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El Al and Royal Jordanian Airlines both fly to Amman, Jordan's capital, from Tel Aviv's Ben Gurion Airport. This option has limited appeal, as you must be at the airport two hours before flight time for the 15-minute flight, then drive three hours from Amman to Petra.
Twice a week, Arkia Airlines offers one-day guided tours in which you fly from Tel Aviv to Eilat at 6:30 am, drive to Petra in an air-conditioned bus, spend three hours walking through Petra, and take a return flight arriving in Tel Aviv at 9 pm. The rate per person is about $300 (www.arkia.com).