*Originally posted by wolfgang59*

**That is what I thought. But when I did the calculations it didnt stack up!
**

Assume engines are OFF. assume Ship mass of 1,000,000 kg

Determine new velocity and calculate ship's loss in KE .

Sorry - I prefer my calculations without so many numbers in them ðŸ™‚

OK, the one thing we know is that momentum is conserved.

v = Initial spaceship velocity = 1,000,000 m/s

V = Final spaceship velocity

u = Final astronaut velocity wrt ship = 1m/s

m = astronaut mass = 100 kg

M = spaceship mass (without astronaut) = 1,000,000 kg

OK, we know is that momentum is conserved.

(M + m)v = MV + m(V + u)

=> V = v - mu/(M + m)

=> V = 1000000 - 1/10001 (~ 999999.9999)

Increase in KE of astronaut

= 0.5m(V + u)^2 - 0.5mv^2

= 0.5m[v + Mu/(M + m)]^2 - 0.5mv^2

= 0.5mMu[2v + Mu/(M + m)]/(M + m)

"Increase" in KE of ship (going to be -ve)

= 0.5MV^2 - 0.5Mv^2

= 0.5M[v - mu/(M + m)^2] - 0.5Mv^2

= 0.5Mmu[mu/(M + m) - 2v]/(M + m)

And the increase in total KE:

= 0.5Mmu^2/(M + m)

This is independent of v - which it has to be, because the increase in energy must be frame-independent. The energy comes from the work done by the astronaut in walking.