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

2,28'TlE PLANETS.,
at the stilun, we may procced to explain the mode of finding tho
sevceral elements before enumerated; although our linits will
not lpermit us to enter further into detail on this subject, than
to explain thile leading principles on which each of these ctcmenits is determined.x'
37 1. First, to determine thoe position of the Nbcdes, and tho.inc/in atiton of the Orbit.
Th.cse two ecllments, which deter- Fig. 72.
mine the situation of the orbit (Art.
367), may be derivcd from two lheliocentric lonritudes and latitudes. Let A. N I S
ANURS lbe an are of the ecliptic, A
the vernal equinox, NQ,an are of a planet's or'bit, and N its
node. Let ARl, AS, be the two heliocentric longitudes;'UPR,
QS, the corresponding hclioccntric latitudes, which lave been
determined as by Art. 369.
By iNapicr's rule,
siln N.::..: tan QS x cot P'lt,
and sin Nit::.tan:Pit x cot PNIt.
Eliminating cot PitNR, we have
sin NS sin NiR
tanl QS tanl Pit,
substituting AS -. AN for NS, and AR.I...... AN for INtR, then
sin AS x cos AN-... cos AS x sin AN
tan QS
sin Alt x cos AN... -.- cos AR x sin AN
tan PItr.. (cos AR x tan QS... cos AS x tan PitR) sin AN.:-.
(sin Anti x tan QS sin AS x tan P-R) cos AN'.
sin AN sin AlR x tan QS.- sin AS xtanPiPR
-.-11. —,,-.... (:;ta nl A N )................................-.
cosAN (cos ARi x tan QS -...... cos AS x tail 1.I..h.us AN, tho longitude of the node is found; for all tho
quantities on the second member of the equation are known.
Again, since AN is tfound, we may deluce firom the first
o Most of these clements admit of bcing determined in scvceral different ways,
an explanation of which may be found in the largecr works on Astronomy.