The Hubble constant (H) is important in predicting the ultimate fate of
our universe, related to the concept of its critical density.

The velocity of recession of
a galaxy can be considered as its escape velocity from the rest of the Universe

By
Hubble's formula:

Velocity of recession (v) = HR where R is the distance of the
galaxy.

But the escape velocity is given by the formula:

Escape velocity (v)
= [2GM/R]^{1/2} so v^{2} = 2GM/R

where G is the gravitational constant (see Gravitation
section)

Therefore:

v^{2} = 2GM/R = [2Gr4/3]pR^{3}]/R = 8/3[GrpR^{2}]

But
from the first equation v^{2}= H^{2}R^{2} and so:

[We have assumed both constant v and a constant value of the Hubble constant (H) in this simplified calculation.]

If the density of the Universe is greater than this the universe will contract, if it is less it will expand for ever!

Take H = 70 kms

Critical density (r) = 3H

The mass of a proton is 1.66x10