Superman can die on Earth
I appears that Superman only suffers the effects of aging up to a certain point, due to the effects of the yellow sun. It seems that although he might have a "peak" performance age range, his powers will at most grow relatively weaker but still remain, and that he won't suffer the actual physical breakdown of cells and organs etc due to aging, so long as he remains exposed to yellow sunlight.
However, he WILL presumably die of old age eventually, if some other factor doesn't kill him first, because eventually the yellow sun won't be a yellow sun anymore, and as that changes Superman's powers will fade. The only way out of this would presumably be for Superman to build a ship that will take him to another planetary system orbiting a yellow star, where he'll once again be exposed to yellow sunlight to maintain his abilities.
What isn't clear in that scenario is whether traveling to another yellow star, which would produce a period in which he no longer had any powers, would cause any cellular changes or DNA damage etc that might prevent him from resuming his powers once he attained exposure to yellow sunlight again.
But if no such problems emerged due to the period of time without powers, then hypothetically Superman could just go from one yellow star system to another indefinitely, or until he'd lived long enough that any other limitations in his biological makeup could eventually arise. For example, hypothetically speaking, each time he must endure a prolonged lack of yellow sunlight should cause his cells to experience at least some minute degree of aging, even if only mere minutes, and over time eventually all of that non-exposure time should add up to an amount of aging that might actually impact Superman's ability to recharge himself on yellow sunlight.
This would of course take hundreds upon thousands of millions of years, though, since each star would have a very long lifespan before he had to travel. Nevertheless, eventually after probably many billions of years, Superman would reach a point where he'd experienced enough actual aging that he might be "elderly" and unable to continue this process for any number of reasons.
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