Well donw. Obviously, some sort of mass reduction is in effect, because otherwise the trip to Jupiter, for example, would be so completely wrong it's even out of the realm of error on the part of a character; not to mention the fact that we might as well have people get out and push if those calculated accelerations were the true case.
Even so, that degree of mass reduction is (to me) obviously a case of the writers a/o CGI people not bothering to research some simple particle mechanics before putting osmething onscreen. It should be common knowledge that 'Trek fans have a better grasp of physics than most TV viewers; why insult us without at least offering a canon explanation for what we see?