In a hypothetical situation if we needed to move the earth slightly to avoid being hit by an asteroid
- Could we harness Jupiter’s gravitational force to do so?
- Is there another more efficient way to move the earth?
- Would we need rockets?
In a hypothetical situation if we needed to move the earth slightly to avoid being hit by an asteroid
In short, your question reads is as if you have asked: "How can I change the flow of a river so that it fills my water-pail?". Answer: you do not. If you can could change the trajectory of a river you sure as heck can pick up the pail, carry it to the river and dunk it in. If you cannot even do that simple thing, then you cannot change the trajectory of a river.
First, if we can move(*) Earth, we can move the asteroid, since the asteroid is several magnitudes less massive than Earth. If we can already move the asteroid, we do not need to move Earth. If you cannot move the asteroid, then you cannot move Earth.
Second, in order to make Jupiter's gravity affect Earth differently than it does now, we need to move Jupiter. If we can move Jupiter, then we can move Earth, because Earth is several magnitudes less massive than Jupiter. If we can already move Earth, we do not need to move Jupiter. And conversely: if you cannot move Earth, you cannot move Jupiter.
And since we cannot move Jupiter to any meaningful extent, the answer to your question is: no, we cannot use the gravity of Jupiter to move Earth out of the way of an oncoming asteroid.
(*) In this context, "move" means "change the trajectory of".
We couldn't use Jupiter's gravity as it stands without moving something. If you can move Jupiter, you can move Earth, or even better still the asteroid in question, so there wouldn't be any reason for it.
Using mass to move other things via gravity is possible however. It's actually one of our plans in case we do need to move some space rocks out of our way. They call this a gravity tractor.
The gravitational force of a nearby space vehicle, though minuscule, is able to alter the trajectory of a much larger asteroid if the vehicle spends enough time close to it; all that is required is that the vehicle thrust in a consistent direction relative to the asteroid's trajectory, and that neither the vehicle nor its expelled reaction mass come in direct contact with the asteroid.
If time weren't an issue and you really need to move Earth, using the moon to move it would be the "easiest" method. Less danger this way. You don't have to worry so much about killing everyone on the surface of the moon if you fowl something up. Move the moon in a bit closer and drag Earth away with it.
This still wouldn't be easy at all. The most practical solution at the moment would be Ion Thrusters probably. You need a whole lot of them and a whole lot of power to get it all working.
Again none of this would be quick, easy or cheap. Stick to moving the dangerous space rocks instead.
Not really.
If you could make the distance between Jupiter and Earth shorter, then Jupiter's gravitational influence on the Earth would be closer, and stronger. I guess is that you could achieve this through creating a sizeable wormhole, and placing it on the side of the Earth corresponding to the direction you want to move it. However, if you could manufacture wormholes that size, you could just make the asteroid transverse a wormhole, clearing it of any collision. Perhaps the wormhole you're creating can only successfully travel energy or gravitational forces. In which case, you could just use Jupiter's gravity tunneled through the wormhole to alter the asteroid's course.
Actually, so long as the asteroid is less massive than the Earth, it would be easier to perturb the orbit of the asteroid than the orbit of the Earth.
There's no real scenario I can think of that justifies expending that much energy to move the Earth.