Thursday, January 3, 2013


A little over a day ago, the Earth approached the point in its orbit closest to the Sun, called perihelion.  This means that the Earth was getting more sunlight than in any day of the year (and to close approximation, still is).  This is a peculiar fact for us northern hemisphere denizens, since this is also our winter, and we don't quite get the most sunlight at all right now thank you very much.

No, if we wanted the most intense sunlight, we would want to go to our opposing Tropic, the Tropic of Capricorn, at the 23.5° S latitude.  There, solar insolation (power per square meter) at the top of the atmosphere (TOA) reaches 1413 W/m^2 at its peak during the day, the highest of any other latitude on Earth.  This reduces some as the light goes through our atmosphere and is reflected by clouds and particulates, but otherwise Antofagasta in Chile, São Paulo (São Paulo) in Brazil, Rockhampton (Queensland) in Australia, Polokwane in South Africa – these are our tanning destinations!

Now I'm not much of a tanning person myself (for several reasons, one being more genetically-oriented), but I'm a huge fan of free energy like anyone else.  If I wanted a winter vacation home and cared only about how much energy I could produce using solar panels, where should I go?  While peak insolation is highest at the Southern Tropic, total solar insolation is not at this time of year.  If you thought that perihelion during the northern winter was peculiar, you probably don't know this: to gather the most sunlight I need to go to the South Pole:

Larger version here.

The above graph shows average 24-hour TOA insolation at different solar declinations ("delta"), for all latitudes, and is corrected for changing Earth-Sun distance throughout the year (perihelion and aphelion are roughly concomitant with the solstices, off by ~11 days).

The main reason that solar insolation increases toward the poles, after you hit the Polar Circles, is that there's no longer any nighttime.  The light that the poles get while the rest of the Earth is in shadow outweighs the difference in insolation during the day.

A winter vacation home here would have the added bonus of increased efficiency too, since solar panels tend to work better in cold temperatures.  If, however, you're not the type that likes winter, if you're instead one of those "tanning" types that likes to have as much Sun as possible, then you'd be better off just living closer to the equator.  In fact, what this graph would imply is that you should live somewhere south of the equator, around the 2/3° S latitudes.

In this respect, the above graph is actually wrong.  This is because it is a single-day snapshot, with an equal number of days during the summer as during the winter.  If we define the split between summer and winter at the days where the Earth-Sun distance is perpendicular to the distance when at perihelion or aphelion (i.e. the two days in the year the Earth receives the same insolation in both hemispheres), the northern hemisphere's winter is shorter than the southern hemisphere's.  The flip side of that coin is that our summer is longer – we have a longer summer while we're further away, and the southern hemisphere has a shorter summer while it is closer.  This is because the Earth moves faster in its orbit while it is closer to the Sun, during perihelion; slower while it's further away.

The countering time and distance effects cancel each other out more or less completely.  If you wanted to bask in the most sun throughout the year, you'd want to live right on the equator.

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