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The Macedonian phalanx had limited protection from missiles in the form of their long spears, but it's true that it was vulnerable to missile fire. For example, during the Battle of Ipsus (fought among Alexander's successor states), Seleucus's horse archers devastated the enemy phalanx, causing many to flee.
However, the phalanx did not fight alone. A typical formation would involve cavalry on the flanks, skirmishers in the front, light infantry in the back (including archers). Although the phalanx itself cannot respond well to enemy archers, the other formations can. Phillip II and Alexander were pioneers in this kind of combined arms, particularly the powerful heavy cavalry charge.
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Phalangistes were equiped with a small sword appropriate for battle face to face and the sarissa could stand on the ground. In this hypothetical battle archers against phallanxes , sarissas soldiers would leave their sarissa on the ground and run against archers with loose formation to confront them to a close combat. So as I see it the archers should run away which is exactly what they did because they were lacking armour and hand to hand skill combat.
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Horse archers were the most dangerous weapon of persian armies but at that time persians appreciated elephants and chariots. What is less appreciated but it was the main factor of phalanx success was the Hypaspists. They were exactly what phalanx was not. They were mobile , light and skilled. They were used amazingly by Phillipus when winning the battle of Chaeroneia. When that kind of soldiers ceased to exist in battlefields, phalanxes become more and more vulnerable . The politics of that time overestimated the use of phalanx for political reasons so later after Alexander's era none knew how to use phalanxes with the proper way. So the secret of phalanx were the Hypaspists and the cavalry which brought the final strike to enemy. Phalanx can not win a battle alone and that was proved beyond any doubt later in the macedonian -roman wars where the cavalry never attacked the Roman armies and the phalanx where left without support when needed so they were slaughtered easily by roman legions when their formation broke.