# Cosmology questions

Hi, I'm new to this forum, but saw that everyone was so kind and helpful, so was wondering if anyone could help me with a couple of things..

How does one calculate the age of the universe using Hubble's constant, if the constant is in km/s/Mpc?

Do we know the critical density of the universe? I always thought that experts had a few pretty good estimates, but then someone told me today that this wasn't true..

Does anyone know a thought experiment for length contraction that does not involve a train and a tunnel? For some reaosn this thought experiment always confuses me...I knew one once with a rocket travelling to alpha centauri at 0.8c, but am not sure if this is allowed if it assumes time dilation..

If anyone could help I would be so grateful! I have an exam on all of this tomorrow!

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For the age of the universe, I've tried multiplying the constant by 1x10^3, then changing the Mpc into light years..is this correct?

If H is the Hubble constant, then the age of the universe can be determined as the inverse of the constant, that is 1/H.
EDIT: But this is ofcourse a very crude estimation.

The age depends on what model you are using. For example, the age using the Einstein-de Sitter model is given by

$$\frac{2}{3}H^{-1}$$.

The critical density is also dependent on the choice of model so noone "knows" this density.

Dick
Homework Helper
The hubble constant has the units of 1/sec. An estimate of the age of the universe is given by 1/H. The exact age depends on your exact model of the universes evolution. E.g. assuming it is matter dominated (should be a good approximation) we get 3/(2*H). We know the critical density exactly as well as we know H. They define each other. What we don't know is the real density. A difference between these two would indicate the universe is spatially curved to a significant degree. Current consensus is that it is not.

Dick
Homework Helper
The hubble constant has the units of 1/sec. An estimate of the age of the universe is given by 1/H. The exact age depends on your exact model of the universes evolution. E.g. assuming it is matter dominated (should be a good approximation) we get 3/(2*H). We know the critical density exactly as well as we know H. They define each other. What we don't know is the real density. A difference between these two would indicate the universe is spatially curved to a significant degree. Current consensus is that it is not.

Thanks for your help so far! My problem is determining the age of the universe from the units I have been given, km/s/Mpc...how does one change these units ino units suitable for the 1/H method?

Dick
Homework Helper
1 Mpc=3*10^19 km. Put this in and cancel the km.

Hey thanks!!

We know the critical density exactly as well as we know H. They define each other.
We do not know H exactly, but it is estimated to be around 70 km/s/Mpc with an error of ~10%.

Dick