Upvote:1
At the time of Alexander, the Persian Empire was an unstable empire whose pieces were falling into the hands of satraps, or local lords. One of these satraps, Bagaos, killed several kings of Persia before one of his "puppets," Darius III managed to kill him. Hence the Persians were far from united against Alexander, although they managed to field impressively large armies.
Darius II was not a particularly capable commander, who was unable to lead his admittedly inferior, but much more numerous troops against those of the highly talented Alexander, at the battles of Issus and Arbela. Nor was he able to attack Alexander during his seven month siege of Tyre, between the two battles.
Darius fled each time, and after Arbela was assassinated by his cousin Bessus, who proclaimed himself King, but was captured and executed by Alexander as a rebel.
Upvote:4
To a large extent both Alexander and his father were inspired by the Ten THousand, as well as the Greeks' dramatic victories against the invasions by Darius and Xerxes.
In these campaigns the Greek heavy hoplite infantry had proved itself more than a match for the best that the Persians could muster. Once united under the Macedonian mantle, a force of sufficient size to contemplate overthrowing the Persian empire could be contemplated.
Although the spear is usually listed as the hoplite's primary weapon, this is misleading. The hoplite shield was cleverly built to both enable the wearer to rest it on his shoulder while covering his leftward colleague, or to wield it as a very effective weapon. Due to the manner in which it strapped onto the wearer's forearm, it was easily maneuvered by a hoplite both as a ram to knock his opponent over, and as a blunt knife to deliver a severs blow from it's edge. Although less maneuverable than the later Roman maniple, the phalanx was a tactical battlefield unit which the Persians simply were unable to handle without overwhelming numbers.
With the how dealt with , now consider the why. As much as anything, I believe it was to prove his worth to his father, and because he could.