Reply-To: MA Lloyd On Mon, 6 May 1996, Stan Berry wrote: > I like Sean's approach. Gravitational forces would dominate, > and this give a good benchmark number, but it is a slight underestimate > because there is also a tiny bit of tensile strength for the crust. > However: > * Even a few percent (or less) of Sean's number would crack the planet > and send large chunks flying. Nope, you need somewhere around 10% to crack the planet. Lets cover this in a little detail (Sean, how about dropping this in the archive?): IMPORTANT CONSTANTS Me (mass of the Earth) 5.97 x 10^27 grams Ml (mass of the Lithosphere) 2.37 x 10^25 grams Mw (mass of water in the lithosphere) 2.6 x 10^24 grams Mo (mass of water in oceans) 1.66 x 10^24 grams Ma (mass of atmosphere) 5.14 x 10^21 grams re (radius of the Earth) 6.37 x 10^6 meters G (Newtonian gravitation constant) 6.67 x 10^-11 Nm^2/kg^2 Eesc (current escape energy for Earth) 6.24 x 10^4 J/g c (speed of light) 3.00 x 10^8 m/s Cr (typical heat capacity of rock) 1.1 J/gK Cw (heat capacity liquid water) 4.19 J/g Tf (typical melting point of crust) 1250 K Hr (typical heat of fusion of rock) 150 J/g Hv (water vaporization (CwT+Hvap)) 2700 J/g sFe(surface energy of 95% liquid iron) 1.8 J/m^2 ENERGIES REQUIRED TO Heat the oceans to boiling (assume starting T averages 5C) Mo*Cw*(373-278) = 6.6 x 10^26 J Vaporize the oceans Mo*Hv = 4.5 x 10^27 J Dehydrate the crust Mw*Hv = 7.0 x 10^27 J Melt the (dry) crust (Cr*(Tf-278) + Hr) * Ml = 2.9 x 10^28 J Blow off the atmosphere Eesc*Ma = 3.2 x 10^26 J Blow off the oceans Eesc*Mo = 1.0 x 10^29 J Blow off the crust Eesc*Ml = 1.5 x 10^30 J Total gravitational disruption 0.6 * G*Me^2/re = 2.24 x 10^32 J Gravitation is all you really need worry about. To account for the actual non gravitational interactions, assume the planet is entirely liquid iron and compute the surface energy of breaking it into 1 mm radius spheres = 5.8 x 10^24 J In actual fact you can't 'split the Earth', its a liquid, and will deform plastically. If you could though, the required energy to separate equal sized pieces of it and put them into orbit so they do not recombine is (2^1/3)*G*Me^2/16re = 2.94 x 10^31 J. Double that if you want them to fly apart rather than orbit, and increase a little for the assumption they start as spheres in contact rather than hemispheres (do the integration yourself) APPLYING THE ENERGY Antimatter will release 2*mc^2 = 1.8 x 10^17 J/kg A relativistic rock has kinetic energy of (r-1)*m*c^2, where r is the relativistic gamma term (1/(1-(v/c)^2), so at 86.6% of the speed of light it has as much energy as if it were made of antimatter. A typical rock, or anti-rock, will mass 1.47 x 10^4 * (r^3) kg, where r is the radius of the rock in meters, so the anti-rock or .87c meteor delivers about 2.64 x 10^21 * (r^3) J.