The Cosmos: Infinite or Finite

The Cosmos: Infinite or Finite

INTRODUCTION. You will remember the question that the little boy asked his great astronomer father, Tycho Brahe. Prof. Brahe pondered the true answer to that question of why the sky is dark at night for a long time. Let's go through his reasoning, and then YOU can go outside to have a look to determine if the universe is infinite or finite. (Warning, this project is not for the mathematically challenged!)

Brahe started out by making two assumptions

that all the stars were rather randomly scattered throughout the universe. (His assumption still holds if we assume that all the galaxies - or groups of galaxies are thusly scattered randomly within the universe.
that the universe is infinite

Brahe imagined that the solar system was at the center of a huge sphere that contained a certain number of stars. In the picture, 5 are shown in the central circle, that represents the innermost sphere. He then imagined that that central sphere was at the center of another sphere that was twice as large, and that in turn was at the center of a bigger sphere with a radius three times as great as that of the first sphere, and so on and on and on... He then wanted to fill those spheres with the proper number of stars. Since stars were scattered randomly and thus rather predictably, he needed only to know the relative volumes of the spheres, and then subtract the volumes of the inner spheres. He used the following equation, which, though not important to this study, has an interesting possibility for another project.

Relative number of stars in larger "shell" = N³ - (N-1)³

This equation holds because of the upper equation next to the title, above. It is for the volume of a sphere and you will see upon thinking about it that the volumes are proportional according to the cube (third power) of the radii. Thus if you double the radius, your ball will be 8 times (2x2x2 = 2³) that of the original ball.

However, Brahe also knew something about how brightness dims the further the light or star is from the observer. (Brightness is also termed 'luminosity', "L".) It dims according the lower formula next to the title. That is, it dims by the square root of the distance (D^-2. Thus Brahe knew that the numbers of stars increased faster the more shells he added than the overall brightness would fade as the distance increased. He added shells and more shells - an infinite number of shells - since he was assuming that the universe was infinite, remember?

Thus he reasoned that no matter which way he looked into the sky, there would always be a star in the line of his sight and light would be coming from it to his eyes. Thus every and all points in the sky should be as bright as the surface of the sun - DAY OR NIGHT! Nothing could hide behind clouds, because the incoming heat and light from the surrounding universe would vaporize the clouds and make them glow also.

Now here is your project: go outside and look at the sky. Is it glowing white hot no matter which direction you look and whatever hour you choose? If it is, it is infinite; if it is not, then it must be finite.