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NO*

Basically: long, long ago Earth got hit by an asteroid, the size of Mars. However, instead of destroying Earth, it simply merged with it and the debris became the moon. Even if you have an asteroid big enough (today we don’t), the debris isn’t going to magically disappear: You’re going to have an asteroid belt between Mars and Venus. Moving a planet into an asteroid belt is probably a bad idea.

*I mean, trivially, yes, you can build an asteroid equal in size and make Earth into an asteroid belt if you have that technology. Then you have to move Mars into an asteroid belt, costing tons of energy, and then you need a better planetary defense system. Total cost would probably be a lot more than the cost of the thermobaric weapons necessary to reduce every city with population greater than one million to ash.

Rocks are not Free, Citizen! (Much of this answer is essentially the arguments from Rocks are Not Free stripped of the universe-specific verbiage.

Essentially, even if you find the right rock, the amount of time, resources and fuel required to change the rocks orbit to make it intersect with earth are, put mildly, astronomical.

If you have the technology to do something like this, "conventional" bombing is liable to give a better cost/effect ratio.

Edit to address second point:

Given that the energy requirements to move a planet in any semblance of a human timescale (rather than the millions of years) are even more astronomical than an actual rock... you're still looking at most solutions (like maintaining a terraformed ecosystem on Mars in its current orbit) being vastly more efficient.

It's fair to say that if they can move mars at all, moving an asteroid of any size is going to be easier.

So broadly, yes. Throwing an asteroid big enough to splat earth like a sledgehammer on a biscuit is by definition possible if you can complete the rest of the plan.

As another answer commented, Earth has taken a rock the size of mars in the distant past and since stabilised its orbit enough we can barely tell. I'm not completely au-fait with the mathematics involved, but what you really want is to smack Earth with an asteroid travelling at a significant fraction of the speed of light.

This will blast earth to shrapnel and then as the sole stewards of the solar system you can clear the debris and move Mars to the better position in the solar system at your leisure.

Of course, if you can accelerate anything to useful proportions of the speed of light, moving mars is more or less an afternoon's work.

Good luck hiding your involvement though. It's hard to imagine that the forces able to impart that much velocity on anything would be subtle.

As some related reading, I refer you to This Treatise on Planet-Busting

Here's an extract from the preamble:

The Earth is built to last. It is a 4,550,000,000-year-old, 5,973,600,000,000,000,000,000-tonne ball of iron. It has taken more devastating asteroid hits in its lifetime than you've had hot dinners, and lo, it still orbits merrily. So my first piece of advice to you, dear would-be Earth-destroyer, is: do NOT think this will be easy.

Essentially you don't want to destroy Earth. You want to destroy Earthlings, pretending it wasn't you and then take over their place.

If you insist on moving Mars to Earth's orbit you may consider achieving your goal in a slightly different manner.

1. Drop an asteroid large enough to cause mass extinction on Earth. There are high chances all Earthlings die as a result but even if some doesn't they will be technologically downgraded and you can claim they already died.


2. Move Earth out of it orbit (claiming there is no sentient life form there anymore so you're not performing a genocide)


3. Move Mars to the cleared orbit

Thanks to that approach rather than simply destroying Earth you don't have asteroid belt in the old Earth orbit. You really don't want to place your planet in the middle of asteroid belt

Note, I'm ignoring if the technology is possible (you said it exists so I take it for granted). Can an asteroid kill most of the life from the planet surface? It did already. Several times.

It might give you a nice plot later (someone discovers the Earth surface wasn't really wiped of any life, especially some Earthlings survived at least the genocide you indeed have caused - it can have interstellar repercussions if there are any other alien life forms that might worry about that).

Can an asteroid be used as a planetary attack weapon?

Absolutely.

Is it wise to do so?

Probably not.

Consider that if Mars can move asteroids like this, then Earth probably can too. And when Mars starts maneuvering the asteroid into an attack vector, do you think Earth will sit there and let it happen? Of course not. They should have plenty of time, as it'd almost certainly take months (at least) to move the asteroid. Earth would either try to intercept the asteroid or redirect their own towards Mars. Or possibly both. You'd have a Mutually Assured Destruction scenario.

If the Martians can move the entire planet, they could move it to a closer solar orbit instead. Since they can move planets, they should be able to easily handle any adjustments needed due to two planets being in such close orbits.

I might be a little confused, but can't mars and earth exist in the same orbit on opposite sides of the sun and not collide?

If anything, there might already be a planet in Earth's exact orbit behind the sun right now, and we've never seen it because the sun is in the way (if we didn't have telescopes in space to prove otherwise)

Exactly this scenario takes place in Kim Stanley Robinson's 'Mars' trilogy.

During the first Martian revolution, the revolutionaries target an asteroid (which they call 'Nemesis') at Earth. It gets destroyed though, and was generally considered to be a bad idea by other revolutionary factions as it makes it easy for Earth to present them as murderous extremists.

Let's take for granted that they can move an asteroid at leisure, and then Mars.

Doing that will take a huge lot of energy: only the delta V between Mars and Earth is 6 km/s, which for the mass of Mars, $6.39times 10^23$ kg, gives an energy expenditure of $230times 10^29$ J, which is roughly the amount of energy emitted by the entire Sun in 1000 seconds.

Now, if you have the capability of manipulating that amount of energy, a cleaner way to do the job would be to simply inject it into the mantel of the Earth. The subsequent increase in volcanic activity would wipe out humanity and leave the orbit free from debris. As bonus the martians would get a free planet!

Why not a smaller meteor and just 'reset' life on Earth (think dinosaurs being wiped out).
Mars' 'year' would have to speed up lot, wouldn't it (shorter revolutions around the sun) to move closer to the sun?. What impact would that have on the Martians? Where does the energy for that come from?

Sure you can use an asteroid to destroy earth. In fact, there's a giant asteroid already circling earth on a monthly basis. That's right, the moon. Actually, since it's locked into earths gravity instead of the suns that makes it a moon, and if it had its own orbit it would be considered a dwarf planet.

But ignoring those details, we now have a giant weapon relatively close to the earth that can wipe out all life and potentially even change earths orbit a bit. https://youtu.be/i_OgGF92k_M

Because the moon is tidally locked with earth, we can do whatever we want to the dark side without any interference. We slowly set up giant lasers, or Kepler drives, or whatever propulsion system to send the moon careening towards earth.

Those poor lunar base colonists will wake up one day and contact earth saying "hey, you seem closer than before" and then the two massive bodies will collide, scouring the surface of both clean, turning earth into a giant fireball, and leaving you free to knock it out of orbit and replace it with mars at your leisure.

I think that we've established that the asteroid idea might have some downsides, so here's an alternative:

Provided that Martians have the ability to move planets (and Earth doesn't), why not just move Earth out of its orbit a little, or into its orbit a little? Once it's far enough out of place, it'll spiral in toward the sun or wander off toward the edge of the solar system, with very little chance of colliding with anything else of importance. They'll have no way to correct their course and they'll all either burn/radiation to death or freeze to death (your choice!) This also leaves the orbit open for Mars to inhabit.

Some lucky few may manage to board a rocket and evacuate Earth in time, but I suppose that's an inevitability regardless of how you choose to (attempt to?) bring about their demise.

This could be done, but literally anything else is easier.

In order to turn the Earth into a debris field, you need to overcome its gravitational binding energy; You need to deliver enough energy via your asteroid to accelerate the matter that makes up Earth to escape velocity. This comes out to "2x10^32 Joules, or about 12 days of the Sun's total energy output!." This is a ludicrous amount of energy. Collecting and storing it would require engineering feats that dwarf the complexity of just terraforming Mars. Keeping it secret from the Earthers is a completely separate issue.

Ceres is the largest asteroid in the solar system, weighing 8.958 × 10^20 kg. If it were moving at 670 km/s it would have enough energy to demolish Earth. That is 60 times greater than Earth's escape velocity, which is the speed most impacting asteroids hit the Earth at. It is also greater than the Sun's escape velocity from the surface of the sun. This means that you would have to accelerate Ceres from its current velocity into an Earth impact trajectory, at that ridiculous speed in a short period of time.

Once you are done with all of this, you now have a debris field in Earth orbit. It will endanger the now relocated Mars for eons to come.

It would be much much simpler to just move Mars to the third Lagrange point. Mars would be on the other side of the sun from Earth, and it could just sit there in its new orbit. Because Lagrange point orbits are not stable long term, this would require a little bit of stationkeeping, small adjustments to its orbit. If you can move Mar's orbit entirely, station keeping should not be an issue.

If you really want to use a foreign body to strike Earth, here's a solution that will address some of the concerns voiced so far:

Use something heavier than Earth

Collisions are modeled in Newtonian physics by the equation

$$m_1v_1,1 + m_2v_2,1 = m_1v_1,2 + m_2v_2,2$$

Given that a collision between Earth and something heavier is mostly inelsatic (that is, the two bodies stick together instead of bouncing off), you can treat their end velocities as equal:

$$m_1v_1,1 + m_2v_2,1 = left(m_1 + m_2right)v_2$$

In other words, the heavier one of the two bodies is, the more its initial velocity affects the velocity of the system after collision. No doubt there are relativistic considerations as well (feel free to comment) but the concept should be roughly the same. Treating the Earth as stationary, if you ram something exactly Earth-weight into it, the two will then move off at half of the something's initial velocity. If you use something heavier, they'll move faster.

This approach has these advantages:

1. Removes Earth from its orbit, so Mars can replace it.


2. Wipes out all the humans who don't escape via rocket.


3. Can collide at a slower speed, meaning less debris to cause problems for Mars once it moves to Earth's former orbit.