Planetery Defense Batteries

What are the best arcs of fire to use to represent a ground based, 
direct fire, beam weapon?
I like 180 degrees (3 arc), horizon to horizon, but a friend has 
suggested 270 degrees (I don;t understand how or why) or even 360 
degrees.
I think the problem lies with whatever model you use to represent a 3-D 
planet on a 2-D map. If the table is the plane of the eliptic (which I 
suspect we all subconsciously assume) the a polar base would be able to 
fire 360 degrees unless the ships came too close, then the curve of the 
planet would block the guns. Alternativly an equitorial base would only 
have a 180 degree arc of fire.
What do you think?

Michael.

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