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

.1:j, tI A-[MOON.
haut a.rtain, if woe confino our attention to the moon's ])att ill
its rlttio,ls to tlhe s,?,n, itste ad of the eartll, and tr e it ts a
visilblt lile in the solar s 1stm, wse shtall s e tlat it loset cit.tirel3 its cltaracter of a small circle Oln thte cirenlmnl c n( c (olt e Of a
larle one. ()n the other hlandl it c.an Iharlly lbe dtistitngutisltcd
from,, the earth's orh)it itself, making 25 sliglt undulations'atenI1ately inside and outside of it, and never deviating g ftiomn it
inmre thantl one: 400tht part of its radis, as representeltd il
Fig. I4.1
Fig. 17'.
-..............-.."-.::...............s-~~'..........,~............
If \\e 1regarid nlow th:le /hoerc.s' to whllich t-he Ilmoonl is suhijtctedt
in describing this path, itf is clcta l tlat since it (1fifets> so little
fro1ll thlat of tie earth, the moonl must t)0 contlrolled biv neat ly
tlc samtle, fo)rces as those which kee) th}e eartht its it it So
thlat, if the earth were anllnliilatedfl tle lmoon (would still preserve its course romld the sun, with so little clhanllge It:onl its
present orblit, that it would hlardly be noticedl by an observer
who could taket e t we h ltole into vie')mew at- once. Accordilin to
tlhc second law of Ilotion (Nat.?I ltil. Art. 1"2), thlle,loon's Xmotil lrottItnd til eatrth simplyl Co-Cxists w' itti its Ilotionl rulid t1he
salnl; anll thi joint Iffect is i curvel' of tlhat species called ant
epicycloid.
222. T['Ie rlative attraction exerted by the sun and earth-i
upon tlhe mtoon, is found by applying the formula (Art. 17i7)
jO./? Callintg the radius of thle moonl's orl)it::::, thlat of the
eartht's is labout 400; and tthe times are 27.32 and 365.25.
l.entce, attraction to the sunl that to th}e eatrth.....
(dG~,.2.o)
*. ~5).:: 2.2. 1. So tlhat the sll tihough so very far filom
(S7 32)'
the m11oon, exerts upon it 2} times more attraction tlan thle
earthi does. Thle moon, theltefore, is u111ch mlore 1ulllder the influetlcc of the still thltan of thXe carthl; tic latter only eau-sint' it