# Equation for solar radiation at a given latitude on a given exoplanet?

I'm trying to find equations that would help me determine the amount of solar radiation hitting a certain latitude on a certain planet given the following inputs:

• the degrees of latitude of the location in question
• this hemisphere's current season (winter or summer)
• size of the planet
• luminosity of the star(s) the planet orbits

Without taking into consideration wind, air pressure, or any atmospheric effects.

Ideally I would like to determine the average solar radiation of a given location in both the winter and summer.

My end goal is to determine the average surface temperature of a given latitude on a planet using the base solar radiation and the effects of wind, air pressure, and surface ocean currents.

I know it is possible to do this for the entire planet generally, but I would like some way of doing it for a particular latitude and season.

• There's some good info in the Wikipedia article on insolation. Aug 3 '15 at 22:02
• Are you looking for a daily average/total (day+night) for midsummer and midwinter when the 'sun' is transiting, or for the insolation at any given time? Nov 27 '15 at 16:57

## 1 Answer

The rotational period ( or whether a body is tidal locked ) is a factor here. A tidal locked body has a hot spot on one side and a cold spot on another. Rotation may also affects average temperatures.

Season depends on orbital factors. Simply saying it's one season or another does not tell you the distance you are from the star, which is the single most important factor ( combined with the power of the star ).

However in terms of making a very basic calculation you can use a black body radiation calculation and thermal equilibrium to get something. You can see more on this at these links :

http://claesjohnson.blogspot.ie/2010/04/black-body-temperatures-of-planets.html

http://www.acs.org/content/acs/en/climatescience/energybalance/predictedplanetarytemperatures.html

It's a pretty good predictor considering it's simplicity. Note the impact of atmosphere and ocean. Note also that significant energy is being radiated by some bodies.

This slide show has several equations that may help you. It also has an interesting model on the effect of an ice cap, which I'd not seen before.

http://www.math.umn.edu/~mcgehee/Seminars/ClimateChange/presentations/2011-2Fall/20111102Handouts.pdf