Modeling Planetary Temperature for an Online Game Using Limited Factors

[Blissfulpain]

I'm trying to model the possble average world temperature for any given day of the year, for planets at varying distances from a star and composed of multiple materials in different quantities for an online game I'm helping develop.

basically each planet's composition is simplified to land (anything that doesn't fit somewhere else, iron (makes up the core), Carbon and Carbon dioxide, oxygen, atmopsheric toxins and surface water (i have NOT included humidity, though i might, right now it is too complex for my liking). if have approximated most of my proportions to the real world, so if percentages were used to help me with these equati
ons that would be great.. if not, then i'll be happy with whatever you can give me, and i'll convert it to game scale on my own...

here's what I'm trying to do:

1) an equations that models how much energy is given to a planet based on it's distance from a star with an elliptical orbit.
*so far i can do the ellipse equations... i just don't know how quickly the sun's energy falls off and how much it puts out in the first place... also if it can allow for differences in star size, that would be very cool.

this makes question 1 turn into the equation for the TIME OF YEAR and how that effects the energy a planet recieves, NOW i need something that determines how much of that energy is going to effect the temperature (remember this is average world temp.. so i hope that makes it easier)

2) modeling how materials in a planet effect how the star's energy increses it's temperature and how quickly that heat escapes...
*right now i have water act as a large buffer and keep the temp from fluctuating (decreases the range of a random number i tact on the end of the time of year equation), then % Carbon Dioxide increases possible temp, and also total planet sie also acts as a buffer the same as water and decreases the fluctuations.

my main problem is that i can make the equation equal what i want it to on an ideal earthlike planet, but if i change the planet variables around or the star sor the star size, it all seems much to unreasonable... so i decided that it would be easiest to model it off the real thing, using real variables... i don't know all the greenhouse gas types and i don't know all the factors that can effect a planet's temperature, so if you feel I've OVER simplified a planet's composition or whatever, then feel free to include that as one of the factors in an equation or if you think I've put something in that doesn't have a large impact then i'll take it out, if works well...

i CAN write the equations with the mistakes I've made and everything to give you a better starting point, but it was just that the numbers in them are based on the scale of the game, and are often not realistic. also as aforementioned, they haven't worked and have silly mistakes in them. i can also explain how things are scaled in the game, if you think that would help. (though it might take a long post to explain )

thx, bliss

p.s. I figured this was the most appropriate place to write this thread.. sorry if it’s not

 

[wolram]

http://www.lokopernik.info/sat/planets.html

It is obvious that a planet orbiting its central star along an elliptical orbit is the hottest at the periastron (at the distance a(1-e)), and the coldest at the apoastron (the distance from the star to the planet is a(1+e)). According to (2) eccentricity e and semimajor axis a of all ecospheric bodies should satisfy the following system:
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i looked at this site a while ago but it was far to
complex mathmaticaly for me, but i think you will
find your answer here

 

[Nereid]

Some stuff is pretty easy to do (e.g. albedo, variation in solar energy by distance from the Sun), others very very hard (green house gases, feedback loops involving water - ice/snow cover, clouds, ocean evaporation, ...)

What sort of time scales are you looking to model things over? a year, decade, century, ... 100 million years??

 

[Blissfulpain]

i only plan to model it on a day to day basis... but just for 1 year, then it'll repeat... 360 days would take 12 hours in the game (2 min per day) so i'll add a small fluctuation with a random number...

alright... well i don't want to go that complex just yet. if i start out with something simple then i can always build it up later if there's the opportunity to.

If i can start from the basics... how much energy does a planet get from a star, and is there an equation that models that already. if i know that the sun produces approximately "3.86e33 ergs/second or 386 billion billion megawatts" (http://seds.lpl.arizona.edu/nineplanets/nineplanets/sol.html ) as a base... then how quickly does that fall off? i suppose it move out in a sphereical fasion, yes?... I'm going to have to think about this... if i figure it out on my own i'll post to see what you think about it.

 

[Nereid]

Here's an interesting exchange, in our own PF!
https://www.physicsforums.com/showthread.php?s=&postid=91061#post91061

You can think of the radiant energy from a star as expanding spherically, as you already noted. This means, all other things being equal, that the energy falling on a square metre of surface will vary - decrease - as the square (second power) of the distance from the star's surface (there are various second-order things you need to worry about if you want to be super-precise, but for your purposes I think this should be good enough).

 

[Blissfulpain]

oh, ok... i think i got myself mixed up somewhere. i figured that surcafe area would have something to do with it... so if the sun's energy expands sphericaly then i figured that the 3.86e33 ergs/second is spread evenly around the current sun's surface area. 1,390,000 kilometers in diameter. surface area of a sphere is 4piR^2 so 6.06x10^12 km of surfaec are or 6.06x10^15 m^2 then radius changes to the distance from Earth into 149,600,000 km... which turns into 2.81x10^23 m^2 for all that energy to spread out across... which makes it 3.86^33 erg/s or 1.37x10^10 erg/s per m^2... hmm ya

so i get 1.37x10^10 erg/second per meter squared.
so i think i can use the equation (3.86x10^33)/(4pi(distance in meters)^2)

and in that distance section i could put the ellipse equation for the orbit the planet has... i'll have to think about how the "energy" given to the planet effects it, like how much is converted by green house gasses... arghs I'm going to have to pay attention to conservation of energy now lol

 

[Nereid]

i'll have to think about how the "energy" given to the planet effects it, like how much is converted by green house gasses

Yes, and I wish you well!

Some parts are relatively easy - albedo, for example, is simply a measure of how much of the incident radiation is reflected straight back and how much is absorbed. Of course, to the 1st order, what a planet receives from the Sun matches what it emits to space - in the case of the Earth, the emission is primarily in the IR range. The really tricky part is between absorbtion and subsequent emission!

 

[Blissfulpain]

well thanks for all your help. i'll right the final equation once i figure it all out, including how I've decided to have green house gasses effect it and everything. I still haven't decided how much depth i want though (i may ignore albedo, because it just makes way to much of a feed back loop, ie. low temp means ice, means less heat, means MORE ICE! then all the plants would die and that would cause volcanoes that emit co2, to accumulate and heat up the planet again! that would just make me want to rip out my hair!)... but i got lots of other stuff to keep it realistic