How is it that Strider doesn't fear them?
I don't think it has anything necessarily to do with his heritage, his being an
heir of Elendil and so on. This is turning your question into a larger
one, but here goes: Tolkien makes a great deal of heritage, certainly; of
Aragorn's being the direct descendant of Elendil in the 39th generation and so
on. But if it's just Aragorn's bloodline, then why didn't his father (or
grandfather and so on) do all the things which Aragorn did? Why didn't
one of them return and become King? For that matter, how did they ever
lose the Kingdom? An important theme running through the LotR as far as
the character Aragorn is concerned is that he makes good where all his
ancestors (with the possible exception of Elendil himself) failed.
Isildur could not resist the lure of the Ring; Aragorn can. Different
ancestors of his over time lost two kingdoms; Aragorn regains them both.
What Aragorn does he does not by virtue of his
bloodline. Tolkien emphasises very strongly anyway that Númenórean blood
is being mixed and that the Númenóreans' lifespan is declining. Thus,
Isildur's son Valandil, the King of Arnor, lives over 247 years; whereas
Aragorn only lives for 210. Isildur's Númenórean blood should have been
perfectly pure, yet Isildur failed; and so on. If you will, Tolkien is
having it both ways: Aragorn succeeds by virtue of his own efforts; but he also
happens to be the 39th heir of Elendil in direct descent. There's a
certain sentimental attachment to bloodline present in Tolkien if you
will.
(As for actual Elvish blood, somebody calculated it up; it
was some infinitesimally small quantity -- probably just a fraction of a red
corpuscle after 60-odd generations.)
Why does Strider not fear the Wraiths? For the same
reason he can resist the Ring's lure; and can stand up to Sauron over the
Palantír. He may have had plenty of self-doubt as to whether or not
he would be up to these challenges; and he may partly have hoped that he'd
never have to meet them; but he had spent the last decades preparing to meet
them.
Moreover, he was defending four friends of whom he had already
grown fond. There is a certain psychological edge which comes from
defending someone else: many people are far more vigorous in the defense of
another than they would be in the defense of themselves.
Finally, if the Riders got the Ring, then everything was
over. Knowing that failure was not an option presumably hardened his
resolve as well. Few things concentrate the mind better than the extreme
pressure which the certain knowledge brings, the knowledge that one has to
succeed or else to face total
ruin.
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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.