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Hey diddle diddle, that cow’s gonna have a bad day

February 11, 2015

Hey diddle diddle,
The Cat and the fiddle,
The Cow jumped over the moon.

The short answer is that a cow jumping fast enough to escape Earth’s orbit, let alone getting to the moon, would explode in a huge plume of fire and ash.

The escape velocity of Earth from sea level is really fast (11.2 km/s). Rockets are able to go to space without burning up because they continue to apply force all the way up, rather than releasing it all at once and coasting the rest of the way. But a jump doesn’t work like that. Once you jump, that’s it for vertical force. If you are going to go to space with a jump, you have to have sufficient kinetic energy the second you leave the ground to get you all the way there.

KE = (1/2) * mass * velocity^2

According to a Google search, a cow weighs about 600 kg.

(1/2) * (600) * (11,200)^2 = 37,632,000,000 Joules, or 37.6 GJ.

Given that insane speed in a normal Earth atmosphere, I’m just going to assume all of the kinetic energy is converted to thermal energy by friction. A cow is not going to be able to hold together under the force from the air resistance it would encounter at that speed. It would quickly break apart and the surface area would increase to the point where all that speed would quickly convert to heat.

The specific heat of beef is 3.5 kJ/kg C, and I’m going to assume that that’s pretty close to the specific heat of the full cow.

3.5/600 = .005833 kJ per degree C that the cow increases in temperature.
37,632,000 kJ * 0.005833 = 219,507 C change in temperature.

So, it’s hard to get a mental handle on just how overcooked that beef would be. The surface of the Sun is a measly 6,000 K, which isn’t even close to our poor bovine friend. Lightning is a bit closer at 30,000 K, but still you’re off by a factor of 7. Fortunately, it would be cool enough that our hapless cow wouldn’t set off a fusion reaction of the nitrogen in the atmosphere.

Basically, the cow’s better off staying on Earth.

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