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

1RoI(fJ,c;:Ms5. 249:
which the moon must have been placed inl order to compllete
its revoluttion l one year..lurao. G. W —.ere tlie earth's mass equal to' tthe sun's, andt of
colurse 354,000 times as grieat as at )presentt in what tilnt would
thle mlool revolve around it?
Sinlce the masses are as the: culbes of the distances divided tby
the] sq"'ares of the pcriOdiC times, letting the requirled timeo
be denoted by 6, 1 (tthe cartlh's lmass): 35.1000 (the sullt's mass)
J1)3.)3. l 1 354,0300 27.32
92* 7 232W' 7'' 2",.3 "..' V354,.00:
Ill. Gml.'s.,
ComRets, in passing their perilhelion, especially when tliat
happemns to be very near the sul1), as in th;le great comet of 1843,
move with an astonishing rapidity; requirin'lg a velocity not
mIerlely slufficient to genlerate the centrifugal force necessary to
balance the tim powerfull foce of attraction exerted by the sun,
but g'reatly to exceed tlhat fore, silnce they arle carried far
without a, circular orbit into an elliptical or even a hyperbolic
orbit.'ilcn.. T7.h-.t..e perihielion distance of the great comet of 184-3
bcing 502,000 miles fiom the center of the sunll, what llIst
htcave beell its velocity p)e hour, if in a circular orbit?.hno. 8. —-- Ilow mutch nimust the mass of the earth t be increased il orlter that tlhe moon may revolve about it in tihe
same time as ats present, wheln removed to thlree tilmes her
present distance?
AI..o'13. 9,t —... 1 1 ow mul t1ust thle mass. of the earth be incre3ased to make the 1moonl, at her present distance,'revolve in
24 hours?
Pom] O. 0........ lThe semi-di'ameter of Jupiter being 11 timesm
tlhat; of tle carthl, hland the distanlee of its fourth satellite friom
the" center of thle plalnet being. 27 times the radius of the
planet; also the sidereal revolution of the satellite beinFg -16.69
d(ays, while that of tle mtooon is 27.32:t1 days, and her dlistance
60 tilmes the radilus of thle earth': H1ow 1lmtch does the quantity
of natter in Jupiter exceed that of the earthl?.Ans. 32M1.4t9
times.
tonI..-. —s.. Suppose volcanic matter to be thrown from the
moon toward thl eartlh, required thle point where it would be
in equilibrium between tte twro, th;e imass of the moon being