Hi Rob: Did you remember an object is only illuminated by the Sun half the time?
Larry > Hi All, > > Playing Devil's Advocate, I decided to try coming up with a scenario that > attempts to maximize the > thermal equilibrium temperature of a chondritic meteoroid just prior to > encountering the earth's > atmosphere. The typical formula for computing the thermal equilibrium > temperature for an > object without an atmosphere is: > > Te = [S0 * (1-A) / (4*epsilon*sigma)] ^ (1/4) > > where the body is assumed to be spherical (the source of the 4 in the > denominator), S0 is the > solar constant (mean value 1361 W/m^2), A is the bolometric Bond albedo, > epsilon is the > meteoroid's emissivity, and sigma is the Stefan-Boltzmann constant (5.670 > x 10^-8 W/m^2-K^-4). > A, in turn, can be estimated from the following equation: > > A ~= q * pv > > where q is the phase integral and pv is the visible albedo. Using Bowell's > H, G magnitude system, > we can compute q from: > > q = 0.290 + .684*G > > The commonly used value for the slope parameter, G, is 0.15, in which > case: > > q = 0.393 > A = 0.393 * pv > > For very dark asteroids (e.g. Trojan asteroids, Hildas, Cybeles), the > albedo can be 5% or lower. > However, most NEOs have semi-major axes less than 3 a.u. and albedos > averaging closer > to 20%. > > The final missing value is the emissivity. For regolith, a range of > 0.9-0.95 is often mentioned. > However, emissivity and albedo work hand-in-hand (epsilon + pv ~= 1). So > if we're going > to choose an emissivity of 0.9, we should set the albedo, pv, to 10%. > > So what is a typical equilibrium temperature for a spherical NEO with 10% > albedo, 0.9 > emissivity, 1 a.u. from the sun? > > A = .393*10% = .0393 > > Te = [1361 * (1-.0393) / (4*0.9*5.67 x 10^-8)]^0.25 = 282.9 K or about > 49.6 F > > So, cool, but certainly not freezing. How can we get a warmer answer? One > way is to pick the > time of year when the earth is closest to the sun (early January) and the > solar constant is > higher: about 1414 W/m^2. This raises the temperature in the above > example to 285.6 K, > or 54.4 F. Still not warm, but warmer. Lowering the emissivity will help, > too. Let the albedo > increase to 20%, and set the emissivity to 0.8. With the perihelion solar > constant, the > equilibrium temperature is now up to 291.1 K (64.3 F). Lowering the > emissivity further > is probably not realistic for most earth-crossing asteroids, so we're at > the limit of what > we can achieve via S0 and emissivity. > > However, there *is* a way to get a big increase in the equilibrium > temperature which > I'll cover in the next installment. --Rob > ______________________________________________ > > Visit our Facebook page https://www.facebook.com/meteoritecentral and the > Archives at http://www.meteorite-list-archives.com > Meteorite-list mailing list > Meteorite-list@meteoritecentral.com > https://pairlist3.pair.net/mailman/listinfo/meteorite-list > ______________________________________________ Visit our Facebook page https://www.facebook.com/meteoritecentral and the Archives at http://www.meteorite-list-archives.com Meteorite-list mailing list Meteorite-list@meteoritecentral.com https://pairlist3.pair.net/mailman/listinfo/meteorite-list
