STEP ONE: Calculate greenhouse effect, if any, from 4.5.1.

STEP TWO: Modify base temperature by greenhouse effecr and albedo to get the surface temperature of the world, on 4.5.2.

4.5.1 Greenhouse Effect The Greenhouse gas pressure is the combined pressure, in atm, of the greenhouse gasses carbon dioxide, methane, sulfur dioxide and nitrous oxides. Water vapor is also included if it is a major part of the atmosphere. Note this combined pressure, Pgr. GF = 1 + (P0.5 x 0.01 x 1d10) + (Pgr0.5 x 0.1) + (Wv x 0.1) ... where: P is the atmospheric pressure Pgr is the greenhouse gas pressure Wv is the water vapour factor (from 4.2.3)

4.5.2 Surface Temperature (in Kelvin) Tsurface = Tbase x A x GF ... where A is the albedo factor (from 4.4.1).

GREENHOUSE EFFECT:

The greenhouse effect of certain gasses prevent heat from escaping the atmosphere. Gasses like carbon dioxide, water vapor, CFCs and methane are highly effective for this. The small parts of greenhouse gasses likely to be present on all worlds with an atmosphere is simulated by the P^0.5 x 0.01 x 1d10 factor (such as the small amounts of greenhouse gasses on Earth). Large amounts of greenhouse gasses do not add up to produce an arithmetically higher greenhouse effect.

SPECIAL CASES:

Certain gasses, like CFC's, are very effective greenhouse gasses. Small amounts can have a strong effect. If a greenhouse gas freezes out during the cooler periods and vaporizes during the warmer ones, this could amplify normal seasonal temperature variations.

CHECKING BACK:

The final surface temperature should be back-checked towards hydrosphere and atmospheric composition. It is possible that the world is significantly cooler or warmer than it began. This can affect a hydrosphere (freezing it). If a hydrosphere is heated so much it would boil, it is lost and contributes to the greenhouse effect by heating the planet further. If gasses are cooled enough to freeze out or become liquid, they may still be a part of the atmosphere. After all, on warmer spots on a world temperatures may be high enough to vaporize them. The Surface Temperature is an average. Equator region will be warmer.

VARIATIONS:

This is discussed in more detail in Appendix 1. But these are some basics.

Variations with day: Temperatures rise during the day and fall during the night. The longer the rotation period, the greater differences.

Variations with latitude: High latitudes are cooler and equatorial regions warmer. Solar infall falls in at an angle that increases towards the poles.

Variations with seasons: Axial tilt of a world makes solar infall on a given area vary with which pole is tilted towards the primary. Low axial tilt give small effects, but extreme axial tilts (close to 90 degrees) may give very strong effects as one pole is in perpetual "day" during a full season.

Variations with eccentricity: Eccentric orbits produce variations in solar infall. These are easy to calculate, assuming albedo and greenhouse effects will be the same. If not, it gets more complicated. Very eccentric orbits may give very strong effects -a low albedo factor and low greenhouse effect at furthest separation, and a higher albedo factor and greenhouse effect when closer.

MODERATING FACTORS:

Thick atmospheres, preferably cloudy and greenhouse-effective, moderate temperature. A strong enough greenhouse effect could moderate even very long days. Oceans also moderate temperature as they "store" heat. This is further discussed in Appendix 1.

GAIA?:

Some people believe that a living ecosphere could regulate itself. IE the life adjusts greenhouse levels (and perhaps albedo) to allow a world to have an optimal or at least decent temperature. This has not been considered here at all. If you feel "habitable" or "Earth-like" worlds are too uncommon, just tweak the equations/rolls a bit.