An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

132'TlE; tOON.
cases is to draw the moon from the earthl in a direction perpendicular to tile line of the quiadratures. 1 1tce, tie generll l
result is, tthat by tlhe disturltilng force of tlle stun, the,'gravity to
tfhe eart i is increa.St(/ (t t1lb qt'atcuI'tUes, t(d diiinis is/d tg
the sIzfqies. It is found by3 c-lctdeultion tllat the taverage
amount of this disturbing force is;'Is' of ttCe moon's tgravity to
the eartlh.'W:
229. Wit-l tlese general princitples in view, we mayfly nowNV
proeeel to investigate the figure of thle moon's orbit, atnd tlhe
irre1cularities to wlhich the motions of this body arce sutbject.
230. Tl'7fi ture t/ the toon.'s o,;bit'is an elilpse, (avi2ng the
eaIthtl in, one ofJ the Jbci.
Tilhe elliptical figure of the moonl's orbit, is revealed to us by
observations onl iher cthanges in appart lt dialmeter, (anll iln her
horizontal par:dlax. ilrst, we:may t leaslurc fiol dy to day
the apptarent diameter of thle moon. l ts variations beitng invcrsely as tie distances (frt. 163), tlhey give us at once tthe
elatttbve di-stance of eachl point of observzation ftromn the foicus.
Seconldly, tihm variations on tlhe 1mooln's lorizontal parallax,
wvIichie also are inversely as tle (listances (Art. 82), lead to tlhe
samie results. ()lbsrvations otl the angular velocities, comlined w ithl the chlanges in thle lengths of the radius vector, afford thle metans of laying down a plot of the lunar orbit, as ill
the case of tile sun) represenltcl ill figur 32. flte orbit is
slhown to be nearly an ellipse, I)because it is found to hlave. thl
properties of an ellipse.'TIc tloonl's greatest and least aplarecnt diiamneterns are resl)ectivel1 33'.5.18 and 29'.365, Awlile hler corresponding chtaniges of
paratllax (are 61'.,. anJ-nd 53'.8.'lthe two ratios oughlt to be equal,
anld we shall finld such to be tle fact very nearly, as expressed
by the foregoing nulmbersl; for,
61.4: 5.S:: 33.518: 29.369.
Th'l}e greattest ad( least distances, of th}e mIoon fiom the earthl,
derived fiom tlhe parallaxes, are 63.:.841 9:and S.9 164^ or ne1arly
64' antId 56( the radius of tlhe eartht beintg ta kc for unit.y.
I eonce, takling tlhe aritltletical mllan, wtichl. is 59.879, we lind
* Playfair.