When you arrive at Amman airport, sleep the first night (or whatever might be left of it!) in Madaba and not in Amman. It is closer to the airport (see the map) and the hotels there can arrange to pick you up for much less than an airport taxi would charge to take you to Amman. The usual price is 12JD.
There is a larger version of this map on the page entitled "Tourist's map of Jordan south of Amman
First day : take the bus that runs each day in season from Madaba (see the Madaba page for full details of this bus) to Petra via the Kings' Highway which is a spectacular mountain road. It usually leaves at 10am (you would have time for a quick trip to a bank!), stops for an hour at Kerak to allow a visit to the castle and for a short quarter of an hour at Wadi Mujib - a very dramatic canyon which is sometimes called "The Grand Canyon of the Middle East". This canyon isn't actually marked on the map, but it's the wiggly bit north of Kerak. The bus continues via Tafila and Shobak (no stops) and arrives in Wadi Mousa/Petra at around 4pm where it will drop you off wherever you want. See below for possible variations to this first day programme.
Second and third day : visit to Petra.
Fourth day : take the early morning bus to Wadi Rum, visit Wadi Rum during the day and sleep the night in the desert.
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