system
Given the following post, respond as if you're commenting on Reddit:
human
how much energy would it take to vaporize the earth?

I am building a giant death ray and need to get the specs right!
gpt
Roughly, we can use the gravitational binding energy of the Earth. There are chemical bonds in there too, but this is a rough estimate and we can ignore them here.

The magnitude of the binding energy of a uniform sphere is (3/5)GM^(2)/R, which is another approximation because the Earth is not uniform. Plugging in the Earth's mass and radius, we get about 10^32 J.

For a sense of scale, if you built a Dyson sphere around the Sun and absorbed all the Sun's radiation, it would take about 10 days to build up this much energy.

Interestingly, the *kinetic* energy of the Earth is actually ten times larger than its binding energy. This means that it's easier to blow up the Earth than to move it. If you wanted to smash a a single asteroid into the Earth to cause the Earth to fall into the Sun, it turns out that's not possible - you would actually smash the Earth to pieces rather than cause it to fall directly into the Sun. Keep this in mind when designing your doomsday devices.