# Hubble Constant and Age of the Universe

I wasn't sure whether or not to post this in the Astronomy section but as this is homework, I decided to post it here.

## Homework Statement

Suppose the Universe was much younger, eg 10,000 yrs old. Find the Hubble constant for such a Universe. Compare with the currently accepted value. What would we observe if this value of Ho was correct?

## Homework Equations

I know that we approximate the age of the universe using 1/Ho but I don't know how to reverse the equation.

## The Attempt at a Solution

Honestly I'm stumped. I was told elsewhere that the Hubble constant would be the same no matter what the age but I have a feeling that my professor wants real calculations.

Any help would be greatly appreciated!

gneill
Mentor
What would be the approximate value of H0 for a 10,000 year old universe? Express the result in both km/s/Mpc and km/s/ly.

We have various methods of finding the distances to objects in space (the so-called "cosmic distance ladder"). With this new value of H0, what sort of recession velocities (red shifts) would we expect to see versus what is actually observed, especially for some relatively close-by objects that we can determine the distance to by various means?

Ok, so I've tried the equation by putting the years into seconds:
10000 years = 3.1 x 10ˆ11 s, 3.1 x 10ˆ11 = (3.1 x 10^19)/Ho. This gives me a constant of 1 x 10ˆ8 which seems far too large.

gneill
Mentor
So about 1 x 108 km/s/Mpc ? In what way is that too large? In other words, if the value of H0 were that large, what things should we observe that clearly we don't see?

Expressed as km/s/ly instead, the value becomes about 30. We can see a lot of objects within several light years of us, and they don't seem to be flying away. In fact, the Milky Way galaxy is several hundred thousand light years across and it is gravitationally bound (not flying apart), and we are part of a local cluster of galaxies that is much greater in size and it's also gravitationally bound (not flying apart).

Ok, so that value would be correct? Sorry, I'm still confused. Would the 30 value be in megalightyears, not regular lightyears?

gneill
Mentor
km/s/ly

I'm adding here because I looked this up before posting, and found this comment here; "we approximate the age of the universe using 1/Ho."

Over my few decades of thinking, I developed my own view of the Universe and came to the conclusion that Age=1/Hubble. I then noted Hubble was, indeed, a s^-1 term, and that reducing it down did indeed give a reasonable value.

Some years ago I asked a science journalist about my theory, backed up by that bit of data, and he said he'd never heard of it and it was 'just co-incidence'. I filed it in the back of the brain-box, and just now thought to look this up here.

So, my question; I have my way of coming to that conclusion, but how does 'the mainstream' come to the conclusion age=~1/Hubble?