Hi Ashley,

Glad to see that your original description is more or less 
confirmed.  For others let me warn that the base of the 
teepee is in a plane running through the (bary)center of 
the earth. It is NOT in a plane tangent to the earth. So 
the icecream cone mentioned is not the whole teepee.  The 
icecream cone is much smaller has a crumbly edge since the 
earth is irregular oblate spheroid. 
But I have some nagging questions too for Ashley.

(1) How high is the satelite.  It had better be pretty high
or else the satelite will not really be pointing
its beam towards the center of the earth!!
If the satelite is low it will be pointing "down" which 
(I guess wildly, nodding to tedd) 
may be roughly defined by its visual horizon...

(2) How do you propose to calculate the coordinates
of your observation point on the earth from latitude, 
longitude and elevation above sealevel?  I guess
a database is required.  Or does one assume that
"sealevel" is a perfect oblate spheroid?  

Cheers

Laurent S