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

OF CEtNTRAi FORCl'CESl...........S GRtAiTATION.
1t.70. WVtx a beody Inmoves in a curve of any kind, wce reecognlize, tec. efife(:t of tiwot /'ces: oni, ant itmiulse, whlich: acstinlg
alone would Ihave ctaused a uniforl motionl inl a stnrait hlt linel
and whose influence is alway)s rctained in the curv\ -ot ionl;
thie other, ant accelerating force, thich conltinuallly nSges tte
body towardt somte point out of the oritital ille of motionh.
Tlhe first, is (catlled tlhe rqj id force, tile other the cel:tri/)etal
f1orce. If tlhe action of the latter wvere to cease at any moment,
the b)ody by its inertia would frotm itat ilolient continue unifoi)lnly in tthe direction inl whichl it was then movintg. S8ttu
motion int the talngent na i IC r arded at the effect of' at illlpulse first givL ll ilt the (dircctiol of thlat talgclnt. Titis supposted
imlputls is tte ll projcctile fiu c fior tle om llotent ill question; but
it is itl truttt tlte resllltatt tof tle, original inlipulse, and the infi —
niit series of actiolsi alrea(l prodluced by the centri t etal f)ree.
Thle cent ripetat l fotrce is of nlecessity infinitely sitatIt colpared
witLt tile )projttil fiorce. Flor, if not, thte civte w\(oulil deplart
b a lin-it gle ao fitfrom the tanlg'ent; whers, i by thle very
inature of tlIe relation of a curve to its tangent, the angle is infititely smatll; tlt lrefore, te deflectintg o0ce is infilitely small.
aBut it prodluces finite deflcction after a tince, because its action
is illcessatly repeate(d.
17:1. l'roml a long and laborio;us exatn11111tion of tile recorded observations of Tyetio 71raliahc, Kepler delduced three lawvs
1(relatinll to tlhe mov ements of the planlt4s, whi}tch are thterefore
called kecpler's laws.
1. Tlh7le (r'JbiU qft: ever'y.'pJlanet is an Cldsel, atavintg flte tsu't, ki
one foe as.
92. 7['tie tradius vector VI eatc orbit describes equal a.'eas it
eqtual times.
3. [l7' squar'es of the c)erzod ie times of the sever?'al)ltnets'aUry as the cubes of thfeit t mean distancezs.