South Bend news-times. (South Bend, Ind.) 1913-1938, 1915-02-18


Which star has the gerater area.
dimensions Of bOth.-Gerard Golding,
Chicago"
The area" or disk Of no stad is
visible, even with the most powerful
telescopes. The stars are all so re-
mote that they become mere points
of light although these points are
virtually magnihed into spurious or
seeming disks by attraction OF the
light. The larger the telescope the
smaller the spurious disk OF a star
with the same magnifying power.
But the star looks brighter with the
larger telescope. because more Of its
light is concentrated in its telescope
image
The differences OF brightness
similarly affect the naked eve. and
the brighter the star the larger il
looks. although in every case the real
diameter OF the star subtends an
angle too small TO be usually appre-
ciated
But there is an indirect method of
estimating the probable size OF vari-
GUS stars. which gives some very in
teresting results. BY taking into ac-
count both the relative distance and
the relative brightness we can deter
mine the actual amount Of light
emitted by any star whose distance is
measurable by using the sun as a
standard. To illustrate the method
take the two stars that you inquire
abOut-Sirius and Capella. To our
eyes Sirius appears about five times as
bright as Capella. but this is an IL
luhOry superiority, due TO the fact
that Capella is much more distant
than Sirius. II they were at an equal
distance Capella would far Outshine
Sirius. According to the best esti-
mates. Capella is about 200 times
more luminous than the sun, and
Sirius only 40 times.
Here is the principle on which
such calculations rest: First. COM
pare, by means OF careful measure
ments, the amount Of light that we
receive from the star in question with
the amount received from the sun.
The comparison is not easily made.
and the results obtained by different
observers vary rather widely But we
may take as fairly accurate the esti-
mate which makes the light received
on the earth from Sirius one-seven-
thousand milliOnth Of that received
from the sun. Now. the distance of
Sirius Is about $50. 600 times the dis
lance Of the sun. and if both were
equal in actual luminosity then the
sun, at Sirius distance. ought TO ap-
pear just as bright as Sirius
remembering that light varies in
Nersely as the square of the distance
let US calculate how bright the sun
would be at $4,000 times its present
distance. The square Of $4,000 is. in
round numbers, 2S00OO,OOO. coo
which, taken inversely. shows that
the light Of the sun. at the distance of
Sirius. would be reduced TO only one
2SO-thousandmilli Of its pres
ent amount. But Sirius. at that same
distance, gives one seven-thousand-
millionth OF the suns present light
whence IL follows that Sirius must be
IN reality, $50 divided by seven. or 20
times more luminous than the sun.
To form some idea of the size Of
the stars, or the area of their sur
faces, we must begin by making an
assumption concerning their surface
brightness as compared with that of
the sun, per unit area. Suppose. for
simphcity's sake. that we assume
that the amount of light emitted
from each square mile of Sirius is the
same as that from each square mile
of the sun. Then. since the titaI W.
minoSity OF Sirius is 40 times the
sun :. and since the areas Of circles
vary as the squares of their diam
eterS Gin this case one of the circles.
he disk Of Sirius. is 40 times greater
IN area than the Other). the diameter
OF Sirius must be the square root Of
40. which is about Is times the di-