I am going to assume you read part 1 which you can find here.

Part 2 is going to focus more specifically on moving REALLY big things through space in order to destroy other REALLY big things.

Potentially useful links,

Delta V calculator

Hohmann Transfer Calculator

As established in part 1 even the best bi-propellant rockets would require multiple Earth masses of fuel in order to move any decent sized REALLY big thing like Mars.

As this is going more in depth lets look at the other side of the equation and see how much fuel it would take to move Mars to Earth with the Ideal Light/Photon Pressure Drive(ILPD).

Here is the equation in Wolfram Alpha if you don't trust me for some reason.

And we get 641,748,317,369,946,729,349,120 kg or 6.42*10²³ kg of fuel needed for the transfer. For reference this mass is about 9 times the mass of Luna.

Similar to the last problem I am sure many will realize, it would take an even larger amount of mass to move the fuel mass to your REALLY big thing making the whole process sort of self defeating.

With that in mind, pretty much the only way to move a REALLY big thing into another REALLY big thing for the purposes of destroying it will be to convert the REALLY big thing you are moving into the required fuel (fun fact: this will slightly lower the total amount of fuel you actually need).

9 lunar masses of fuel is obviously a MUCH more reasonable amount than a Saturn mass of fuel. That means we actually have the mathematical possibility of doing the Hohmann Transfer with REALLY things that don't mass more than Saturn. But that high efficiency has it's own cost, there are still a few problems additional problems that need to be solved before this will work.

The first problem is getting the fuel. The Light Pressure Drive is basically any laser or light. For those who may be scratching their heads about how lasers and light sources can be used as a means of propulsion do remember that light has mass and therefor momentum thus in accordance with Newtons 3rd Law (the "equal and opposite reaction" one) it will produce force and thus it will work as a means of propulsion.

For those other people vaguely wondering why lasers are the most efficient (in terms of fuel usage) means of propulsion it is possible to create, specific impulse (the measure of a rocket/fuel's efficiency) relates to the propellant's exhaust velocity and it's mass. It is of course more complicated than this but basically, high velocity is good, low mass is good.

Well the speed of light is the highest velocity attainable in our universe according to Relativity and it "masses" considerably less than an even an electron. So it is basically impossible to beat in terms of efficiency without breaking out the soft science fiction technobabble (tachyon rockets anyone?).

So getting back to the subject at hand, our light pressure drive uses energy directly. So in our example above you would need to use around nine lunar masses of energy.

Getting all this energy is a problem.

Burning all the fossil fuels on Earth would be a drop in a bucket compared to the total kinetic energy of the Earth's oceans. But even if the entire ocean was moving at 100 kps it would still only have less than a billionth of the required total energy (not even accounting for the fact the process of getting that energy would be.

So at this point you either come up with some magic way of doing matter/energy conversion or you start capturing the energy coming in from the sun.

Of course without building massive megastructures to harvest solar energy, the energy/second from sunlight is totally insignificant compared to what is needed. Like Sol would become a red giant and eat the Earth before you changed the Earth's velocity by an appreciable amount.

Which leads me into the second problem with using the Ideal Light Pressure Drive, it takes a gazillion years to actually impart any meaningful velocity into the REALLY big thing.

Calculating the acceleration you will get out of an ILPD is a two step process.

1. Identify the amount of momentum your drive produces per second.

The momentum of light is equal to it's mass divided by the speed of light or (p = E/c).

For the purposes of this "E" equals the amount of energy the ILPD emits in one second.

Armed with that information we use the normal momentum formula (p = m*v) to figure out what our REALLY big thing's velocity would be if it had that much momentum.

Then once we get that velocity number we divide it by seconds to get the change in velocity per second also known as the object's acceleration.

So if we were to simply this method into one equation it would be, ((E/c)/m)/s = v.

Alright lets put a number in there that would even make ICS wankers wet themselves, the gold standard of BIGGATONS the Yottaton (4.184 × 10³³ joules) and see what kind of acceleration we will get out of our body.

Lets pick Venus for this because it gets overlooked as a perfectly reasonable planet quite a lot.

Mass of Venus = 4.86732e24 kilograms

((1 Yt/c)/Venus)/s = 2.867 m/s² or 292 milligravites.

You can accelerate Venus with a laser powerful enough to destroy it 10 times over in a second and it accelerates at ~.3 g.

While this ~.3g is perfectly fine and would let you collide give the Earth a big ol' wallop in a day or two a yottaton/second laser is not exactly a piece of tech most people have laying around in their backyards.

Using a "reasonable" (reasonable as in, reasonable with 10-20 years of R&D) amount of energy like a gigawatt for example gets you numbers more like 6.85*10^-25 m/s² (well exactly that number but that is besides the point).

Fun fact: starting from a velocity of zero it would take 54,183 years for an object to move a single meter at 6.85*10^-25 m/s² and it would have a velocity of ~1 picometer per second.

So in the vast majority of cases if your ILPD can actually accelerate the REALLY big thing a meaningful amount before the sun it is orbiting expands and eats it in a few billion years you would be better off building two and sticking it in space with one end pointed at the REALLY big thing and the other pointed in the opposite direction so your magic death ray does not move (always remember Newtons 3rd law when you are doing stuff like this) then fry the REALLY big thing with the "rocket exhaust".

Now we are not quite done with this REALLY big thing smashing other REALLY big thing business but these problems did not really fit in a convenient manor. So here are some additional miscellaneous problems.

1. Most REALLY big things spin

Without putting in a shitload of extra work these rockets will be stationary facilities. They will only have brief portions of the day in which they can thrust at a good angle.

Any even slight off axis thrust will greatly reduce efficiency.

Part of the premise of a Hohmann Transfer is that the burn happens instantly. So by taking any amount of time greater than zero to burn through your fuel will increase inefficiency.

Seriously Hohmann Transfer's are the MINIMUM amount of delta v needed to make the orbital change. They will never be the actual delta v of the orbital change.

2. Atmospheres

I mentioned this last time ANY kind of rocket that shoots mass out the back is not going to work effectively in an atmosphere.

The Exhaust needs to have at least escape velocity in order to actually move the REALLY big thing anywhere but having an atmosphere would just trap the rocket exhaust effectively reducing it's Isp to 0.

Light Pressure Drives are not immune to this but they are much better at dealing with an atmosphere than pretty much any other rocket. The specific wavelength they are using also matters and the most effective wave length will depend on the atmosphere.

For example on Earth a blue laser will work better than a red laser but both will work better than a UV laser which could easily be losing 70% efficiency due to it being absorbed in the atmosphere.

In many cases removing the atmosphere would be your first step when trying to destroy a REALLY big thing by moving it.

But it is actually pretty hard to get rid of the atmosphere.

It takes around 77 Pt of energy to make Earth's atmosphere go away.

The problem with that is the oceans would then start boiling due to the low pressure and create a water based atmosphere.

The next step takes around 24 Exatons to deal with all the water. So do realize that many REALLY big things "atmosphere" is very well protected against people trying to remove it.

If you have access to soft sci-fi space magic you can use put your rockets on a large moon and use the moon's gravity to pull the REALLY big thing where you want it to go completely avoiding the atmosphere issue.

Though keep in mind this will have a greater minimum energy than just moving the REALLY big thing. This also requires extremely high amounts of thrust which might be better spent destroying the REALLY big thing in a more conventional manner.

But if you are stuck with high thrust, high efficiency (greater than the ILPD) reactionless drives and have the meta-materials to stop the drive from punching a hole through the moon then go for it.

Just make sure to keep the moon out of the Roche limit or your plan won't work very well.

3. Gravity

As before mentioned, the exhaust velocity of your rocket needs to greater than the escape velocity or else the exhaust will just eventually fall back to the REALLY Big thing.

To convert between Isp and exhaust velocity is pretty simple (Isp = EV/9.8).

So our Shuttle Main Engine with it's exhaust velocity of ~4414.5 will not cut it when trying to move Earth even if the Earth lacked any kind of atmosphere due to the Earth's 11,200 m/s escape velocity.

Just having exhaust velocity greater than escape velocity will not put you in the clear. The gravity of the REALLY big thing will actually lower the rocket's exhaust velocity.

The only way to find out exactly how much this will affect the exhaust velocity is through calculus and hill climbing so that is a bit beyond the scope of this post.

Realize that these are just some of the larger issues you will run into when trying to destroy a REALLY big thing by moving it somewhere else. There is likely a lot of additional problems that I don't know about because I am not an expert in any field of engineering nor rocket science.

So how else can we "destroy" a REALLY big thing by moving it?

I know, you can try building a giant accelerator and hurl chunks of it into space at escape velocity. This conveniently avoids the spinning problem mentioned prior because you don't really care which direction the stuff ends up flying.

The math for the minimum energy goes away from the Hohmann Transfers and back to the GBE of the REALLY big thing.

The first problem you will run into once again is time. If you hurled 1,000 metric tons of material away from the planet every second it would take 1.89*10¹¹ years to "destroy" the planet. Which is around 10 times longer than approximate current age of the universe.

The Sun would eat your silly contraption long before you even got a tenth of the way through.

Alright lets say we solve that problem.

Now we need a way of powering this system that can throw billions/trillions of tons of material at 11 kps. This would be taking at a minimum from 6.05*10¹⁹ to 6.05*10²¹ watts (14 Gt/s to 14 Tt/s) and it would still take millions of years.

You can imagine finding a way to power something that requires more energy than a simultaneous detonation of every single nuclear weapon on Earth every second is fairly hard to do.

Ok lets say we solve that.

Now you need to build a space elevator that can withstand the stupendous forces involved in accelerating billions/trillions of tons of material per second into space.

Either that or you build thousands to millions of space elevators that can put thousands of tons of material out of them per second.

Even in the best cases the elevator will be supporting >7000 loads of material (where a load of material is the mass the accelerator is outputting per second) for a GEO sync elevator.

So even ignoring the mass of the space elevator and using 1000 ton loads they will be supporting 7 million tons of material. Which of course is accelerating away from the Earth at a high enough rate it will reach escape velocity so it's weight will be around 2.5 times that of a resting mass on Earth.

The only other method I know of involving movement is spinning the planet fast enough the angular momentum overcomes it's gravitational binding energy.

But this is not a shortcut in terms of energy thus actually ends up being similar to the space elevator problem in that respect.

It does have a few new unique problems like keeping whatever apparatus is that is causing the REALLY big thing to start spinning super fast from being destroyed by the hypervelocity sand storm that is the ex-crust of the REALLY big thing.

I hope I did not forget anything.

TL;DR: Good luck, you are going to need it.

If you have any questions feel free to ask.