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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!