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Spoilers:

Near the end of the movie, the Enterprise is basically stationary in lunar orbit, with a lovingly detailed lunar landscape looming in the background.

Then, maybe an hour in-movie time later, it's near Earth, with the Earth in the background being the the same size as the Moon was just a little while ago.

During this entire time, the Enterprise did not use its warp engines.

The distance from the Moon to the Earth is an average of 384,400 km.

How the heck did the Enterprise travel that far without warp, and without anyone noticing?

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    I think it was Sulu, but someone on the bridge announces that they're something like about "275,000 km" from Earth after dropping out of warp. And, well, they've other things on their mind right after...
    – HorusKol
    Commented May 23, 2013 at 23:07
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    Another example of Bad Science in this movie that stretches the limits of credulity and makes it unworthy to be called Star Trek.
    – Kim Rudolph
    Commented May 24, 2013 at 0:28
  • @KimRudolph - My favourite part is when they start "falling" toward earth from orbit
    – Robotnik
    Commented May 24, 2013 at 1:45
  • The Earth is larger than the Moon. What makes you think they got any closer, rather than just changing the angle of the camera?
    – Izkata
    Commented May 26, 2013 at 6:59
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    @Tacroy I don't know the proper math to determine the correct distance, but it is possible that the Enterprise was in the correct position that the Earth and the Moon appeared to be near the same size. Because, as you pointed out, the Moon is much smaller than Earth, Enterprise would have to be a lot closer to it for it to look an equal size. Therefore, it is possible that Enterprise didn't actually move as far as you thought it did.
    – Xantec
    Commented May 27, 2013 at 3:31

1 Answer 1

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Impulse engines are actually quite fast (relatively speaking). According to Memory-Alpha:

...the shuttles aboard the Enterprise-D had a maximum impulse velocity of approximately 2.5% of light speed...

We can use this as a notion as to how fast the Enterprise's maximum impulse velocity would be (presumably higher).

The speed of light is 299,792.458 kilometers / second. Multplying that by 2.5% we get 7 494.81145 kilometers per second. We divide the average distance of the Moon to the Earth by the maximum speed impulse presumably has and we can conclude that it would only take 51.2888152777 seconds, less than a minute for the Enterprise to go from the Moon to the Earth (on average).

To traverse a smaller distance would take considerably less time.

EDIT:

The above was calculated for a shuttlecraft aboard the Enterprise-D (more technologically advanced). Thanks to Xantec, we can get a more accurate estimation on how fast the Enterprise could traverse the distance. Assuming the Enterprise's maximum impulse drive moves at 0.8 warp speed, we can establish its velocity by the equation provided by Memory-Alpha:

V=WF^3*C

0.8 cubed is 0.512. We can then use distance/velocity to obtain the time: approximately 2.504 seconds. Still definitely do-able in an hour's time.

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    Perhaps closer to the specs of the new 'Trek Enterprise, the refit Constitution class Enterprise was capable of 0.8 Warp speed at full impulse. Unfortunately, due to changes in how warp factors were calculated over the years, it does become a bit muddied as to exactly how fast that would be.
    – Xantec
    Commented May 24, 2013 at 1:16
  • Hmm! We could go off of how TOS calculated warp factors (V = WF^3 * C) and go from there. It'd be far more accurate to estimate the Constitution Class Enterprise's speed than a shuttlecraft from the Enterprise Galaxy Class. I will update the answer with more accurate numbers.
    – cpmjr123
    Commented May 24, 2013 at 2:40
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    But you're assuming a largely functional Enterprise decided to travel from the Moon to the Earth; in the movie, it was largely disabled and being exploded - in fact it's a plot point that the ship couldn't even muster enough power to hover in Earth's gravity.
    – Tacroy
    Commented May 24, 2013 at 3:47
  • @Xantec - The higher warps might have changed. But Warp 1 is and has always been the speed of light.
    – Xavon_Wrentaile
    Commented Jun 19, 2018 at 23:41
  • @Xavon_Wrentaile True enough.
    – Xantec
    Commented Jun 19, 2018 at 23:55

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