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

'IOUtiR OF'f E EAIT'rTIS tORBIT 89
creased as i13 is dimintishled, tte lproduct of A and'B is alwvays
tlhe same. If, tlterefore, from the sun S (l.Fig. 33), two radii 1)e
drawn to 1',.B, the extrclllties of any small are, as that described in one day, and the angle between tliem be called S,
then SB -IxS gives the same constant preoduct in all parts of tlhe
orbit.
1 68,. 1ee r'ad'ius vector of the solar orbit (lscribe.s equ'al
aetias in. equal tim es; and int. unequal times, areas pr'o)o p ioncal
to the tim-es..lThe solar orbit is so nearly a circle, that T lmlty everywv lere,be regarded as perpe)ndicular to thel radius SB. oi St. I[cnce,
the sctxor described in a given tile, as onelt d(ay,'I'S'i 1/ S'13 x
TBi3. B:13ut a circular are varies both as the angle whicht it subtends, and also as the radius by which it is (dlscribc(d; thcrefore T.Bl. o Sl3x8. I.rence, lSI3 c. S.lxS, Butt (Art.'167)
this is a constant product; therefore, the area T'ST13 is also constnant, and thle radius vector describes equal areaas in equal
times.
T.'11 stnI's orbit may be accurately represented by takinlg
sonMe point, as the perihelion, drawing thle radius vector to that
point, and, considering thiis line as unity, drawin other radtii
makitg angles - witlt each othelr suchl tlhat the ilncluded areas
\shall be! proportional to the tilmhes, and of a lengtlt required by
the distance of each pI)oint as givel in the table (Art. 164). On
connlectinle tilhe radii, we shall thus see at once how little tle
earth's orbit dep:arts from a perfect circle. Sniall as the difference aplpears between the greatest and least distanceis, yet it
amllounts to nearly i - of the perihelion distance, a quantity no
less thlan 3,000,000, of miles.
169. The forcgoing method of determiniiing the figure of
the eartlh's orbit is founded on observations; but this figure is
sublject to mimlerous irregularities, the nature of w-hiech cannot
be clearly underlstood witllout a knowledge of the leading
principles of Universal Gravitation..An acqutintan lc e with
tlese will also be indispensable to our undlerstanding th1e causes
of the llnmrows irregularities, whicll (as Nwill Ihereafte appeai)
attend thle motions of thle moon and planets.'To the law\s of
universal lgravitationi, therefore, let us next apply our attention.