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

seri\.. f observations upon telm at the times of their greate.st
elongadions, as described in Art. 308. If the length of the
radius vector be thus obtaiined at each return to tle point of
greatest elongation, there will be found among them all, one
tllat is a maximum, and( another that is a minimumllll. The
latter point, is approximately the place of the perielclion. Thus
(Fig. 60), if in a lonlg series of observatiollns ol the greatest
clongations of M5ecrcury, the value of Sl1 were, at a certain
time, to be the least of all, we should know thlat that point is
the place of pcrihcelionl, anld, of course, tltat the point diamelltcically opposite is thle place of the aphelion. lMorcovr, by ealculating thle distances of the planet firom t~he sun at these two
points, as described in Art. 308, we aseritain the length of tlhe
least and greatest radius vector; and lhalf the diftrelnce of
tlhese two lilies constitutes the eccentricity)
FVor the superiorl plalelts, we mighlt llsuppose the method desctried ill Art. 3T75, to be pi)lsuld every year at tlhe time of
opposition, till a rladius vector is found, which is less tlhan any
other; that is aplproximately the place of perihtelion. For
the mnlost distant plancts-, htowever, thl angle of retrogradationl
Xey, or eXS, is so miniute, tllat the calculated value of Sm is
lvery uncerttain. Moreover, tltc distant planets pass their
apllelion and )erillelion at long' intervals. So that, in a given
case, it lmay b1) necessary to vwait 40 years for Uranus, or 80:for Neptuie, to pass cithcle of the apsides.
But trligonomeitrcy, building on a Fig. 7,4.
few insstrumt ental obseirvations, af- )fordis othler modes of arriving at these
eleicentts of a tpl, ticta;ly orbit, on /
of whlicll is derived froml tthe greatest
eqiuatw (f t/te ce~ntecr(Art.9,00). F1|or
since the two points ill tlhe orbit o..\.....
wller t his becomes greatest aro F
equally distant firom the aps.ides, by
bisecting the interval between these
two points, we obtain the position of i
th e picrilhelion and aphelion. Let X
AlBWi:i (Fig. 74) be the orblit of tho
plallet, atvilng t}he sulnl ill the focus;
at S. In an ellipse, tle squmar e root of the productl of the semi