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

ItLEMlIANTS~ OF T'lE l'PANETA;'RY Ol'1rs. 20
p)Cliodic timcs fi'om observationl, (Ceplcr ncxt endeavored tc
asccrtain if tlhere was any relation between the distances tand
times of revolution, lhaving a strongl passion for tracing analogics in nature. Ie saw at onlce ttlat the more distaht a planet
is fr'om the sln, the slower it movcs; so tlhat thle periodic timlcs
of thle rmoter planets are increased on two accounts: firlst,
b)ccausc they have a longer patll to travetrse; and secondly,
because they actually move imore slowly in their orbits thalln
the planets nearer the sun. Saturln, for example, is 0-} tilmecs
filther fi'om the siun thlan the earth is; and since the cilcumlferences of circles are as their radii, the orbit of Saturn must
be larger than the eartht's in the same ratio; so that if the
periodic time of Saturn were longer thlan the earth's, merel
because its orbit is larger, that period would be 9) y)ears,
wlheceas it is 30 years. Ileence it is evident that the p)erio(dic
times of th}e planllts increase in a greater ratio than tlheir distances firom the snl, but in a less ratio than the squares of the
distances, for thcnl tle time of Saturn would be about 90 years.
(Kepler then compared the squares of tlce times withl thl e ctubes
of the distances, and foiund an exact agreement between te.ll.
Tiiels hec discovered the famous lavw, the sqrares qf the p)eriodic
times of (dl the }lantets carte as the cetbe of theb' mea(?t dlistlnces
from' the sustn.'
366. Thlis law is strictly ttrue only in relation to placiets
w+hose quantlity of matter in comparison with that of tlhe central b)ody is inalp)prciable. When this is not the case), the
periodic timne is shortened in the ratio of the square root of the
slun's mass divided by thl sun's 1)lus the lplanct's mass, as cx/ M.-. -
pressed by the formula (,: -:) I'. [ The m,,ass of the planiets
is, however, so small comparecd to the sun's, tlhat this modification of thle law is unnecessary except wA]tre extreme accuracy
is required.
ELEI.'.tiNTS'f OmF'IlE, PLAN',TARY OfXl'S.
367. The particulars nccessary to be knomwn in order to
determine the prccise situation of a pllanet at any instant, are
- Vince's Complete Systcmt i., p. 98.
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