We begin by taking the year we were born. Then we subtract the oldest human being at that time. This will be the starting date for anyone to whom we might have had obligations. Finally, we calculate the probable maximal age at the time we are most likely to die. We add that to our probable death date and thereby get the last year anyone will be alive to whom we might have obligations. Let's use myself as an example.
I was born 1971. Some quick research tells me that the oldest persons around this time were 110 years old. By 2050, life expectancy is estimated to be in the mid-80's. So lets assume I will die in 2056. By then, we can expect that someone born that year will roughly have a maximal age of 125. Therefore, I personally only have potential obligations for people alive in the years between 1861-2181. Sounds reasonable, since claiming that we have any idea what the world will be like beyond 2181 seems completely unreasonable. I presume Benjamin's argument for his limiting formula is that we still have some responsibility for conditions after our death, but only in so far as they have an effect on those who were born while we were alive. Well, lets put this idea to the test. How about another little thought experiment.
Astronomy is the field where science has perfected its predictive powers beyond anything else. Knowing the full moons for the next centuries is not hocus pocus. It's not like trying to predict on June 1, 2010, what the weather will be like in New York on February 2, 2056. So lets assume that astronomers discover a massive celestial body tumbling towards our solar system. After some fancy Einsteinian calculations they determine that the thing is headed straight for Earth. They predict that there is a 99% likelihood that it will directly impact with our planet on February 2, 2506. They firmly believe that it will be a straight hit. And it's a massive stellar object. If we don't manage to somehow divert it, our species is almost certainly headed for complete extinction. So the question is, do we have any moral obligation to invest efforts in diverting it?
Anyone alive today has only a negligible chance akin to a miracle of being alive by the time of the impact. Anyone living now will with almost similar certainty never even know anyone who will ever meet anyone who will be alive by then. Does that reduce our responsibility to take even the slightest action to zero? Should this piece of writing has survived the test of time and you happen to be reading this after 2506, then you can obviously just move up the date. Anyone reading this can also change the probability of impact in order to experiment with what moral obligations we have to our distant descendants. If you think we have no responsibility, then who born what year would?
Assuming an increase of longevity due to the amazing field of medicine, let's guesstimate a life span of 120 and a maximal age of 150 by the 26'th century. Then, according to Benjamin's formula, the magic start date is roughly 2236. Until then we can kick back and pretend it doesn't matter. Because, really, to us it doesn't. We won't be around. And neither will our kids or our grandkids. And it's even extremely unlikely that anyone born today will have great grand children who will be alive. I can certainly imagine that getting closer to February 2, 2506, there will be a lot of cursing at those damned ancestors who knew it was coming put didn't lift a finger. But, again, who cares right? Because they can curse all they want. Whatever is left of us is quite evenly distributed across Earth and no longer constitutes anything than can remotely be considered a curseable whole. Curse all you want, suckers!
For the specifics of the above thought experiment, I myself would feel an obligation to encourage us to immediately start considering in earnest what can be done to save our distant descendants. But to what extreme can the parameters be driven? It's quite certain that our Sun will go red on us and eventually engulf Earth in a plasmic inferno. Does that mean we have an obligation to seek out new habitable planets for when that day comes, possibly even in other solar systems? I think so. The issue is obviously not as pressing as if we knew our planet was on course for a doomsday rendezvous by February 2, 2506. Still, it would seem that we have obligations beyond merely to those alive during our lifetime. It's very different from the moon, which I couldn't care less about. Except, the tides around Mont Saint-Michel are really, really awesome.
P.S. If you're reading this and Earth is soon to be hit by a massive object, and your ancestors knew but did nothing, I apologize profusely for all of us. Not that it's really of any help to you. But perhaps its at least encouraging for your spirits and efforts to know that there were those of us who cared. Too bad we didn't prevail. Good luck, suckers!