The Earth is 4.6 billion years old The universe is 13.8 billion years old. 3 times the age of the Earth Are there other planets with ages that are close to say 1/4 1/5 etc the age of the universe? Why would this happen?
The (approximate) 3:1 ratio is nearly entirely co-incidence. The other planets formed at the same time as the Earth, and are therefore of the same age.
The Earth is quite accurately dated to 4.54 billion years and multiplying by three gives 13.62 billion, quite a bit less than the age of the universe.
There are other planets around other stars, some formed early in the universe, some formed recently. There is no reason to expect simple ratios of ages between planets and the universe.
The closeness to a 1/3 ratio is coincidence but the observation that the Earth is a lot younger than the universe may be quite profound.
Firstly, the Earth cannot be as old as the universe. The first galaxies and stars likely formed about 0.5-1 billion years after the big bang, once primordial hydrogen and helium had time to cool and clump.
Earth-like planets could not form around these stars, since there were no heavy elements like carbon, oxygen, silicon and iron present.
These elements are made inside stars and then dispersed into the interstellar medium for new generations of stars to incorporate that material. This process takes some time.
When the Earth formed, it was extremely hot, it was also being bombarded by asteroids and other sub-planetary bodies. There was no chance of forming life for 0.5 billion years or so.
Once life formed, it didn't have the capacity to estimate the age of the Earth and of the universe. That is a recent development and has apparently taken about 4 billion years of evolution.
If we assume that our galaxy took 1 billion years to form, that adequate chemical enrichment took another 2-3 billion years and that the time taken for a planet to cool and have evolved intelligent life is 4 billion years, then we arrive at the conclusion that the universe as we see it would have to be at least 7-8 billion years old and that our planet would then be less than about half the age of the universe.
A more interesting question is why is the 1/3 fraction quite close to, but still significantly smaller than, the apparent maximum of 1/2? We do know that small, rocky planets have formed around stars with a wide variety of ages - anything from a few million years to estimated ages of around 10 billion years (e.g. Weiss et al. 2021), though how common they are around very old stars is still to be determined. Was the early galaxy inhospitable to life for some reason? Are we just part of a distribution, with many other older planets out there hosting more ancient life-forms?
At least 40% of the field stars (thus outside globular clusters) seem to have planets, if not more.
Planets form around the protostar, thus at the same time as the stars. Assuming that the laws of physics are universal, then the distribution of planetary ages will be the same as the stellar ages: there will be planets of all ages, very young ones, very old ones. The very old ones will be smaller in mass in average as the remaining old stars are lower in mass (the higher-mass stars already reached their end of life and doing so likely lost their planet system in the end phase).