Of Time, Space, and Other Things by Isaac Asimov

Author:Isaac Asimov
Language: eng
Format: mobi
ISBN: 9780380003259
Publisher: Avon
Published: 1965-01-01T00:00:00+00:00

far as Star B, Star A delivers only % the light. If Star A

were five times as far as Star B, Star A would deliver

1/2r, the light, and so on.

This holds for our shells. The average star in a shell

2000 light-years from us would be only 1/4 as bright in

appearance as the average star in a shell only 1000 light-

years from us. (Assumption 3 tells us, of course, that the

intrinsic brightness of the average star in both shells is the

same, so that distance is the only factor we need consider.)

Again, the average star in a shell 3000 light-years from us

would be only % as bright in appearance as the average

star in the 10004ight-year shell, and so on.

But as you work your way outward, each succeeding

shell is more voluminous than the one before. Since each

shell is thin enough to be considered, without appreciable

error, to be the surface of the sphere made up of all the

shells within, we can see that the volume of the shells in-

creases as the surface of the spheres would-that is, as

the square of the radius. The 2000-light-year shell would

have four times the volume of the 1000-light-year shell.

The 3000-light-year shell would have nine times the

volume of the 1000-light-year shell, and so on.

If we consider the stars to be evenly distributed through

space (Assumption 2), then the number of stars in any

given shell is proportional to the volume of the shell. If

the 2000-light-year shell is four times as voluminous as the

1000-light-year shell, it contains four times as many stars.

If the 3000-light-year shell is nine times as voluminous as

the 1000-light-year shell, it contains nine times as many

stars, and so on.

Well, then, if the 2000-light-year shell contains four

,times as many stars as the IOOG-light-year shell, and if

each star in the former is % as bright (on the average)

as each star of the latter, then the total light delivered by

the 20GO-light-year shell is 4 times Y4 that of the 1000-

fight-year shell. In other words, the 2000-light-year shell

delivers just as much total light as the 1000-light-year

shell. The total brightness of the 3000-light-year shell is

9 times % that of the 1000-light-year shell, and the bright-

ness of the two shells is equal again.

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