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Boom!!

8 Nov 2002

A comparison between an asteroidal or cometary body impacting the Earth and a small amount of antimatter exploding. This particular investigation was inspired in part by Peter Hamilton's The Night's Dawn trilogy and by the increasing media coverage concerning the threat of Near Earth Objects.

• 100 meter diameter rock, density 1.0 kg/L = 1000 kg/m^3  I'm assuming a density equivalent to water for simplicity's sake.  Densities of asteroidal and/or cometary bodies are theorized to vary quite widely depending on their make up.  Both over and under 1.0 kg/L.
• Impact velocity: Minimum = Earth escape velocity = 11.2 km/sec
• (Cometary) Maximum = sun-centered parabolic orbital velocity (at Earth orbit) + Earth orbital velocity = 71.8 km/sec
• e = 1/2 mv^2
• m = 4/3 Pi r^3 * 1000 kg/m^3 = 523.6e6 kg
• e_min = 0.5 * 523.6e6 * 11200^2 = 32.8e15 J
• e_max = 0.5 * 523.6e6 * 71800^2 = 1.35e18 J
• 4.18e15 J = 1 MT equivalent explosive yield
• e_min = 7.85 Megatons
• e_max = 323.0 Megatons !!!!!
• e_typical (20 km/s) = 25 Megatons  

For comparison, the largest nuclear device ever set off was approximately 60 Megatons.

This is an interesting thing to look at because if you do the same calculation with a 10 m diameter rock at a reasonable approach speed of 40 km/sec you get an energy release equivalent to 100 kilotons of TNT.  That's five times the power of the Hiroshima bomb. Doesn't it worry you that a paltry 10 m rock can unleash that much destruction over some part of the Earth? Read Rain of Iron and Ice to learn more.

More esoteric matters:

• 1 kg of antimatter, total mass-energy conversion
• e = mc^2
• e = 1 * (300e6 m/s)^2 = 90e15 J
• 4.18e15 J = 1 MT equivalent explosive yield
• 90e15 J = 21.5 Megatons

Wow. That's a hell of a lot. The character Kingsley Pryor in The Naked God who unleashed an antimatter detonation on the Avon asteroid and it's surrounding environs couldn't have been carrying much in his torso. Let's say he had a quarter of a kilo inside. At a distance of 23 km, that equates to an energy density of 13.5 MJ/m^2. If we assume a blast duration of 10 microseconds, that gives us an intensity of 1.35 TW/m^2 (1.35e12 W/m^2). That's rather a large flux. Thankfully it only lasts the 10 µs.

We must also be concerned with the potential mass of antihydrogen that was lodged in Pritchard's torso. If we assume that it is normal solid diatomic hydrogen (-262° C), than it has a density of 0.088 g/cm^3. This leads to a volume of 2.84 L for a mass of 0.25 kg. I think that would be obvious. If we assume solid diatomic tritium (density = 0.31 g/cm^3), the volume requirement drops to 0.81 L which seems much more concealable. If we strive for true esotericsm and specify metallic hydrogen (which I don't believe is what Peter F. Hamilton was thinking when he wrote the scene), we find a volume of 0.284 L, which is eminently concealable. I think we'll stick with an assumption of 0.25 kg of solid tritium.

Also from The Night's Dawn series: Mr. Hamilton continuously talks of the beauty of Jupiter as viewed from the habitats. For that matter, Charles Sheffield, Arthur C. Clarke, and many others have glorified the view of Jupiter from someplace in orbit about it. But is it really that spectacular? At least, is it quite as spectacular as they write about? Let's see...

• Diameter of Jupiter = 142,984 km
• Orbital radius of Io = 422,000 km (center to center distance)
• Orbital radius of Hamiltonian Habitat = 550,000 km
• Orbital radius of Europa = 671,000 km
• Orbital radius of Ganymede = 1,070,000 km
• Orbital radius of Callisto = 1,883,000 km
• degree of sky coverage by Jupiter at:
• Io = 19.2 degrees
• Habitat = 14.6 degrees
• Europa = 12.2 degrees
• Ganymede = 7.6 degrees
• Callisto = 4.4 degrees

By comparison, the degree of sky covered by the moon is 0.52 degrees. So, from the orbit of Io, (i.e. near the orbit of Discovery, 2001 style) Jupiter will look 40 times bigger than the full moon. Big? Definitely. Taking up a quarter or more of the sky? No.