2.3 Infinite Universe
A finite Universe can be thought as a confined
space in which lay a finite number of galaxies as shown in Figure 2.6.
It would be a collapsing Universe as the gravitational force of each
galaxy attracts all other galaxies inwards towards a point which
position depends on the distribution of the galaxies themselves.
The figure shows an infinite line of galaxies all spaced equally from each other and having the same mass. Now, we know that the equation for the gravitational force acting on two isolated masses is:
where r is the distance between each galaxy. Hence, the force acting on the galaxy placed at position zero along the infinite line towards the positive direction would be:
and the force acting in the negative direction would be:
which means that F+ve=F-ve and the galaxies are in equilibrium. However, if we take the galaxy at position -1 out of the line, then the two forces would be:
which means that m0 will experience a
force towards the positive direction along the infinite line, and so
do all other galaxies placed along the positive direction of the line.
As far as the negative direction, it is simply a matter of applying
the same reasoning to the galaxy placed at position -2 and so on. We
will conclude that for m-2 the force
pulling towards the negative direction is greater than the force
acting towards the positive direction. That is same for all the
galaxies placed along the negative direction, and extending it for all
other dimensions of space you can see how the surrounding stars would
be expanding when we are left with a hole and collapsing when we have
an extra galaxy.
Figure 2.6 Finite Universe
Figure 2.8 Galaxies along an infinite line.
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