This problem is formally identical to the determination of the age of the Universe from the Hubble constant. It is interesting to note that an asteroid that is 2 light hours from the explosion at the time we arrive would be moving twice as fast, so we would get the same answer for the time if used its distance and velocity. In fact, we would get the same answer for any of the asteroids; that is, they all left the center at the same time. This is what an explosion looks like. So this is why we think of an explosion when we see the Hubble relation. The difference in the two situations is that we can look at the results of the planet explosion from the outside; the asteroids are moving into the pre-existing space. For the Universe, space-time is expanding with the matter and we are part of this expansion, along with everything else!
Next, Wien's Law tells us that (lambda)_{max}T = constant, so
That is, the redshift (1 + z) of the CBR was only half as much as at present. Since the redshift is just proportional to the scale size of the Universe, the Universe was also half as big then:
Zarkon's Law is clearly the same as the Hubble Law, but the constant of proportionality will be different because the velocities of expansion decrease with size according to
so
Since the constant of proportionality is V/a, the ratio of Zarkon's constant to the Hubble Constant is
so if we assume H_{o} = 30 km s^{-1} per 10^{6} ly,
Note that this shows that the Hubble "constant" is not really a constant, but decreases as a^{-3/2} as the Universe expands.
The age of the Universe in Zarkon's time would then have been