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Apollo Missions - Travel time to moon [duplicate]

I must be missing something - escape velocity is about 25,000mph. The distance to the moon about 240,000 miles. That computes to about a 9 hour flight. Why did it take 3 days for Apollo missions to reach the moon?

Answer*

As already explained in other answers, essentially all of the distance is covered by unpowered flight - gaining altitude away from Earth while under the influence of Earth's gravity, the "upward" velocity will gradually diminish. At LEO distance this is about 10m/s<sup>-2</sup>, although this gravitational acceleration does fall off with square of distance. 

This is a good thing because the craft wants to arrive at the Moon at a speed which requires the least adjustment (least propellant) to enter lunar orbit - the Moon orbits the Earth at about 1km/s (round numbers) and a low altitude orbit around the Moon requires a speed of about 1.6km/s. To arrive in a retrograde orbit basically means the craft must end up at the far side of the Moon with zero radial velocity and about 600m/s retrograde to Earth. To accomplish this, it's a good thing that radial velocity away from Earth is being lost due to gravity almost the entire way out, but this means the trip will take much longer than the 9 hours suggested by simple arithmetic.

Another factor is that the path from Earth to Moon is not traveled in a straight line. Departure from LEO is essentially tangential to Earth's surface; Earth's gravity pulls the trajectory into a curve. The lowest energy transfer occurs if the craft aims to enter lunar orbit retrograde (as I previously mentioned), so the overall path is actually somewhat S-shaped, making total path a bit longer.

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