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

I;.,A':MN'TN no'Ot: TH l,NL'AE'ltY oRrt'r. 22,9
equation above, the value of:1PNR', which is thile inclnation of
tlee o'bit.
372. Secondly, to find the I:eriodic Thime.
ihlis element is leallrned, by marking the interval tfhat passes
fiom the timne when a planct is in one of the nodes until it returns to the samPe 1node. We may knowY wYihent a planet is at
the node, because then its latitude is nothling. If, fiom a scrics
of observations oif the right ascension and declination of a
planct, we deduce the latitudes, and find that one of the" observations gives the latitude 0, we infer that the planet was at
that moment at the node. Butt it, as comm1ilonly hbappens, no
observation gives exactly 0, then we take two latitudes that
are nearest to 0, but on opposite sides of thle ecliptic, one south
and the othellr lnorth, and as thle sum of the arcs of latitude is
to the whbole interval, so is one of the. arcs to the corrcsponding
time in which it waYs described, which time being added to the
first observation, or sullbtacted from the second, will give the
prie- ise momenlt wlhen the plallet was at the node.'By rleceated observations it is folund that tle nodes of the
lplanllts have,a very slow retrograde motioll.
373. If the orbit of a planlet cut thle cliptic at righlt angles,
thlen small changes of place would be attended by al)preciableo
difilrenccs of latitude; but in fact the planetary orbits are in
general but little inclined to the ecliptic, and some of t]hem lio
almnost in the same, )lane w e \ithl it. lirtiee arises a difilculty in
ascertaining the exact time when a planct reaches its node.
Amnonlg tile most valuable observations for determining tle
elementts of a planet's orbit), ar those made when a superior
p)lanet is in or near its lpposition to the sl1un, for then tile heliocenttic. and geocentric longitutdes are the same. When a number of oppositions are obs'erved, tlhe planet's motion in lonlgit\ude, as would be observed fiom theml suln, will be klown.'llhe
inferior )lanets also, wen ch in superior conjunctionl, have thllir
geocentric and heliocentric longitudes the same. -When n illnferior conjunction, these longitudes difler 1800; but tlhe inferior
planets can s:eldom le observed in superior conjunction, oil
accounlt of their proxiinity to thle sun, nor in inferior conjunction exceplt in their translsits, which occur too rarely to admlit of