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Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Panama City, Florida to Amman as you normally would.
In terms of precipitation, rainfall in Amman ranges from 0.0 - 2.4 inches per month. January is typically the wettest month, when rainfall can reach 2.4 in. May is typically the driest time to visit Amman when rainfall is around 0.0 in.
If weather is an important factor for your trip to Amman, use this chart to help with planning. For those seeking warmer temperatures, July is the ideal time of year to visit, when temperatures reach an average of 77.0 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 44.6 F).