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

CE4NTRALI FolCiES. 93
as the perentdicular'fro m tthe centet' (o/giforce to the tangent iat
/that oi..n t..
L4et SY (Fig. 341-) be p}clpelndicular to PTQ; tn tl te area
S]Q: -(....-]QxSY, whliCt varies as PQxSY; P...;,Q
lu11t P]Q o V, the velocity at 1'; and tile area SPQ is constant;'. V - or the velocity varies inversely as tlhe perpendiclllar from S upon the line in whrlicll the body is moving;
in other words, upon the tangent of its path, if it describes
ll C1llX'V(3
In tlhe orbits of the planets, since, the)y are very nearly circuilar, SY' meets the path almost at the point where the body
is movilng, and tlerefore is about equal to t]he radius vrector;
so that in thle planetary orbits, the ab1solute velocity varies 1in\versely as thle radius vector very nearly.'e have ltalready
noticed this to be seinsibly true inl thlse ease of th1e earth's orbit.
(Arts. 165) 166.) It follows from the above reasoning, that in
a circular orb)it, where the radius vector is constant, the velocity of tthe )ody is uniforln.
1 7,5. When T a body moves inll a curve, since by its inertia it
tends at eact1 point to proceed in the talnlent at that point,
there is a conltinunal outward press\ure directed f.'om the center
of force; thtis is called: the centtirtgal force. it may be regardcd as tlhat inllinitesilaI component of tlhe prcjectile fitrcc, whiellch
opposes tihe action of t}he centripetal, the nmotion aloing tle curve
being the other comllltnlnt. If tlhe body is maintainted at the
stame distance fi'omt the center (tlhat is, in tile cirt'ClfercelftC of a
circle), the cntlrifitgall force equal tlte cCentripetalt; but in orblits
of otfher form 1ns, it is sometimes greater and sometirnmes less thlan
the cewntripetal.
176. In a circular orbit, tle centrattfor'ce (either centrietal or centrifiugal) varies as tle sqtuare qf- the veloccity duivitdted by
tle uraditts.
If.. tel uniforml velocity in thle orblit, and:t tclle ininitely small portion of time of describing the miniute are Ab,
and x;:the radius of the circle, then Ab — vi. 3 But Ab, or its