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From: lebofsky at lpl.arizona.edu <
lebofsky_at_meteoritecentral.com>
Date: Fri, 1 Jul 2016 07:47:05 -0700 Message-ID: <5bd74a741271c7683013a70d6e2bec86.squirrel_at_webmail.lpl.arizona.edu> 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
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Received on Fri 01 Jul 2016 10:47:05 AM PDT |
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