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Babylonian destruction of Jerusalem happened 586 B.C. When the Babylonians destroyed Jerusalem and the kingdom of Judah, The Edomites were the allies of the Babylonians. Evidence for this is found in the Hebrew scriptures themselves ( 1 Ezras chapter 4) where we read the words of Zorobabel about 70 years after the Babylonian destruction of Jerusalem had said in a prayer ''Thou has also vowed to build up the temple, which the Edomites burned when Judea was made desolate by the Chaldees (Babylonians)'' This is verified in the non apocraphal books of scripture such as Psalms 137:7, which was a psalm written by Asaph during the Babylonian captivity where it says ''Remember, O Lord, the children of Edom in the day of Jerusalem; who said, Rase it, rase it, even to the foundation thereof. 8. O daughter of Babylon, who art to be destroyed; happy shall he be, that rewardeth thee as thou hast served us.''
upon the destruction of ancient Israel & Judah, the Edomites & some 'Arab' tribes had coexisted in the southern parts of what we now know as Jordan. Around the 6th century B.C and onwards, upon the Assyrian & Babylonian destruction & deportation of most of the Israelites/Judahites, in droves the Edomites migrated northward to fill the vaccume. This is explained by Ezekiel 35:7 (this is a prophecy of God against the Edomites)