World-building Blog & Celestial Architect Spreadsheet

Hello,

I've recently started a blog on the topic of world-building. The blog will follow the my process from defining a solar system to building a life-bearing planet, including geography, ocean currents, alien biomes, & weather. I'll also be linking to my sources, and providing a few tools to make things easier for others.

What may be of the greatest interest is the spreadsheet i've constructed to calculate out a lot of the details based on a few variables. Once i resolve problems with my FTP, i'll have v 1.1 up which includes the calculations about a moon. Based on Solar mass, distance of planet, mass and radius of the planet and it's moon, and a few other variables, it will describe the orbital periods, goldilocks zone, density, surface area, gravity, roche's limit, and apparent sizes of bodies from the planet, etc.

I'm more of a artist than a mathematician, so i'd also welcome the spotting of any error i may have.


There are two calculations i'd like help with.

Temperature
I have a calculation for temperature that i got off a now defunct website, but it seems rather ad-hoc to me. It produces about the right temperature for earth, but i have little confidence that it works beyond that. BTW this is for terrestrial planets, i'm not expecting a simple formula to cover gas giants too.

T = 374(1-A)I1/4

where:
T = Temp in Kelvins
I = Insolation
A = Albedo

For planets with an earth-like atmosphere, he modifies it like so:

T = 374 ´ 1.1(1-A)I1/4

Can anyone confirm that this is on target, or suggest a better formula?


Brightness of a Moon
I have the feeling this should be obvious, but can someone provide the formula for how bright a hypothetical moon would be at full? I'm not sure how to work in the moon's diameter. I'm willing to assume that the moon's insolation is the same as the planet's even though it may be a bit further or nearer to the sun as it goes around.

I found this equation for a planet's temperature on wikipedia:

http://en.wikipedia.org/wiki/Black_body#Temperature_relation_between_a_planet_and_its_star

It seems to work better that what i had, but i tested it on Mercury, and it was ~100K too high for Mercury's mean equatorial temp, and even more off for higher latitudes. So it seem that something isn't quite right, but i don't know what.

The wikipedia discussion page is crowded with some sort of global warming debate, chances of getting answers there seem slim.

Several issues: firstly what do you mean by "average" temperature - note that for the time averaged quantity you do not just put the semimajor axis into the equation, there are various scaling factors involved. Mercury is a tricky case since there will be a longitude dependence on the maximum temperature thanks to the orbital eccentricity and the 2:3 resonance between rotation and orbital periods.

Secondly the equation quoted on the Wikipedia page assumes that the heat is evenly redistributed across the entire planet, this is not the case for Mercury.

Thirdly on the real planet Mercury the rocks take time to heat up and cool down, whereas the equation given is for a system that has already reached equilibrium.

Lazarus wrote:

Several issues: firstly what do you mean by "average" temperature - note that for the time averaged quantity you do not just put the semimajor axis into the equation, there are various scaling factors involved. Mercury is a tricky case since there will be a longitude dependence on the maximum temperature thanks to the orbital eccentricity and the 2:3 resonance between rotation and orbital periods.

Secondly the equation quoted on the Wikipedia page assumes that the heat is evenly redistributed across the entire planet, this is not the case for Mercury.

Thirdly on the real planet Mercury the rocks take time to heat up and cool down, whereas the equation given is for a system that has already reached equilibrium.

OK, i didn't think that formula would be accurate with eccentric planets. But somehow i had never realized that Mercury wasn't nearly circular like earth. That's my mistake.