but dont you see your using mavity in your argument right there the moment you put earth in the equation. the reason why you even made those calculations is because the rocket has to fight earths mavity (gravitational pull) which completely nullifies your entire argument. hence if he used his rocket in space he wouldnt get jack from it.
he would if he accelerates in space *ie between solar systems where there s no mavity of significance) at exactly 9.8m/s^-2 constantly, he will be pushed to the back of the craft at 1G and will weight hat he does on earth.