On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection — I

Abstract

One of the methods discussed in deflecting the orbit of an Earth‐colliding asteroid is the use of nuclear explosives. In assessing its feasibility, apart from political considerations, it is important to quantify how effective it is in orbit deflection. The transfer of radiation incident at the surface is governed by a non‐linear diffusion equation. For low‐yield explosions with a slab geometry (S0≃108 kJ μs−1), the temperature at depth x and time t is well approximated by a similarity solution of the form T(x, t)=T0f(ξ), ξ=x/(T n0t)1/2, with T0 given by (S0/σ)1/4, where σ is the Stefan–Boltzmann constant, n is an index that specifies the radiation transfer and f(ξ) is the solution of a non‐linear differential equation subject to the condition f(0)=1 and limξ→∞f(ξ)=0. For high‐yield explosions (S0≃1010 kJ μs−1), numerical solutions to the non‐linear diffusion equation can be obtained. These solutions have properties similar to the case of low‐yield explosions. If the duration of the explosion is d×10−8 s, where d is close to 3, the fraction of energy absorbed by the surface is found to be 7, 12 and 23 per cent for S0=108, 109 and 1010 kJ μs−1 respectively.

On the transfer of radiation at asteroidal surfaces in relation to their orbit deflection — II

“…The first problem was discussed by Simonenko et al (1994) in an approximate way, but has been examined more closely by the present author (Yabushita 1996(Yabushita , 1998. The second problem has been discussed by a number of authors (Simonenko et al 1994;Ahrens & Harris 1994).…”

“…The equation is highly non-linear, but the solution can be obtained analytically (in the case of low incident flux) and numerically (in the case of high incident flux). Assuming that the irradiation lasts for 0.03 s, the energy absorbed by the surface lies between 7 per cent (for low incident flux) and 23 per cent (for high incident flux) (Yabushita 1998).…”

“…When the surface is heated by the radiation, the temperature profile is of the form shown in fig. 2 of Yabushita (1998). Depending on the radiation flux at the surface, the duration of irradiation of 0.03 s corresponds to a dimensionless time of 30, 63 and 133 for S 0 ¼ 10 10 , 10 9 and 10 8 kJ cm ¹2 s ¹1 respectively.…”