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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.

D J Sims
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  • 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. – Russell Borogove Jul 21 '23 at 01:54
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    "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." – Organic Marble Jul 21 '23 at 02:01
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    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? – Organic Marble Jul 21 '23 at 02:04
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    I suspect these mathematical inconsistencies have the same cause as the mathematically wrong Chinese electricity statistics. – Ray Butterworth Jul 21 '23 at 02:39
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    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. – antlersoft Jul 21 '23 at 14:35

1 Answers1

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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.

Russell Borogove
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  • That doesn't solve the problem. The exhaust velocity is higher. All the particles in the fuel must have KE – D J Sims Jul 21 '23 at 01:55
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    The exhaust velocity is much lower. 2150 tons of kerosene-oxygen at ~2600-3000 m/s, the rest hydrogen/oxygen at ~4300 m/s. – Russell Borogove Jul 21 '23 at 01:59
  • It's mathematically impossible for the exhaust velocity to be lower than the rocket is going – D J Sims Jul 21 '23 at 02:03
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    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. – Russell Borogove Jul 21 '23 at 02:06
  • That's because they have solar panels and other power sources obviously – D J Sims Jul 21 '23 at 02:06
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    Ah, yes, I forgot about flapping the solar panels to increase velocity. I'll edit my answer to cover that. – Russell Borogove Jul 21 '23 at 02:07
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    "It's mathematically impossible for the exhaust velocity to be lower than the rocket is going" Wrong. Very wrong. Read the "conceptual question" here https://pressbooks.online.ucf.edu/osuniversityphysics/chapter/9-7-rocket-propulsion/ "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." – Organic Marble Jul 21 '23 at 02:10
  • That's because you're assuming the fuel was already accelerated, the total end kinetic energy has to be greater than the rocket – D J Sims Jul 21 '23 at 02:13
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    @Expe What's your actual question? – Russell Borogove Jul 21 '23 at 02:16
  • See what the KE has to be – D J Sims Jul 21 '23 at 02:17
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    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. – Russell Borogove Jul 21 '23 at 02:33
  • The actual total energy consumed is 25tj with 17tj of fuel, 50% by newtons third law so you need 25tj on 8tj of fuel or 300% impossible – D J Sims Jul 21 '23 at 02:36
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    I'm not assuming anything, I'm pointing out your incorrect assertion. Once you obtain a grasp of the fundamentals, you will perceive your errors. – Organic Marble Jul 21 '23 at 03:01
  • Then you failed to answer the question if you didn't list your assumptions. – D J Sims Jul 21 '23 at 08:02
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    "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. – Christopher James Huff Jul 21 '23 at 17:32