How Much Energy Would It Take to Blow Earth to Smithereens?
A mathematical formula shows what would be needed to reduce the planet to cosmic dust
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An apocalypse needs a lot or just a little energy—depending on what you compare it with. But what’s really exciting is the math behind this ultimate destructive event.
If you want to destroy Earth, you have many options—at least when it comes to the extinction of humanity. Nuclear war, climate crisis or species extinction: over the course of human history, we have unfortunately found plenty of ways to destroy ourselves. But the planet doesn’t really care.
To actually destroy the planet, you would have to work a little harder. A collision with a large asteroid, for example, could make it uninhabitable and melt Earth’s crust, but even that wouldn’t destroy the Earth. If you wanted to pulverize it completely so that nothing remained, you would have to use the following formula:
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EG = 3GM2⁄5R
This equation describes gravitational binding energy. It corresponds to the energy required if the components of a body held together by gravitational force are to be moved infinitely far apart. The formula applies to a homogeneous sphere. Although Earth is not a perfect homogeneous sphere, the equation suffices to at least calculate the correct order of magnitude of its binding energy. If you do this, you get a result of around 200 nonillion joules (two followed by 32 zeros). This corresponds roughly to the energy that would be obtained if the mass of the entire asteroid Eros (which has an average diameter of almost 17 kilometers) could be converted directly into energy. On the other hand, it corresponds to…
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