How close can Jupiter be to Earth without making Earth unhabitable? How close can Jupiter be to Earth without making Earth unhabitable? What's the closest distance possible? Can Jupiter be twice or three or four times as close to Earth as Mars without having any negative impact? If so, how big would Jupiter appear in the skies compared to the Moon?
 A: Here's a fun article discussing the same for Saturn. Some points it makes:

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*If Saturn gets too close to the Earth, it would eject the Moon.

*Earth would pull on Saturn's rings, which would "[create] a long plume first reaching toward the Earth, then dragging after it once it was through".

*Except when Saturn is that close to the Earth, it would also get hotter (since it's closer to the Sun), which means the ices in the rings would melt and Saturn would be surrounded by a cloud of water vapor, which would be blown away by solar wind. It would become a mega comet.

*But there'd be nobody left to see the mega comet, because Saturn's approach would destroy the Earth due to tidal forces. This part is most relevant to your question:


When Saturn is still 20 times farther away than the Moon—well over 7 million kilometers distant—the tidal force it exerts on Earth is equal to the Moon’s. By the time it’s a million kilometers away that force has increased by a factor of more than 400! That would cause disaster on a global scale, mostly in the form of apocalyptic floods as huge tidal waves marched across the planet, destroying everything in their path.
By the time Saturn is at the same distance as the Moon, its tides would be many thousands of times stronger than the Moon’s. Fault lines would rupture, volcanoes would blow their tops, and anything left on the surface of the Earth would be wiped out.
And then comes the final blow. Judging from where we hit the rings, Nick depicts Saturn passing about 130,000 km from Earth. At closest approach, the tidal force Saturn wreaks on Earth would be a staggering 200,000 times the Moon’s! This distance is well inside Saturn’s Roche Limit, the distance from Saturn where the bigger planet’s tidal force is so strong it literally tears our planet apart.

All that's left is to repeat the calculations with Jupiter's mass instead of Saturn's. Jupiter's mass is $1.8982 \times 10^{27} kg$, while Saturn's is $5.6834 \times 10^{26} kg$. Therefore Jupiter is about $3.34$ times as massive as Saturn. From $F = GMm/r^2$, its tidal forces would be $3.34$ times as strong as Saturn's at the same distance. Therefore its effects are as strong as Saturn's at a distance that is $\approx \sqrt{3.34} = 1.82$ times as far.
So if Saturn destroys the Earth at a distance of a million kilometers, Jupiter would destroy the Earth at a distance of $1.82$ million kilometers - or about $4.5$ times the distance of the Moon. If that sounds close, remember that Mars at its closest (Mars is sometimes on the opposite side of the Sun) is about $56$ million kilometers away, so yeah, Jupiter can come closer than Mars without destroying the Earth.
How big would it look? The Moon's radius is $1737.4 km$, and it is about $384,400 km$ away on average. This means the full Moon subtends about $1737.4/384400$ radians. Jupiter's radius is about $69,911 km$. At $1.82$ million kilometers away, it would subtend about $69911/1820000$ radians, or about $8.5$ times the size of the full Moon.
A: First, it's estimated that Jupiter’s magnetic field is roughly 20,000 times stronger than Earth’s. This magnetosphere has trapped within it charged particles originating from the Sun. These form intense radiation belts around Jupiter. These belts are similar to the Earth’s Van Allen belts, but are many millions of times more energetic, largely composed of relativistic electrons with velocities that almost reach the speed of light. This means these particles can easily ionize other molecules when they collide. The magnetosphere of Jupiter extends to seven million kilometers, so if Jupiter was at this distance or closer, the effects of such ionization on biomolecules and other molecules inside biological life would be deadly.
There is also the fact that if Jupiter comes closer to earth, the effects of its gravitational field will be extremely destructive and a nice example is covered in Allure's answer using Saturn instead of Jupiter, but with the same principle. The tidal forces involved would be more than enough to ensure the end of human life. The moon closest to Jupiter, called Io at a distance of 470,000km, experiences tidal forces almost 20,000 times stronger than the tidal forces experienced on Earth due to the Moon. This means that there'd be tidal bulges on earth about one hundred meters high had earth been as close to Jupiter as Io is. Needless to say that even if earth was a hundred times that far away from Jupiter, the tidal forces and bulges generated would mean we'd all drown.
Also, it should be pointed out that many astronomers conclude that the gravitational field generated by Jupiter pulls away potential deadly asteroids from possible collisions with earth. If Jupiter was even 25% of the distance from where it is currently, it's likely that humankind would already be extinct due to multiple asteroid strikes.
