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When a rocket goes up some of the energy from burning fuel is stored as gravitational potential energy in it, when it falls back the potential energy is now converted to kinetic energy and heat energy.

But when you have a rocket that uses thrust to brake it's decent, for example some of the spaceX rockets, then you are burning fuel to slow it down which is like decreasing kinetic energy by applying more energy to it.

How does conservation of energy hold on this case?

Where does the lost kinetic energy and the energy from braking thrust go?

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Applying thrust with a rocket means than you shoot out big amounts of gas by burned rocket fuel. While burning, the fuel rapidly expands into its gas form, and this gas wants to leave. The energy of that gas was the chemically stored energy in the fuel.

  • Now, during ascend, the gas shoots itself out as exhaust by pushing up in the rocket. The rocket gains kinetic energy, that comes from the chemically stored energy.

  • During descend, the same gas is shooting itself out, but this time at higher speed (with more kinetic energy), because the rocket is like "a wall" that does not move away while the gas pushes. When you push on something that doesn't move, you feel yourself being pushes further away instead (this leads to the momentum conservation law).

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  • $\begingroup$ Huh? Are you talking about accent or decent ? $\endgroup$ – user1062760 Feb 10 '18 at 14:39
  • $\begingroup$ @user1062760 I have updated and improved the answer to be more informing. Sorry for the bad formulations. $\endgroup$ – Steeven Feb 10 '18 at 16:06
  • $\begingroup$ So you're saying the kinetic energy of the exhaust gases during decent is the sum of kinetic energy lost by the rocket and the chemical energy of the burning fuel? $\endgroup$ – user1062760 Feb 11 '18 at 20:22
  • $\begingroup$ @user1062760 Plus all the energy lost as heat, yes $\endgroup$ – Steeven Feb 11 '18 at 22:03

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