What would happen if Jupiter and Earth were at the same distance as the Moon is from Earth?
If Spock came with a super machine capable of moving planets, and placed Earth so close to Jupiter as the Earth's moon, the gravity of Jupiter would make us fall into it?
That's no good idea. Earth wouldn't necessarily fall into Jupiter in the short run, provided it orbits Jupiter fast enough (within about 1.7 days), and on a circular orbit, but we would risk to collide with Io, destroy it by tidal forces, or change its orbit heavily.
The other Galilean moons would get out of sync and change their orbits over time.
Tides would be severe on Earth, not just limited to oceans, but also for "solid" ground, as long as Earth isn't tidally locked. This would result in severe earth quakes and volcanism.
Our days would be dim due to the distance to the sun. After tidal locking of Earth and ejection/destruction of Io the tides as heat source would be lost, oceans would freeze, temperature would fall to about -160°C mean temperature. During the polar night oxygen would probably condense from the atmosphere and form lakes, may be even nitrogen. By this atmospheric pressure would drop.
Since Spock is smart enough to know these consequences in advance, he wouldn't do it.
Some, but not all, of the bad effects could be alleviated by changing the conditions a bit: Move Jupiter into Earth's current orbit around the Sun, and put Earth into a circular orbit around Jupiter in tidally locked rotation. Once Earth's shape settles down from the new tidal forces, conditions shouldn't be *too* bad. Interactions with Jupiter's other moons might be a problem -- so move them. Interactions with Jupiter's magnetic field and radiation belts would still be, ahem, interesting. We should get some truly spectacular auroras, and we could see how Jupiter reacts to the extra heat.
@KeithThompson Even with your improvements, I think (can't do the math to be sure), but 384,000 KM (are we doing distance from Surface or from Center - with Jupiter, that matters a lot), but that would be close to the liquid roche limit. Add the magnetic field and I think Earth would fairly quickly lose it's atmosphere and oceans, giving Jupiter a temporary, very pretty ring system, which solar heating and Jupiter's hot van Allen belt would make mince-meat out of fairly quickly, leaving the Earth a barren, dead, rock. Still not a great outcome for us, even with your adjustments.
I think it would be outside the Roche Limit at 384000 Km, as all four inner moons of Jupiter are closer than that (Metis, Adrastea, Amalthea and Thebe), and Amalthea (at least) is either ice or a rubble pile, since it has a density of around $0.9 g/cm^3$. EDIT: Just looked it up. Thebe is (officially) outside the fluid Roche limit, Amalthea inside (though somehow is holding together despite its composition).