The way the Apollo missions worked was the craft that launched from Earth had two separate parts, the command module, which carried the three man crew from the Earth to the Moon and back, and the lunar module, which took two of the crew to land on the moon and then rendezvous back with the command module. This meant the lunar module didn’t have to carry many supplies (which was the source of some drama with Apollo 13) which meant it was lighter. Also the Earth’s gravity is 6 times stronger than the Moon’s, plus the Moon doesn’t have an atmosphere and atmospheric drag socks up a lot of energy when launching from Earth. Also adding even a little bit of weight means you need a lot more fuel, because not only do you need extra fuel to carry that weight but you also need more fuel to carry the extra fuel, then you need more fuel to carry that fuel and so on. This all adds up to needing a ginormous rocket to take off from Earth, but the lunar module only needed a much smaller rocket to take off from the Moon.
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