Asteroid Destruction Calculator

Written: 2002-06-03
Last Revised: 2002-06-04

This form will calculate energy requirements for various methods of destroying asteroids. Please note that with very large asteroids, gravity can become significant, thus reducing the usefulness of this data. For an Earth-sized planetary body, gravitational binding energy handily exceeds both fragmentation and vapourization energy.

Input Values

Diameter (metres)

Calculated Values

Volume (m³)		Fragmentation Energy (igneous rock)
	Hard Granite	Nickel-Iron	Ice
Mass (tons)
Melt Energy
Vapourization Energy
Cratering Energy
Gravitational Binding Energy

Notes

Fragmentation energy is the energy required to shatter the asteroid so that no individual fragment exceeds 10 m in diameter. From "Deflection and Fragmentation of Near Earth Asteroids" by T.J. Ahrens and A.W. Harris, it is projected that a 1 kiloton buried explosive will fragment a 100m diameter asteroid (based on experiments with terrestrial igneous rock), a 1 megaton explosive will fragment a 1km diameter asteroid, and a 1 gigaton explosive will fragment a 10km diameter asteroid. Using these figures as a basis, we can produce an approximation Y = (d/100)³, where d is diameter in metres and Y is yield in kilotons. Note that a soft rocky asteroid can actually require as much as three times more energy, because it will tend to break up into larger pieces. Hard rock figures are used in order to be more conservative, and also because reduction into such small fragments is not strictly necessary for our purposes. These figures are good general-use figures, when you're dealing with rocky asteroids and you don't have enough information to categorize them as granite or nickel-iron.
Granite is not silicon, but the thermophysical properties for elemental silicon are much more readily available than those of granite, so I used those figures for the melt and vapourization energies (the specific heat for granite is 800 J/kgK, which is only 13% higher than the specific heat for silicon, but I haven't been able to locate a source for the latent heat of fusion). The energy required to melt silicon (heat it from 150K to melting point and then add latent heat of fusion) is roughly 2.65 MJ/kg. The energy required to melt and then vapourize it is roughly 13.23 MJ/kg. Density is roughly 2330 kg/m³. If any readers have access to more accurate thermophysical property data on granite, I would appreciate the input.
Nickel-iron asteroids are not pure iron, but the thermophysical properties of nickel are sufficiently close to those of iron that the use of elemental iron is a reasonable approximation for melt and vapourization energies. The energy required to melt iron (heat it from 150K to melting point and then add latent heat of fusion) is roughly 1.28 MJ/kg. The energy required to melt and then vapourize it is roughly 7.63 MJ/kg. Density is roughly 7870 kg/m³.
Ice asteroids can be assumed to be fairly ordinary, so figures for terrestrial ice are used for melt and vapourization energies. The energy required to melt ice (heat it from 150K to melting point and then add latent heat of fusion) is roughly 0.59 MJ/kg. The energy required to melt and then vapourize it is roughly 2.84 MJ/kg. Density is roughly 900 kg/m³.
Cratering energy is the energy required to blast out a crater of depth equal to the radius of the asteroid, which should easily result in its catastrophic disruption. It is calculated based on bulk property data collated from material testing experiments, and extrapolated using numerical modelling techniques based on terrestrial cratering experiments. From "Energy Coupling to Asteroids and Comets", by B.P. Shafer et al., the thermophysical properties for hard granite asteroids are density = 2650 kg/m³, UTS = 374 MPa, and cratering depth = 88.4 m/kT^1/3. From the same source, the thermophysical properties for nickel-iron asteroids are density = 7856 kg/m³, UTS = 600 MPa, and cratering depth = 29.8 m/kT^1/3. And finally, the thermophysical properties for ice asteroids are density = 917 kg/m³, UTS = 17.5 MPa, and cratering depth = 138.4 m/kT^1/3. Note that soft shale has a cratering depth equal to that of granite, so the granite cratering figures can be used for silicaceous asteroids in general.