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

CE,:NTXA A(lt FORCS. 101
will happen wl lhen thle centrifugal force ttas cbeen increas-ed so
as to just equal gratvity (A't. 175). As the mleal distance
now ctuals thte 1adius of the earth, the time of revolution is
easily found to )e i1. 24mt. 39s. Any ilncrase of' projectile
force beyo1nd this wvill again produce an ellipse as PK1(, wllo0e
PJtri ye is at P; and we can ilmla1gine the velocity of pr)ojectio
intcreasced until the ellipse becomes o1ne of extrome eccentlricity,
a(nd tthen changes into a parlabola, andl tahen itto an thyper)bola,
inl which last cases the body will never return, or cvcen reach
the poinit of apogee.:18. If we sutI)pose thpe )projectile motion of the earth or
any other planet, to hlave beenl lproduced by a singlle im)ulse,
tihat ilpiutlse may also have cauttsed the diurnal rotation of the
body. If it; had been directed in a line passing troughll the
center of gravity of thle p1latlct then it would have causedt a
protgressive nlotion, without rotation on ithe axis. 3Bu t if tlhe
line of thle iml-pulse did not pass thlrough the center of gravity,
tlhen besides thte motion forward, there would also 1)0e a rotation whose velocity w\ould dtcptld oni the distance of tlhe line
friom the center'. According to th-e ctalcullation m-1(ade by hecrnouilli, the earth's progressive and rothtly motions might }11ave
both been produced by tte applicationt of a fo:rcc it a linl
passing twrenty-four miles fironi tle center of the earth, on thle
sid(e most remote firom tte snll.
Hlfad it; betl directed through a point lying onl the side near-,est the stll, the diurnal Irot.at-ion would obviously hlave blee
rctrograde.
186. 3But if a force were applied to a planet ass we have
been supposing, w\lhat etlect w\%ould b)e p)roduced on tihe systeml
as a \wrole?'o siiplify the case, Supl)pOse tlle sun and one
planet at rest, an-d at a givetIn distance ap1art. XLet them hbegin
to attract cachl other, and at the sale instant let anll ipulse b1)
applied to the planet at rigilt angles to the linle joining the two,
anld of suflicienlt intetnsity to cause revolution in a circle; w\ill
that circle be described about the- sun as a stationart body?
It w\ill not, but around tlhe common center of gravity as mov7F'ranactur, Utain., p. 49.