>Ashley ~)~
>
>>  >So, you could look at this like the intersection of two spheres. The
>>>circle of reception would be the locus of all points common to the
>>>surfaces of both spheres.
>>>
>>>This may make for a simpler problem.
>>
>>Sort of. When you bring this circle out to the 2D latitude,longitude 
>>used for the map (one of the rectangular ones) then it is only a 
>>true circle if the satellite is directly over the equator, as it 
>>moves further away from the equator the circle deforms such that 
>>when it reaches its heighest latitude above about 60û it actually 
>>looks a little like a sinewave.
>
>There are a couple of problems I see here.
>
>1. Unless the satellite is actually "on the fly" redirecting it's 
>parabolic dish (which I don't think it does), then the "footprint" 
>will be close to a "circle" regardless of where the satellite is 
>located. Now, "circle" is loosely used here because it is actually a 
>circle projection onto an oblate spheroid (the Earth) which will 
>never be a prefect circle.
>
Most satellites are actually directed in their orbit such that as it follows the almost circular orbit or really eliptical orbit the dish actually points down, ie the satellite spins on one or more axis very slowly such that the dish is pointed to earth other wise it would get to a point where it is possible that the dish is poijnting in the wrong direction.

>2. This is also a map projection problem. You are trying to project 
>an image on a map -- a map which is a distorted representation of 
>surface data. You see, when determining where points are on a map 
>(i.e., survey), one eventually has to render those points in two 
>dimensions, but they are actually taken in three dimensions. That's 
>the reason that maps, as one travels north (or south), show man-made 
>square rectangles (such as townships, counties, etc.) that are not 
>actually square, but are narrower toward the end closest to the pole. 
>In other words, your north-south direction can remain constant in 
>defining things like townships, but your east-west direction must 
>shorten to accommodate for approaching a pole. When you take this 
>phenomena out to a global consideration, then you have things like 
>Antarctica looking much larger than it actually is.
>

The map projection I use directly relates latitude and longitude (altitude makes no difference) to screen cordinates similar to a mercator projection.

>>I have actually done this part (to generate the footprint) as this 
>>is how I can tell if the function is producing the correct result. I 
>>now have to work the other way to determine if a location is within 
>>this footprint.
>
>My guess is that the actual "footprint" remains just about the same 
>all over the planet, but changes when projected on current maps. The 
>only exception to this would be if the satellite changes the altitude 
>of its orbit -- the higher the orbit, the larger the "footprint". 
>Also, there should be some minor differences in "footprints" between 
>polar and equatorial satellites -- the polar having a larger range of 
>distortion. But, outside of that, the "footprint" should remain 
>fairly constant -- unless you want to consider atmosphere differences 
>and how that effects radio transmissions, but I think that's beyond 
>what you want.
>

The foot print is a circle roughly the same size all over the earth but it's shape changes in the map projection due to the distortions towards the poles ie as it gets closer to the poles the distances expand.

>>A cone is used because the dishes used on many satellites and probes 
>>are parabolic, especially the ones in higher orbits. Yes some of the 
>>lower orbit satellites use normal antennas which would produce the 
>>sphere but the function used is generic for sensors and comms which 
>>facilitates the use of a cone rather than a sphere.
>
>This problem can still be thought of as the intersection of two 
>spheres -- keep in mind that a cone is nothing more than a 3-D arc of 
>a larger sphere. Think of it as when you use a flashlight -- you have 
>the center of the light that is focused by the internal parabolic 
>reflector, but the light is not confined to just that focus. In fact, 
>the light spreads out much further than where the beam is directed.
>
>But, in any event, the intersection of a cone with a sphere, or a 
>sphere with a sphere, should render the exact same result. I seem to 
>think that finding the intersection of two spheres would be easier 
>than trying to define the intersection of a cone with a sphere.
>

I have already done this code with the cone. The cone effect can be explained with a torch since light is in fact just another form of electromagnetic radiation.

>>I am open to other suggestions if code can be provided or guided to.
>
>Before developing code, it's usually best to define the problem in 
>simplest terms. As it is now, from what I've read, I still don't 
>think the problem has been defined. For example, it's not finding a 
>point within a cone (no offense to the mosquitoes and tee pee 
>example), but rather where the cone (or sphere) intersects the Earth 
>AND how to show that intersection on a map -- isn't that the problem 
>here?

The problem is that I have a location on the surface of earth that I want to know if it is within the transmission cone of the satellite. The location could say be the radio telescope at Parkes which has a latitude of -33.10 , a longitude of 148.13 and I don't know the actual altitude. The satellite's position is calulated and the various data obtained about the transmission cone. It then needs to calculate if Parkes is visible from the satellite.

  Ashley ~)~

=============================================================
Ashley Butterworth
Email: macbse@...
=============================================================


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