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

22(6''tm3u PT, ANETrS.
35:1,)936 times that of the earttl. felicnce it apptears tlat the sun
conltainus tore ttlan thlree hllndred and fiftyi-four thousand times
as much matter as tlhe carth. llndccd, the sunllll contains ciglt
hundred timles as 1much matter as all the planlts.
Another method, well suited to popular illustration, of wcighing the earth aglainst the sunll is the followilng, Knltiowilg tho
radii of the solar and lunar orbits respectively, wre canl easily
filnd the space whlich thle moon descends toward tlhe earth, and
thlo carlth toward th;e sun, in any givren time, as al ]lour.
lThus (F.ig.'5), if wve know the radius AE, of, the orbit, we can
Fig. 76.
A ]:
detelrmine. thle lengthl of the are Ab, describcd in an hol'ur and
also the lenIgth of thle hlypotenuse 13)1',.'But BE........ AE-13b,
t.Ih space throug1 h which t1he central attracts the revolving body
in the given timel. It was slhown (Art. 182) that thle ar1th
dlraws thle moon from a tangent,.00536 of an inlcl in a scecond:
if a calculation of the same kind be made il relation to tlte
orblit of the carth, it will be fomlmdf tat the sunl draws time carth
nearly.12 of aln inch per second frol a tanlGenlt; that is, the
sun exerts a force 2- greater on tthe earth thian the carth does
on the moon. ~But wcere th sun at t he same l stance as the
10oon,t1,his force of attraction would l)e t]he square of 400, or:160,000 times as g'reat as it is now; that is, it would be
2- xf-60,000 tilmes as g;reat as the earth's; attraction, and, colnscquently, must have 2- x i(0,000. 352,000 timecs as much
lmatter. — a result atgreeing nearly with the folrmer. TI'lle agrcemenlt \wol(l 1b exact if more prtecise nu1 lbers were eml)loyed,
but our object is here merely to illustratt tllhe method.