I can't tell if this is sacarstic or not but I decided to do the math.

Mass of earth: 5.972 × 10^24 kg

Launch capacity per year: 15,500 tons

Years to get rid of earth: 385,290,322,580,645,161 years.

I think if we every have to worry about this it becomes more a question of where are we going? And do we have enough carbon to cycle for fuel to do this.

I didn't account for the decreased gravity over time as you chip away at the planet. Woops!

Over that time span you should probably account for the 48.5 tons of material that falls to Earth annually as well.

Gravitational binding energy of Earth is about 10^32 joules, so you'd need to pump that much in to dismantle Earth. The entire solar output reaching Earth is about 10^17 Watts, so it would take 10^8 years to dismantle Earth without leaving it if you could capture every Joules as it entered the atmosphere

On the other hand if you could capture the Sun's entire output - not just that arriving at Earth - you'd have enough energy to do it in a week or two.

Wouldn't the reduced mass of the Earth's sphere of influence be reduced over time, thereby reducing the energy required to launch subsequent payloads?

Yes, there's all sorts of odd things that would happen with rotational energy too, hence you don't need as much as if you calculated it based on lifting 1kg at a time from the earth's surface. You'd need about 10^32 joules. If you didn't account for that you'd need about twice as much energy, which is about 10^32 joules.

In theory you could simply vaporize the earth with antimatter, converting it to energy, rather than trying to disasemble it. That would produce far more energy than the gravitational binding energy, so unless you happen to have a planet sized lump of antimatter around you'd have to generate it with more than 10^32 joules.

Yes

Also worth noting that the Earth receives about 43 tons of new mass every day, mostly from meteorites. Coincidentally, this works out to 15,695 tons of new mass every year.

Are we going to run out of some chemical elements?

You might be interested in https://what-if.xkcd.com/7/

> Is there enough energy to move the entire current human population off-planet?