The spaceship kinetic energy before braking was 43574*2400²/2 = 125.4 GJ and after braking 32676*1500²/2 = 36.76 GJ, i.e. change in kinetic energy due braking was 88.64 GJ, i.e. **fuel consumption was 8.13 MJ/kg**.

No, Heiwa, your calculations are wrong. You have to consider the kinetic energy of the total system, which includes both the inert mass of the spacecraft

*and the propellant*.

I'm going to use your mass and velocity figures, but that is in no way an admission that I agree with them because I haven't looked up the figures to verified whether they are correct or not. Furthermore, the calculation I'm about to perform is just a "back of the envelope" calculation to get us close.

I concede that the kinetic energy before the burn is 43574*2400²/2 = 125.4 GJ. I'll also concede that the kinetic energy of the spacecraft and remaining propellant after the burn is 32676*1500²/2 = 36.76 GJ. But you must recognize that the expelled mass also has kinetic energy, thus the total kinetic energy after the burn is that of the spacecraft plus that of the mass expelled during the burn in the form of exhaust gas.

The exhaust gas velocity relative to the spacecraft is equal to the engine specific impulse times g

_{o}, or 314 s * 9.807 m/s

^{2} = 3079 m/s. The exhaust is expelled in the direction of travel, therefore the true velocity of the exhaust is the velocity of the spacecraft + 3079 m/s. Let's make it simple and assume the spacecraft velocity is the average of the initial and final velocities, i.e. (2400+1500)/2 = 1950 m/s. We then have an exhaust velocity of 1950 + 3079 = 5029 m/s. Therefore, the kinetic energy of the expelled mass is 10898*5029²/2 = 137.8 GJ.

We now see that the kinetic energy of the total system at the end of the burn is 36.76 + 137.8 = 174.6 GJ. Kinetic energy was added to the system in the amount of 174.6 - 125.4 = 49.2 GJ. This energy came from the chemical energy of the propellant that was released during combustion, first as thermal energy and then as kinetic energy as the gas was expanded in the engine nozzle. The energy released from the propellant on a mass basis is 49.2 GJ / 10898 = 4.5 MJ/kg. This number is in the ballpark of what should be expected from the type of propellant used. (I've calculated that the actual change in enthalpy of the propellant is about 5.16 MJ/kg.)

Everything works out just fine. No problems here.