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Forum » SpaceEngine » Mods and Addons » Calculating Star and Planet Temperatures
Calculating Star and Planet Temperatures
AmwhereDate: Tuesday, 21.08.2012, 03:36 | Message # 1
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I hope you all will understand what I mean. smile
(I was just going to PM this to SE... but it's too big!!!! :P)

I'm working on a simple program that will parse out the system export file into a report (with more random stuff, like life types, etc.) Since neither planet or star temperature is in the file, I'm trying to figure out a way to calculate them. However, I'm running into a problem.

I'm using this system for the example: RS 0-0-0-0-20656-0-0-0

So, given the temperature of 52500K, I come up with a flux of 430,775,415,000 W/m, for a total flux of 3.5836*10^33 W, or roughly 8816766 x Sol.
Here's what I calculated for the temperature of the planets using this Luminosity and a albedo of .3. (SE temp is in brackets):
1: 1971 [1975]
2: 1475 [1478]
3: 1182 [1185]
4: 1106 [1109]
5: 790 [793]

So, it seems that the planets are treating the star as if it had 8 million x Sol or so luminosity. For it's given luminosity of 133450 x Sol, I get a calculated temp of roughly 18400 K.

Am I wrong? Is SE wrong? Is the universe wrong? smile

Also, any idea about handling the planetary temperatures in multiple star systems?

[Moderator notice: Amwhere, can you please rename your post title to something more descriptive and relevant to your opening thread content.]

Done. I hope.


Edited by Amwhere - Tuesday, 21.08.2012, 18:31
 
SpaceEngineerDate: Tuesday, 21.08.2012, 21:16 | Message # 2
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Which formulas did you use?




 
AmwhereDate: Tuesday, 21.08.2012, 23:12 | Message # 3
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Luminosity from Temperature (sourced from http://bartonpaullevenson.com/Albedos.html):

Flux = (StarTemp ^ 4) * Sigma
Total Flux = Flux * StarArea

For SE's Sol (5860 K, 695999500 meter radius)
Flux = 66865817.7 W/sq m
Area (4 * Pi * r^2)= 6087342241334610000 sq meters
Total Flux = 4.0704E+026 Watts

So, for the example star (52500 K, 25729327000 m radius):
Flux = 430775415000 W/sq m
Area = 8318915580155050000000 sq m
Total Flux = 3.5836E+033 Watts

So, Example / Sol = 8.81 million.

I figured out temperature from luminosity this way (and this is where my math is a little questionable):
Total Flux = Solar Flux * Luminosity
Flux = Total Flux / area
Temperature = (Flux / Sigma) ^ .25

So, for the example:

Total Flux = 5.4319E+031 Watts
Flux = 6510833165 W/sq m
Temperature ~= 18400 K
 
paradanDate: Wednesday, 05.09.2012, 21:42 | Message # 4
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temperature can get really complex , terrain, hydro%, axil tilt, atmosphere density and composition, and rotational period all play a part .

you can get a general value, thats good enough for most things by using this formula:

T(in Kelvin) = 255 / (distance in AU / (Luminosity^0.5)^0.5)

for multiple star systems, calculate each star individually and add em together ( I think..)
of course its gonna change as the wheels go round.
 
AmwhereDate: Wednesday, 05.09.2012, 23:53 | Message # 5
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Well, I managed to get pretty gosh darn close to what calculates - and I did have to make the "wheels go round".
See:
http://amwhere.weebly.com/sol.html
http://amwhere.weebly.com/rs-8403-173-9-95333980-2.html
 
tassoDate: Tuesday, 13.08.2013, 22:24 | Message # 6
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Sorry i don't even know if this is the right place to write but pretty muche nobody talks about temperatures so..
just a question.. sorry for my bad english by the way

is it right that SE calculate the temperature (average temperature) of a planet only correlated with the SIZE of his star?
for example if the sun had a temperature of 1000k less than the right temp, would be insane to say that the earth could be colder?
so, is that possible to find a modify of the script that could set the irradiation rate of a star if you modify either the size or the surface temperature?

thank you anyway smile
 
WatsisnameDate: Wednesday, 14.08.2013, 01:13 | Message # 7
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Planetary temperature depends not on the size of the star, but instead the luminosity of the star, distance of planet, and reflectivity of the planet's surface. Luminosity in turn is a function of size and surface temperature, so the size is already included in the calculation implicitly.

You are correct that if the Sun were 1000K colder, then Earth would be colder as well. And if the sun were larger, but the same temperature, then Earth would be hotter because the luminosity and therefore amount of sunlight it receives is greater. The Earth would also be cooler if it were farther away.

If you want formula, it is
T = fourth root of L(1-A)/(16*pi*a^2*sigma), where T is temperature in Kelvin, L is the luminosity of the star in Watts (Sun's is 3.84x10^26 W), A is albedo of planet (percent of light reflected, expressed as decimal between 0 and 1), a is the distance of the planet in meters, and sigma is the Stefan-Boltzmann constant or 5.67x10^-8 W*m^-2*K^-4.

And the relation of solar luminosity to temperature and size is:
L = 4*pi*r^2*sigma*T^4, where r is the star's radius in meters. You can plug this in to the first formula if you like.

There may be other ways to express the formula and I'm not sure what SE actually uses, but this is the result of simple radiative flux balance and should give accurate results. The rest then is just the greenhouse effect of the planet's atmosphere, which SE gives separately.





 
tassoDate: Wednesday, 14.08.2013, 11:42 | Message # 8
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Thank you for the immediate answer.. smile
now i wonder how is it possible to implement this formula in Space Engine, because so far, temperature of planets simply changes just by increasing or decreasing their star size.. and also by editing a different star class dry
 
HarbingerDawnDate: Wednesday, 14.08.2013, 12:31 | Message # 9
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Quote (tasso)
now i wonder how is it possible to implement this formula in Space Engine, because so far, temperature of planets simply changes just by increasing or decreasing their star size.. and also by editing a different star class

So if you change the star's luminosity, the planet's temperature doesn't change? Maybe you should recheck that.





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tassoDate: Wednesday, 14.08.2013, 12:58 | Message # 10
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yep.. nothing change by changing luminisity
planet temp change only by
modifying distance from star
modifying star radius
instead modifying temperature of star surface, luminisity, mass etc.. nothing happen
i dunno.. i don't think i've installed SE wrong tongue
 
WatsisnameDate: Wednesday, 14.08.2013, 21:23 | Message # 11
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Okay. I don't know since I can't check right now, but from what you're saying it sounds like SE combines the two expressions I gave above, so that the temperature of the planet is determined by star's radius and temperature and distance of planet. That would be:

TP = fourth root of (RS2TS4(1-A))/(4a2)

Where TP is planet temperature
RS is star's radius
TS is star's temperature
a is planet's distance from star.

Edit: Oh, you're saying you've changed star luminosity, surface temperature, and mass, and all of those do nothing? That's definitely weird. The expression for planet temperature must depend on one of those. Radius alone isn't enough.





 
Gondor2222Date: Thursday, 15.08.2013, 00:44 | Message # 12
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Perhaps SE auto-calculates luminosity from the star's class letter+arabic numeral and radius, rather than its surface temperature and radius? I suspect this is a possibility because the class letter and arabic numeral is essentially a rounded surface temperature for the star.

Edited by Gondor2222 - Thursday, 15.08.2013, 00:45
 
WatsisnameDate: Thursday, 15.08.2013, 02:37 | Message # 13
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I think you are right, Gondor.




 
tassoDate: Thursday, 15.08.2013, 23:13 | Message # 14
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Right Gondor, in fact if i change stars classes it does change something but for istance if i have a certain star with certain measures and i edit a class like A0 II, SE generate reeally hot star who makes my planet very hot for example 850K
if i edit again my star WHITHOUT change any parameter a part from the class (for example M9 V) i'll obtain a new star who will gives my planet for example 620K or less..
but what i mean is.. class M stars have a RANGE of temperatures (and their luminosity or color also depend on them)
is it possible to create a very cold M-class star (temp range 2,000–3,700 K)? 2000K star can't heat a planet like a 3,700K star even if they stay in the same class (M)..

thank you btw for your answers cool
 
Gondor2222Date: Friday, 16.08.2013, 01:40 | Message # 15
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Quote (tasso)
is it possible to create a very cold M-class star (temp range 2,000–3,700 K)?

If I remember correctly SE supports brown dwarf stellar objects of classes L and T, bringing the main-sequence* stellar object support of SE to OBAFGKMLT.

*Can anyone tell me if it is theoretically correct to call brown dwarves "main-sequence substellar objects" because they are located on the V curve of the Hertzsprung-Russell diagram but aren't stars?
 
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