Every conceivable thing or event falls into one of these three categories, and each is the negation of the other. For example, what is possible isn't necessary, and what is necessary cannot be impossible.
In some ways this is wrapped up with the nature of time -- i.e., of time's arrow. For example, the past is the completely necessary -- for it cannot not be -- whereas the present is the node of possibility, or the "place" where the possible becomes actual.
Hartshorne introduces an interesting twist here, suggesting that the "unconditionally necessary" and the "always" are essentially synonymous. This is because to say that something must be is the same as saying that it cannot possibly not-be.
Therefore, "a thing is eternal if its 'being' is necessary: and if it is eternal its 'being' is necessary." A corollary of this is that "no eternal thing exists potentially" (remember what was said above about the categories excluding one another).
The bottom line is that Unconditional necessity and eternity are equivalent.
Now, God, who is "necessary being," is obviously eternal. Conversely, the cosmos is perpetually becoming. It is never in a final state; or, each moment is the final state of everything that has come previously, except there's no stopping the process. "Each moment a (partly) new total 'reality' comes to be, containing items not in a previous reality."
It very much reminds me of the structure of consciousness, and probably for very good reasons. In another book Hartshorne makes an observation that really clangs my bong, to the effect that most errors in thinking about God are rooted in errors in thinking about human nature.
Again, if we are "in the image of God," then it very much matters that we understand the nature of this image, not just for its own sake ("know thyself"), but in order to gain insight into the ultimate, the eternal, the necessary. There's really no other way, since we cannot comprehend God directly, only indirectly, via analogy. After all, God's most complete revelation is said to be a person. Sounds like a hint to me.
As we've been saying, Hartshorne insists that any form of radical determinism is an impossibility. For one thing, it conflates the three categories, with the result that everything becomes eternal (because necessary). A cosmos without possibility -- i.e., without freedom -- is nonsense; very pure (i.e., completely abstract) nonsense, but nonsense nevertheless.
We now come to a ticklish fork in the theological road, a sorting mechanism that will send you down one path or the other. That is to say, if God is omniscient in the traditional sense, then this eliminates the possible, or at the very least renders it an illusion of time.
For even if you try to escape the consequences by suggesting that we are really and truly free -- even though God knows ahead of time what we will do -- then you've still elevated the can-be to the must-be. Therefore, not only have you covertly made man eternal (because necessary), you've drained the cosmos of any possible human meaning, because meaning is always a relation. And frankly, in making man eternal, you've granted him the prerogative of a god!
Now, to say that the present is the node of possibility is not to say that it contains no necessity at all. Rather, the present is obviously a kind of crossroads of possibility and necessity, of contingency and determinism, of plans and luck. Necessity, while "outside" time, is also "in" time. Not so contingency, which is only in time.
Thus, we could also say that the present moment is the meeting point of time and eternity, bearing in mind that even eternity does not have the "power" to make time run in the opposite direction, which would be the equivalent of transforming the necessary into the contingent. And that would be absurd. There can be no such thing as "contingent possibilities not in time," nor "conceivable accidents in eternity."
Again, eternal things aren't just "possible"; rather, they must be. Which is one reason why we can know of their existence, since contingent things cannot be known before they happen, a priori, whereas eternal things may only be known that way (since they cannot fail to be in any possible cosmos).
Tradition insists that God is not only necessary, but utterly free of contingency, since the former is said to be intrinsically superior to the latter.
Well, says who? Taking your own life as an analogy, if it were completely plotted out in advance, utterly necessary, would this really be a superior form of existence? Well, you can have it. I'll take adventure, creativity, possibility, and surprise, which are only available now, in time.
"God may be wholly immutable, independent, and absolute in whatever senses it is good to be so, and uniquely mutable, dependent, and relative in whatever sense capacity to change, dependence, or relativity (as in sensitive sympathy) is an excellence" (Hartshorne, emphasis mine).