Crazy Eddie wrote:
Really? You started by asserting that Earth's gravity is non-existent at 300,000km, which is DEAD wrong.
I said *effectively 0*, not *absolutely 0*, and for the purposes of this argument it's correct. When things are CLOSE to 0, you can TREAT them as 0 without any significant impact on your calculation (especially in this case, considering the bulk of the acceleration doesn't happen until the ship is very close to Earth). That being said, the figure of 40 hours I gave you assumes it starts to fall (from rest) at a distance r away from the Earth in a field GM_e/r^2 (non- zero). Giving the ship an initial velocity of 15, 20, even 100m/s won't bring that figure down to 5 minutes.
You need to understand how assumptions can or cannot affect calculations. Based on your language and the level of your discussion, I'm going to guess you're either an undergraduate or beginning graduate student (probably the former). Take my advice: solid assumptions that don't necessitate explicit calculations are far from bad science. They're the way things are really done.
You implied that Enterprise would have "fallen" from a stationary position at that altitude, which is impossible. You implied that their position relative to the moon was unchanged, which is ALSO impossible. And then with the simple fact that their actual motion throughout the encounter is unknown, you wave your hands and change the subject.
I never changed the subject. I stated earlier (which you continue to ignore) that they would certainly fall toward Earth, but, without significant (read: very fast) initial velocity in the radial direction, they wouldn't in the time shown in the movie. And that is all correct, your order-epsilon blatherings not withstanding.
You need to hit the books a bit more. In fact, scratch that. You need to get away from the books and really *understand* what it is you're talking about. A solid understanding of physics is knowing when you do and when you *don't* have to do the calculation.