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Post by urania93 on Nov 30, 2019 5:00:08 GMT -5
I'm still half asleep, but I have the feeling that this could actually be a little move complicated...
I would actually start from a energy balance between incoming and emitted energy:
- the incoming energy is basically the sun radiation projected on a sphere. Considering an incoming flux of Fe (at the equator, where in your model the incoming radiation is perpendicular), the relation between the flux and the latitude should look like F(θ) = Fe cosθ. This could be corrected for the surface albedo etc...
- in first approximation, the emitted energy should follow a relation like the Stefan-Boltzmann law, according to which:
q = σT4(θ)
where q is the emittance over all the wavelengths (measured in W/m2, as the flux used above), and σ is a constant. I added that, somehow in this model, T should be dependent on θ.
Even by adding the relation between total energy balance and temperature (introducing stuff like the specific heat etc...), I have the impression that the dependence of T on θ in the previous formula can complicate the situation. I have to think about it...
Also, I'm not sure that by removing the atmosphere the relation between temperature and latitude would remain the same, so it's not said that the right solution of this problem should replicate what we observe on the earth.
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Post by srfoskey on Dec 4, 2019 19:10:33 GMT -5
Given Earth's tilt, the greatest change in irradiance is in the upper-mid latitudes, but if Earth had no tilt, I could imagine the greatest change in irradiance being at the poles.
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Post by 🖕🏿Mörön🖕🏿 on Dec 4, 2019 21:24:11 GMT -5
Just get Universe Sandbox ² on Steam bro.
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Post by Steelernation on Dec 5, 2019 15:24:09 GMT -5
Cos + theta = math = I have no fucking clue how to answer this thread.
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Post by AJ1013 on Dec 5, 2019 15:35:21 GMT -5
Cos + theta = math = I have no fucking clue how to answer this thread. Pretty simple math lol. |
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Post by nei on Dec 5, 2019 16:03:00 GMT -5
there's no way to determine the temperature without:
1) planetary albedo
2) surface heat transport
a water world would have less seasons and transport heat more than a desert planet. Of course a water world would evaporate some water and so would have an atmosphere. Maybe a good way to start would be to assume zero equator to pole heat transport and then see what to do next.
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Post by nei on Dec 6, 2019 18:35:11 GMT -5
Looked it up from an online textbook I had downloaded a while ago, and realized it's not particularly complicated with 0 tilt and 0 heat transport and 0 atmosphere. If there's no heat transport, only factor affecting temperature is local radiation absorbed. Energy going out is 𝜎T 4, T is temperature, set that equal to radiation coming in and you get.  𝜎 is the stefan-boltzman constant. L is the energy the sun’s rays carry, which for earth is about 1368 Watts per square meter, 𝛳 is latitude I made a diagram that hopefully helps.  Arrows represent the sun’s rays, circle represents a slice of the earth at the same latitude. Sun’s rays are coming from a distance much, much further than the diameter of the earth so they're practically parallel and pass through an area equal to a cross-section of the length of the diameter (dashed line), the radiation is spread out over the circumference or 𝜋 * the diameter. That’s where the pi 𝜋 the denominator comes from. Higher latitude means the sun’s rays come at an angle and spread out over a larger area, so the amount of energy absorbed is reduced vs the equator cos(𝛳). This silly formula give 23°C at the equator, -24°C at 60° latitude and absolute zero at the poles (since there’s no sunlight absorbed at a sun angle of 0° and no heat transported). Author of that article labeled that the constant in front of L/𝜎 the "flux factor" or the fraction of sunlight on average absorbed vs the sun directly overhead. Average over one 24 hours on the equinox at the equator is a factor of cos(0)/𝜋 or just over 0.3. Averaging over the entire year for different earth's tilts:  |
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Post by Lommaren on Dec 6, 2019 18:50:00 GMT -5
Looked it up from an online textbook I had downloaded a while ago, and realized it's not particularly complicated with 0 tilt and 0 heat transport and 0 atmosphere. If there's no heat transport, only factor affecting temperature is local radiation absorbed. Energy going out is 𝜎T 4, T is temperature, set that equal to radiation coming in and you get. Okay, if Nei doesn't win the "most knowledgeable poster" award after this thread, we might as well give up on humanity 
Either way, the heat transport factor obviously is essential. Also, a desert planet would have clear skies because there's no water vapour to form clouds with, somewhat resembling the shocking Mars diurnals seen in the Gale Crater.
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Post by urania93 on Dec 7, 2019 4:33:09 GMT -5
Basically I just had to set an equilibrium between the two formulas I wrote above, I'm really disappointed with myself because I was thinking to much more complicated stuff... Anyway, what's the title of that textbook? I'm curious to read also the rest now. Anyway, this purely radiative model is kinda funny, in particular for the result obtained for the poles... Either way, the heat transport factor obviously is essential. Also, a desert planet would have clear skies because there's no water vapour to form clouds with, somewhat resembling the shocking Mars diurnals seen in the Gale Crater.
This model is even more extreme, because we are considering no atmosphere at all (= complete vacuum above the ground). So that the temperature is a property of matter, and not of vacuum, the temperature in this case would be referred to the ground itself (and not to the temp of the atmosphere just above it, as we are used to see in weather measurements), and the only non-radiative heat transport possible would be heat conduction through the ground itself. This model is actually quite extreme in many senses... |
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Post by nei on Dec 7, 2019 9:31:26 GMT -5
Basically I just had to set an equilibrium between the two formulas I wrote above, I'm really disappointed with myself because I was thinking to much more complicated stuff... Anyway, what's the title of that textbook? I'm curious to read also the rest now. Anyway, this purely radiative model is kinda funny, in particular for the result obtained for the poles... yes, it's obviously stupidly simplified, but it's a good start. Add seasons, add heat transport, add a real atmosphere with clouds and a greenhouse efffect and you got yourself a planet…don't feel too bad, I didn't think of it until I looked it up, vaguely imagined something more complicated though I don't remember radiation balance without a bit of a refresher. Book is Principles of Planetary Climate by Pierrhumbert. I downloaded a draft of the book which was floating on the internet 7 years ago, and got taken down, saved it on my google drive, could link it to you if you're interested. It's a very good book about climate and the greenhouse effect in general, far better and much more convincing than those silly videos people post. Lot of work to go through, if AJ1013 wants to do more vector calc for fun I strongly suggest it for him. Here's a short paper by him that I think posted by on the climate change thread that's a good summary of the greenhouse effect geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdfEither way, the heat transport factor obviously is essential. Also, a desert planet would have clear skies because there's no water vapour to form clouds with, somewhat resembling the shocking Mars diurnals seen in the Gale Crater.
This model is even more extreme, because we are considering no atmosphere at all (= complete vacuum above the ground). So that the temperature is a property of matter, and not of vacuum, the temperature in this case would be referred to the ground itself (and not to the temp of the atmosphere just above it, as we are used to see in weather measurements), and the only non-radiative heat transport possible would be heat conduction through the ground itself. This model is actually quite extreme in many senses...[/quote] It's not a terrible model for the model which has no ocean or almost no atmosphere. So heat transport is small. Worse for Mars but a bit closer as Lommaren mentioned |
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Post by urania93 on Dec 7, 2019 14:56:00 GMT -5
yes, it's obviously stupidly simplified, but it's a good start. Add seasons, add heat transport, add a real atmosphere with clouds and a greenhouse efffect and you got yourself a planet…don't feel too bad, I didn't think of it until I looked it up, vaguely imagined something more complicated though I don't remember radiation balance without a bit of a refresher. Book is Principles of Planetary Climate by Pierrhumbert. I downloaded a draft of the book which was floating on the internet 7 years ago, and got taken down, saved it on my google drive, could link it to you if you're interested. It's a very good book about climate and the greenhouse effect in general, far better and much more convincing than those silly videos people post. Lot of work to go through, if AJ1013 wants to do more vector calc for fun I strongly suggest it for him. Here's a short paper by him that I think posted by on the climate change thread that's a good summary of the greenhouse effect geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdfFound the book by myself, thanks. Soon or later I will try to read it better. |
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