On your 3rd day, whether you are staying by Dead Sea or in Petra, on the way to Amman you should make the 82km (161km from Petra) or 1 ¼ hour (2 ¼ hours from Petra) car journey south to Kerak Castle. It is situated on top of the hill where you can see the view of the Dead Sea from afar.
Kerak Castle is a Crusader castle constructed in 1140 under Pagan and Fulk, King of Jerusalem. The castle is an example of Crusader architecture, with a mix of west European, Byzantine and Arab designs. It was used over the centuries up to the rule of the Ottoman Empire. It is interesting to note that some of the destruction that occurred in the castle was due to the local people who removed the stones that contained potassium nitrate which can be used as gunpowder.