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

EALEMI'N'I/S OF' THEII1, PLANtTA;Y O 13I'ST 23 t
tions at thel greatest elolgation, las becn already cxplainll
(see Art. 308). th'lec distance of a s{uperwiot planct lmay be
found f'rol observatiolls Oil its retrograde motion at the timCle
of opposition. The periodic times of two plancts bcilng
know\it, wte of course know their mcan angular velocities,
whtich arle inlverlsely as tlhe times.'Thcreforle let 1%e (Fig'.'3)
)be a vely small portion of the earth's orb)it, anld 1Mm a corr-''sponding portion of that of a superior p1lanet, described on the
y of opposition,.abou............t t.e un, on which.day the t
deazy of oppllositioln, anboult thre sulll S, on whielt drlay th1e tlllre
Iodies lie il one st raight lille SE'MX.'Theln the angles J'Se
and ISm, repr)'esenting the respective angular Nvelocities of thle
two bodies, are known. Now if e~m be joindl, an1d prolonged
t-o meect SMt continued in X:, the angle -EXe, whichl is equall to
the alternate angle Xey, being equal to the retrogradation of
the planet inl the same time (being knLown from observation'),
is also given. Ect, therefore, and. tlhe angle 1EXe behilg given
in tihe ritlht-anglcd triangle EXe, the side EX is easily caleulated, and thtus SX becomes known. Consequcently, in tlhe
triangle S,X, we ]ave given t -he side SX, and the two angles
2SXX. tand miXS, whence the otller sides Sm? and mX arl'e easily
determ ined. Now Sm is tlhe radius vector of t]he orbit of the
suplerior planet at the point tlhrolgh ]which it was passing' at
tlhe time of thle observation. O) col rse, o0e sucl observation
could not be relied on as giving timhe fCea distance; but it
would be a satisfactory alpr t oxialion in the case of anyll planetar3y orbit, since these orbits are "all very ]nearly circular..Anl by repeating the process every yea'r, cas the earth passes
bcetween to'sun and planet, the averag& e of all will ultimately
el)preSS the mean distance, o01 selmli-major axis of the orbit il
questiont.*
37(i. I'onurthly, to determinte.le the t)Ie J?e1i/peele,
the time tif pa ssi:nq it, anl 1 te eccen7tricilty.
A. method applicable to the inferior planets, is to make a.. Sir J...e.rso.h....................................................
o Sir J. Ifcrschclt0.