeavored to supe su the ane I third aw L caw of kepler in it regard to the relations I 1 existing between the dist distances ances and periods of tile the bodies of the solar system yet in the introduction 0 of r liis his new rules lie he has been obliged ph liged most unquestionably q to resort to that very hw in it obtaining his unit of djs distance taice namely miles which lie he assumes to bethe bathe ih bumeter or of the sun at talt precise distance tile periodic time of a I 1 body passing around the sun aun is equal to of 9 4 so sol lar ir da daiy TOW is the ratio of the diameter I 1 of a circle to 6 its circumference athe the circumference being equal ti J A 4 periodic time lime identical with this I 1 ratio is ascertained by th alie e app application ii ell I 1 on 0 of f kappers Kap lers law to require a di distance s t it th SIAM same hs as assumed by AL mr ir cones as hj liaa unit atilt the diameter of the sun suit may or may not agree with this assumed unit it may vary I 1 miles from it indeed there iw is no cause that we 1 ore are adire aware or of which would make the peri oJie aime represented by this ratio to ta agree with time lime as measured by the earths diurnal rotation in preference to the diuri diurnal thi periods of the other planets e ti 9 the lay sa s1 measured on other planets would each alter the assumed unit buethe but the diameter could not net agree with but one for the want of generality therefore in this assumed law I 1 see not the least grounds for believing in the coincidence said to exist between the diameter diamente 5 and the assumed unit ll 11 dividing the distance of the 1 earth from the a sun u I 1 by the unit distance of mr coues the ear earths thi mea moan n distance expressed in these units is obtained limiel namely y 61 the unit di distance of all the other planets 1 I ts is obtained in the same man magneri from attane aliese ese distances and with the td aid of the lie ratio of the of a circle to its diameter mr coues cones deduces the periodic time of each planet from its dista distance ilice without employing the lengthy and hviid tedious process connected with keilers Kep lers law which requires three terms given t to find a fourth the ratio of the circumference of a circle to jo its diameter is altogether kec eairy in tte calculation and ref readers derst the I 1 I 1 a binch more complex ban aban lif if not y aset iab yd istace may be as su sinned tood as a ui I 1 64 feul wak founded upon it itt ft fe results ant the assumption tie ji dr somo L me units unita will wil I 1 malce the in more ore tedious than others T I 1 wilt now g givelis gi i velt velie le following niiles Ri iles which I 1 invented severah years ago for kiy own uke use su ralfe f r I 1 1 to find the mean I 1 side sidereal reil period of a planetary body brou around d the sun hi mean aban days afien only distance dista neb m in miles artes is given ll 11 I 1 divide tho the distance by and the quotient mui multiplied plied into its own square root will be the required period drill or in other words divide the distance by und the cabe be 61 the squar square ro root I 1 0 t of the quotient ali be the ze repaired p od or M sr in AY be att thus 3 I 1 I 1 1 I 1 it 2 I 1 c p r I 1 11 11 1 f I 1 th in 7 to find the distance in only tile the pat pp feua OV bh I 1 multiply the square of the enbe cube root of the period by be the re auh curad ed distance i r v I 1 I 1 1 T I 1 I 1 algebraically th thus us I 1 1 I 1 il r nal nfl from tha reenter of thymn taun I 1 11 body around it in ill I 1 mean solar day I 1 chave have therefore chosen that distance as the un unity aty r 1 I 1 toys it elm I 1 I 1 1 i athe I 1 f tb le 1 planet at primed ji A I 1 milea ila by X e proportional die 7 1011 1 beita malaea ined expressed presed ex i I 1 ofello e a assumed ine 11 antt n as in the se second on co columb umu of the table at 0 ti I 1 J lot t 1 a 5 be assumed i tr or r I 1 j tt I 1 i the I 1 unity I 1 of r ca ic r xa mean distance i II 11 nein sidereal Side reaT HAM akst I 1 from the t period er lod ia A I 1 I 1 I 1 I 1 surl sun in n units 11 I 1 me mean qu solar daff da 95 i i 3 ei ry I 1 tauy W i I 1 r 1 51 I 1 1 1664 mars ar to 6 ato 1 ac I 1 ac 1 ac if in any y ol of f I 1 the hb mean distances in n the second clum dmn be multiplied into its own square root the product will express the solar days in its annu annual al period as in ia the third column por fat instance the square root of the earths unit distance diate ince 51 1 is i 74 these thes two numbers multiplied into each other give M 2563 dalf clays if any one of the perl periods in ali the third column tire are gevea the nit distance in the second olumn column may be found by y squaring lug the cube u be root roof of its period arl 0 a 1 1 this process is far less complex than that of mr conesor Coue sor t W cepl it Is ia foi fonn ded on the he folio wi ng law d that 10 t governs the planets it in i their orbits I 1 the ozithe planets la in different orbits ate ace Invie lly tits th the square roots root 1 of their mean distan distance cop thit that is one planet four times inore distant the centre of nhuon than an r ather has ins qu ehg velocity velo elty fity and 9 time mare j d distant v tant I 1 13 3 9 tit the e velocity andro times mare mire Z distant 1 14 1 4 tile tho velocity ac anuw N vw 1213 1 21 3 la 14 are the Verae square of their respective litlie alstn distances ces and bodies tia hafling vang 49 or 16 arnes grenter orbits and moving lieving with 1 only 19 12 1 9 2 1 13 3 or i 14 1 4 the velocity will require requires 8 27 or 64 tim times as long iong a period to complete their revolutions but 8 27 64 are the cubes of the s square roots of ohp distances stances dl 4 from this I 1 laware derived the two very plain rules which I 1 invented for my own convenience co iu in astronomical investigations investigation a J 1 present them chereb here hoping that thai they rny may be of some rothe utility in facility biting ink the dip researches of oth others Ts ali periodic time of a body e onh only I 1 mite mile distant froth from the he centre of motion in the sun asin assuming all Ms his gravitating forces collected in that thai point would be equal to a very small fraction or of a days day expressed by the following deci decimal tidal which multiplied bitet the cuber cube of the square root of any planetary distance expressed hi miles will give its meau mean sidereal period in solar eolar d days ays thus 1 I 1 11 3 I 1 2 I 1 00 00 00 2563 I 1 11 1 i I 1 mercury si d istance distance is miles there forey 91 9 1 r i 3 i r 1 I 1 I 1 I 1 I 1 I 1 in V I 1 I 1 M t f X 36 7 4 30 X I 1 f IA a time planet or comet met be e divided by 55 the square squar of the cube of the quotient I 1 will be ba ia its mean asic ance in miles thus I 1 I 1 I 1 I 1 j 1 I 1 I 1 a 3 y niile miles s I 1 I 1 I 1 I 1 I 1 I 1 87 a miles hilles I 1 if if alie mean dist destanee di anee of tile the earth from tho the sun be assumed as liiv oi or 1 then the cube of ti tho lo 10 square roo root t of the proportional distance of each pl planet aut mulu tallied til lied into will give I 1 its w mean man sidereal period in hi mehai mean solar days for example mars proportional mean distance from tile the sun is and I 1 1 I 1 3 I 1 2 f i 1 mars afar 1 I X 1796 4 I 1 a S I 1 I 1 mercur mercury i X 87 a 3 12 beims X the proportional distances profound are aro found via as follows I 1 I 1 1 maury y J the tha I 1 distance I 1 I 1 I 1 24 I 1 I 1 I 1 its lt pro proportional proportion portio nal I 1 I 1 destanee dist anee mars lan 11 SM 1 I 1 it artl I 1 I 1 i distance any of the unit winch which we ilav have I 1 13 assumed in the foregoing process has rendered the calculation much more easy and simple than ihan to employ as in keilers Kep lers jaw tho squares I 1 and cubes of ofa three known terms to find the square or cube of the fourth it is ia also alio much less complicated thlin the simpli simplifications fica eions of keilers Ke pleis law introduced by mr COUPS I 1 1 1 I 1 these simple rules are applicable in ill principle to the periodic times aid distances of all the heavenly periodic i b bodies ner 0 ies whether r planets asteroids comets satellites or stars I 1 yours most respectfully ORSON PRATT sen great geal salt lake city oct 24 1854 |