Scott Manley

Watch: How much energy does it take to blow up a planet?

This is awesome.

BEC CREW
12 JAN 2016
 

The prospect of blowing entire planets to smithereens isn't exactly pertinent for us Earthlings, but Star Wars fans will know that in three of the seven films, a device capable of such destruction makes life very difficult for the protagonists. Until we find ourselves locked in a similarly bloody battle with some kind of intergalactic enemy, we really don't need to know precisely how much power it would take to blow up an entire planet... but that doesn't make the mathematical problem-solving behind the scenario any less awesome.

 

In the video above, Scott Manley says it's actually not as hard you might think to figure out the answer, because there are already scientific papers out there that have done all the work for you.

In 2011, a paper addressed the issue by calculating the gravitational binding energy of the typical spherical planet, which involves figuring out what's called the critical escape velocity of a planet - the critical speed above which an object will escape to infinity and never fall back.

"Imagine if you grab a rock from the surface of a planet, and shoot it off at escape velocity," says Manley. "Now repeat that, bit by bit, rock by rock, and as you go on, you're actually going to need slightly less energy because as you throw bits into space, there's less mass of the planet left behind to hold them down."

Those of you with some skills in calculus will be able to add all those values up to form a relatively simple equation that states that the energy equals three-fifths of the gravitational constant, times the mass of the planet squared, and divided by the radius of the planet. Easy!

When Manley runs the particulars of Earth through this equation, he figures out that it'd take about 2.25 x 1032 joules, or 225 million trillion trillion joules. For much larger planets such as Jupiter, you're going to need about 2 x 1036 joules, which means 2 trillion trillion trillion joules of energy.

But the story doesn't end here, because if we're looking specifically at the destruction of the Earth-like planet, Alderaan, in Star Wars, the Death Star inflicts way more energy than the minimum required for massive, heart-wrenching explosions. So exactly how much energy is that?

Watch the video above by Scott Manley to see how he figures out the answer. And if that's not enough, watch him calculate the energy output of the Death Star-like super-weapon featured in The Force Awakens that uses the power of star to threaten entire solar systems across interstellar distances. Maths is just the coolest. 

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