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

248 T'ill PLANE'TS..As the 1moon0 is a body revolving around the earth at a l0known
distance, \and witih a known pie'iodic time, it will evidently
furnlish the necessary standard of comparison. The distance of
til moon from the center of the cart1h being 60 times tie
earth's radius, and, of cour1se, 60 times that of the meteor, its
rate of motion is /60 times less.'lhllo retardation beinag /60,
3
the periodic time will be 60"..Now, wYhat par't of the moonh's
3 3
period is 60v,? ])ivide the noohn's period (27.32 days) by 60':,
and we have for thle an lswerl'1 thour, 2tI: llilnutes, 38.88 seconds.
P'lnoB. 3.-. a\rhat woldl be thle periodic title of a blody revolving about tihe earth at thie distance'of 5000 Imiles from the
centter? Atns. l.h. 519m. 23.28s.
P]iom1. 4..........X.ow 1anelil faster lmust thle earth revolve in order
tllat bodies on its surface may lose all tleir gravity?
Accordingl to problemi 2, thle period of a body revolving at
tte surface of thle eartll, is 1.411(8 lours; and since, in a circular orbit, the force of gravity and the centrifulgal fO'rc are
equcl, therefore a b)ody like that contemplated in probllem 2,
is in equilibrium betteen thellse two forces; consequently, such
a blody may be considered'as having lost all its g}ravity, and
being, Iby tle supl)osition, close to tlhe earthl, we lhave only to inquire tow mucll its velocity exceeds that of tile ealrth..Now, 241:
divided by:1.4-108 gi'ves 17.01; whichi shows tlhat were the
earith to revolve onl its axis abolmit 17 times fast;c1 thall it does
at 1reselnt, tile bodies onl the surface i would lose all their wcigltt;
andll were tle \velocit~y greater ttan this, th;e entrit'ugal fobrc
-would prevail over tlhe centripetal, and the sam would fly oiff
fi'o the earth inl tangents.
PRo1.. 5.. Weelre tlle iooni to be removed so flu frolm tlhe
earth as to revolve about it but once a ytearl how muclt greater
would be its distance than at present, how mlltch less its velocity, and its gravitation toward thale arth?
Its period bleing increased 13.31 tiims, its retardatiol is
13.37::2.3,.73; its distance 2.3782::::. 5.631; and its diminished
gravity 5.6l:...: 31.r1. Or I::::2.373, I):::::5.G6, anld ]-.
31.1t,. O.Mullt.it)1lying tlhe pI'eselIt dista.lnce of the moon,: 238,5[S miles,
1)by 5.03 1, w\ obtaiL about 1,3:343,000 miles for the distaance at