Science of Anime: Destroying a Planet

There are few things that signify overkill like an Earth-shattering kaboom. A lot has been written about how much energy it takes to destroy a planet. But most of those discussions involve things like the Death Star, or how fast an asteroid would have to be moving. What about when your planet-killer is smaller; like a person?

In Dragon Ball Z, Vegeta unleashes a blast capable of destroying the Earth during his fight with Goku. Then everyone’s power levels keep going up at a rapid pace throughout the Namek/Frieza saga. Frieza himself can casually destroy planets in his least powerful form, and in the Cell saga everyone has to avoid aiming down to avoid accidentally destroying Earth.

Ki blasts are a fantasy element in the first place, but that doesn’t mean they should violate conservation of energy, particularly since fighters do have limited energy. So, ignoring the fact that it’s an impossible ability and any concern over power, can a person have that much energy? (The distinction between power and energy is relevant here. Power is the rate at which energy is applied. That’s why turning up a screen’s brightness (a difference in power) uses up a battery (a source of energy) faster.)

Well, not even a big eater like Goku could possibly get that kind of energy from food; the Calories of his own weight in pure sugar would still be pitiful compared even to any conventional explosive. A single Senzu bean is supposed to be equal to ten days’ worth of food, but even a person’s weight in those wouldn’t have enough energy to equal a city-destroying explosion, let along a planet-destroying one.

So even though we know that eating can restore someone’s strength to use ki, the energy involved can’t come only from Calories. But it is consistently implied to be the person’s strength; except for the Spirit Bomb (Genki Dama) technique, DBZ’s characters are not channeling some kind of energy from outside of themselves.

Here is where e=mc2 comes in. If mass is converted to energy, the energy in ergs is equal to the mass in grams multiplied by the square of the speed of light in centimeters per second. Rounding off, c is 30,000,000,000 cm/s (or 3 x 1010 )and squared, that is 9 x 1020. Most DBZ characters are under 100kg, but let’s use that as a round number; 100,000g. So the energy equivalent of a 100kg person is 9 x 1025 ergs.

But the energy to destroy the Earth is 2.24 x 1039 ergs. Even to destroy the moon, something that Roshi did as early as the second tournament, takes 1.24 x 1036 ergs. (I got those figures from here. A Joule is equal to 10,000 ergs.)

So not even total mass-energy conversion (which would obviously be very fatal) would be anywhere near enough for a person (or person-sized weapon, for that matter) to destroy a planet. So, probably fortunately, this one is impossible on multiple levels.

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