Saturn v is 2882 tons. Fuel is 30gj a tons.
Escape velocity (11 km/s). 350 TJ of KE.
The fuel is 85 TJ.
The Saturn v has 3 times less fuel than it would need to escape gravity.
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$\begingroup$ You didn't actually ask anything, but I've answered the implied question straightforwardly. Your post comes off as skeptical; you should be aware that this site doesn't welcome moon landing deniers, though we're always happy to answer good-faith questions. $\endgroup$– Russell BorogoveCommented Jul 21, 2023 at 1:54
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1$\begingroup$ "The Saturn v has 3 times less fuel than it would need to escape gravity." It should be clear to you that you have made a mistake, because....it did. Assuming that by "escape gravity" you mean "put something into orbit bound for the Moon." $\endgroup$– Organic MarbleCommented Jul 21, 2023 at 2:01
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3$\begingroup$ Voting to close as Moon-hoaxer nonsense due to the last comment in the post. How do we know the Apollo Moon landings are real? $\endgroup$– Organic MarbleCommented Jul 21, 2023 at 2:04
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1$\begingroup$ I suspect these mathematical inconsistencies have the same cause as the mathematically wrong Chinese electricity statistics. $\endgroup$– Ray ButterworthCommented Jul 21, 2023 at 2:39
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3$\begingroup$ Your calculation for the required kinetic energy is way off. Only a small part of the rocket required (and thus acquired) the velocity to reach the moon, so the kinetic energy was much lower than your number. Most of the fuel energy (other than waste heat) went into putting kinetic energy into parts of the rocket that never went that fast and were left on the way. $\endgroup$– antlersoftCommented Jul 21, 2023 at 14:35
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Eppur si muove.
Very little of the Saturn V's mass goes translunar -- about 65 tons of it, around 2% of the launch mass. Most of the launch mass of the rocket is propellant, which is burned and exhausted, and returns to Earth.
The moonward-bound portion leaves Earth traveling at about 10.8 km/s, with a kinetic energy of about 3.5 TJ.
Even the lunar-bound portion of the Saturn-Apollo stack doesn't reach Earth's escape velocity, though it does get close. The moon hasn't escaped Earth's gravity, after all, so the spacecraft doesn't need to in order to get there.
answered Jul 21, 2023 at 1:50
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5$\begingroup$ That is incorrect. No chemical rocket engines produce exhaust above around 4600 m/s, and thousands of objects have entered low Earth orbit at 7700 m/s. $\endgroup$ Commented Jul 21, 2023 at 2:06
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9$\begingroup$ Ah, yes, I forgot about flapping the solar panels to increase velocity. I'll edit my answer to cover that. $\endgroup$ Commented Jul 21, 2023 at 2:07
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8$\begingroup$ "It's mathematically impossible for the exhaust velocity to be lower than the rocket is going" Wrong. Very wrong. Read the "conceptual question" here pressbooks.online.ucf.edu/osuniversityphysics/chapter/… "Yes, the rocket speed can exceed the exhaust speed of the gases it ejects. The thrust of the rocket does not depend on the relative speeds of the gases and rocket, it simply depends on conservation of momentum." $\endgroup$ Commented Jul 21, 2023 at 2:10
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3$\begingroup$ The S-IVB and Apollo spacecraft has something on the order of 3.5 TJ of kinetic energy at the end of the translunar injection burn. $\endgroup$ Commented Jul 21, 2023 at 2:33
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3$\begingroup$ "50% by newtons third law": Newton's laws don't work that way. Force is not energy. In fact, not only is the exhaust ejected at much lower velocity, it's ejected backwards from a moving vehicle with its exhaust velocity being relative to that vehicle, so the kinetic energy of the bulk of the exhaust in the frame of the overall system is even lower. Toward the end of a Saturn V first stage burn, nearly all the energy was going into accelerating the upper stages, the exhaust ending up with near zero kinetic energy. $\endgroup$ Commented Jul 21, 2023 at 17:32