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

(:1'NT:iA.\, tces isZ..S, 9
sotlar systml ltroduce inl eachl ot1her's lo)tiot0ns, are' all accounted
for bty a):lvl tl' same law. ~ If a planet moves for a tilme,
towar(I another, it is accellerated; and its acceleration is
greater, as tlle square of thle dlistance is less, and it is rctalrdcd
accordtin to thle tame law1v, wlhcnt t-lpartillg from it.
Since all botdies Illmanifest a tenldency towatrd each othler, it
is natural to siuplose tlhat tile tendlency slould vary as tlhe
quantity of imatter, othler titiitgs being equal. )Bothl ob)selrvation and calculation confirmn, without anyl exceptions, suchl a
Sul)positionl; and therefore a flll statlement of the law of
gravity includes the fact, that it varies dircctly as the (tquantit), of matter.
1 83. Since, as we hlave seenl, gravity just at the earth's
surfa-ce is governed by the salmte law of dlistanttce s it is further
oft; thlerefore the curved paths of proje-ctiles (are of tlce same
nature as tihe orbits of phant-s and satellites; tlthat is, tflhey are
ellipses, one. of whose tfoci is at the earth's center. And there
is no real discrepancy l)utween this statement alid tIlat proved
in M:ecucclllices, thAtt 1he patl of a Ipi rjcctile is a p)arao!lt. In
that (lemonstration, it o as assulctl that thle lines iwn w:lic} thte
gravitating force acts at each poinlt of the patlh, are pa.zrall:l to
eacll otlher, and thi-at the force is co.lnstant, neitther of wrlich is
strictly true; since the verticalls all meet at the c(onter of attraction, and the intensity ft gravit y slightly increases as the
body descends. Knowing tht: distance and period of thet
mioon, it is easy to fixdl( bvy klepletIr' s t-itrd lawr thle period of
rc\iolutiolt ill c1ase8 of a givenl projectile, if its orbit oould be
cotmipleted in accordanllce Cwitlh the law. An.y fotrce, w\\tich mIan
could apply, \vould carrlty tile perigce st: o little beyoltd thle cnlter of the earth, tlhat the mca-t distalce mightt be called olehalf the radius of the earth. Tltlerelfore, calling thie mooxn's
distance 60 radii, and her period 243 days,; we slhould lhave
(G0)a: (ka):: (2'%.)::, tlhe squtare root of which xvAould be
about 3() minutes. JEvery projectile, tlhenl, if it w\ere free to
complete its orbit, untobstructed, and accorlding to the law of
gravity wlhichl prevails outrsidet: of tile earthl, woulld make an
entire revolution, and return to its place in half an htour. Ac0 Nat. Phil., Art. 49.