- #1
TheMan112
- 43
- 1
The Frost Line is the distance from the Sun where the radiation from the Sun becomes too dim to make ice sublimate into vapour. See e.g. http://en.wikipedia.org/wiki/Frost_line_%28astrophysics%29" . It is important because it explains why only terrestrial planets exist inside this boundary.
I'm curious as to how the frost line is calculated though. The Wikipedia page gives a value of 2.7 AU and other sources give similar numbers, but I haven't yet seen a detailed calculation.
I imagine the temperature of an icy particle is the result of a blackbody equivalence equation, i.e:
[tex]\sigma T_{sun}^4 \left( \frac{R_{sun}}{r} \right)^2 = \sigma T_{particle}^4 (1-a)[/tex]
So by solving for r and using the sublimation temperature of water in vacuum (150 K) for Tparticle, the temperature could be found. However, the albedo of the icy particle a is unknown.
If I use a = 0 (perfect black-body) I end up at r = 2.92 AU, which is close, but not very realistic. If I use an albedo like that of the icy bodies of the solar system, a = 0.7 (Europa), I end up with a frost line at about 1.5 AU.
So, what's up with that? How is the 2.7 AU value derived?
Regards
TheMan112
Edit: The luminosity the Sun [tex]\sigma T_{sun}^4[/tex] is multiplied with a dimming factor of 0.6, as the early Sun was 40% dimmer than it is today. I want the frost line at the formation of the solar system in order to investigate it's relevance to planet formation.
I'm curious as to how the frost line is calculated though. The Wikipedia page gives a value of 2.7 AU and other sources give similar numbers, but I haven't yet seen a detailed calculation.
I imagine the temperature of an icy particle is the result of a blackbody equivalence equation, i.e:
[tex]\sigma T_{sun}^4 \left( \frac{R_{sun}}{r} \right)^2 = \sigma T_{particle}^4 (1-a)[/tex]
So by solving for r and using the sublimation temperature of water in vacuum (150 K) for Tparticle, the temperature could be found. However, the albedo of the icy particle a is unknown.
If I use a = 0 (perfect black-body) I end up at r = 2.92 AU, which is close, but not very realistic. If I use an albedo like that of the icy bodies of the solar system, a = 0.7 (Europa), I end up with a frost line at about 1.5 AU.
So, what's up with that? How is the 2.7 AU value derived?
Regards
TheMan112
Edit: The luminosity the Sun [tex]\sigma T_{sun}^4[/tex] is multiplied with a dimming factor of 0.6, as the early Sun was 40% dimmer than it is today. I want the frost line at the formation of the solar system in order to investigate it's relevance to planet formation.
Last edited by a moderator: