The Two Towers by J.R.R Tolkien (Harper Collins 1991, 2007) pp. 547-558)
Three times the sun rises upon the chase of Aragorn, Legolas and Gimli, the three hunters, as they pursue the orcs of Isengard first through the foothills of the Emyn Muil and then across the plains of Rohan. The hunters have run many miles and yet have come no closer to their enemies and their goal, their longing to find and then rescue Merry and Pippin from their captors. Among Men, Dwarves and Elves they have done a deed that will rightly be accounted mighty but the orcs have hardly rested by day or by night.
Hope, what little hope that they had, is fading.
“For many hours they had marched without rest. They were going slowly now, and Gimli’s back was bent. Stone-hard are the Dwarves in labour or journey, but this endless chase began to tell on him, as all hope failed in his heart.”

There have been moments when faint glimmers of hope have been rekindled in their hearts. The green smell, as Legolas puts it, of the wide grasslands, lifts their spirits for a time. And there is the discovery of hobbit footprints and the broach of an elven-cloak. “Not idly do the leaves of Lórien fall,”says Aragorn. It is a sign that at least one hobbit was still alive when the orc company passed that way. Aragorn thinks it was Pippin. But as the hunters begin to realise that they are coming no closer to their quarry so hope fails.

Aragorn never had much hope. He does not even think that what they seek to do has much significance within the great story in which he is a part. At one point he looks southwards across Rohan to the White Mountains that are the northern border of Gondor and in song he yearns to be there.
O Gondor, Gondor! Shall Men behold the Silver Tree,
Or West Wind blow again between the Mountains and the Sea?
And then there is a moment in which Gimli longs for a light such as Frodo bears to guide them in the dark.
“It will be more needed where it is bestowed,” said Aragorn. ‘With him lies the true Quest. Ours is but a small matter in the great deeds of this time. A vain pursuit from its beginning, maybe, which no choice of mine can mar or mend. Well, I have chosen. So let us use this time as best we may.”
So continues Aragorn’s long reflection upon the question of hope that began with the fall of Gandalf in Moria. I say that it began there but perhaps it is more true to say that his whole adult life has been a reflection, a meditation upon this theme. Even the very name, Estel, that was given to him by his mother means Hope. And not hope as in the sense of crossing one’s fingers and trusting to luck but in something that goes much deeper. The Elven king, Finrod Felagund, sought to explain this deeper sense when he says that estel “is not defeated by the ways of the world, for it does not come from experience, but from our nature and first being. If we are indeed the Eruchin, the Children of the One, then He will not suffer Himself to be deprived of His own, not by any Enemy, not even by ourselves.”
Aragorn has sought to embody estel within himself in his long years of service in Gondor, in Rohan, and as the leader of the Rangers of the North. Always he has held before him his longing for personal happiness in his desire to marry Arwen. And he has sought to be the expression of hope for his people, for the fading remnant of Númenor in the North and for the brave but beleaguered defenders of freedom in Gondor. But now he feels that he has been seperated from this hope. The fall of Gandalf has affected him deeply but, so too, has Frodo’s decision to leave the Company and to make the journey to Mordor without them. Aragorn realises that he no longer has any part to play in that journey. He may be determined to rescue the young hobbits or die in the attempt. He may be certain that what he has chosen is right. But he is bitterly aware that he has been pushed, as it would seem, to the margins of the story. For him the loss of hope is not just about whether they will be able to rescue Merry and Pippin but about the sense of destiny that has given him meaning throughout his life. We might say, to use the language of Finrod Felagund, that his sense of hope, of estel, has been founded, not upon a belief that Illuvatar will not leave himself bereft of his children within the world, but upon something much more personal, that he, Aragorn, will be the bearer of that hope. Now, as he begins his pursuit on the third morning after the breaking of the Fellowship that hope is gone and all that remains is toil.

Again, this whole sequence near the beginning of The Two Towers left a deep impression on me when I first read it, because of those agonizing choices Aragorn had to make. During the chase there is yet another one: whether to take a rest and sleep at night, taking the risk that the Orcs will not rest.
You’ve brought out something here I’d never considered before, about Aragorn’s ego. After so many years in service of great goals, he really should have some natural expectation that he’d be with the central quest, i.e., with the Ring. But he chooses to save two hobbits are not even carrying the Ring, and you just have to love him for it. It was a “smaller” task, but exactly what he was needed for (he couldn’t abandon them), and he throws himself into his role as if it was the most important thing in the world. That took some humility — and some trust/hope, as you say, that the Ring would end up where it needed to be.
Many thanks for engaging with this, Kevin. I have been trying to enter, imaginatively, how it felt for Aragorn at this moment. The longing gaze towards Gondor, the exclusion from the Quest of the Ring, the sense that the mission in which he is engaged is a hopeless one. And yet, as you say, he keeps on going anyway. I would follow a leader like that anywhere. In my own small sphere I need to be that leader.