Aragorn's first visit to Moria

[Inziladun]

Originally Posted by Alcuin

In any event, when the Company of the Ring fled after Gandalf fell into the abyss, there was a company of orcs guarding the entrance. We do not know if this was typical after the orcs re-established themselves following the Battle of Azanulbizar: perhaps they were watching for travelers through the Mines (i.e., the Company of the Ring), or perhaps it was normal procedure.

I've always connected the strong Orc-guard on the east-gate to the Company's presence in Moria. I can see them certainly keeping a watch on the Dimrill Dale under normal circumstances, but that's probably all that was required. As long as they had a means to quickly assemble all their forces in Moria if need arose, I don't see why they'd have needed to retain such a strong guard constantly.

Originally Posted by Alcuin

Gandalf said that only he had passed completely through the Mines. Since he exited through the Doors of Durin, he must also have entered from Dimrill Dale. And since he alone had transited the Mines, Aragorn cannot have accompanied him, giving us the additional information that Aragorn also entered and left through Dimrill Dale.

I too, doubt that Aragorn and Gandalf made their journey into Moria together. The dialog between the two doesn't seem to support that. Aragorn almost certainly did enter from the east like Gandalf, though, as neither knew the password to open the west-gate.
However, where does it say that only Gandalf had made the full journey through Moria? Aragorn says of his encounter there:

'I too once passed the Dimrill Gate, but though I also came out again, the memory is very evil.'

I don't think one can extrapolate from that that Aragorn didn't make it all the way thorough.

As for the original question of why Aragorn entered Moria, ask yourself, 'Why did Gandalf"? Lacking an exploratory motive, both would have merely been looking for a shortcut through the Mountains at some point, for whatever reason of needing haste.