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SEC: UNCLASSIFIED - RE: Beam Headings for the Birds



Spherical geometry is a little difficult to understand, but I'll try an
explanation that might make sense to a broad audience. This is NOT meant to
demean anyone, just provide a 'popular' explanation. (It's borrowed from how
I remember explaining it to a sailor on lookout watch in a ship, during a
quiet night watch as I navigated us across the trackless ocean.) Those who
REALLY know what happens can correct me. I have a skin equipped with
material akin to the tiles on the Space Shuttle.



WHAT IF THE WORLD WAS FLAT, OR A CYLINDER, RATHER THAN A SPHERE?

Imagine a 'flat earth'. If you pointed in any direction, the place would be
in that direction (i.e. the angle between your arm and the Latitude and
Longitude lines would make perfect sense!)

Imagine a 'cylindrical earth': Places due north or south would be along the
Longitude lines; Places east or west would be along the Latitudes, around
the curve of the cylinder! As I understand it, places in other directions,
up to half a rotation away, would be at the same angle with respect to the
Lats and Longs. (There would also be a 'short path' and a 'long path'.)

NOW, imagine a 'spherical earth'. Think of a ball. Sense would say that the
'direction' of the other place is the same as where you point. WRONG. The
direction of the shortest distance is still right - shortest is still
shortest (and is called a Great Circle). However, we have defined Poles on
this sphere and the Longitude lines come together there, while the Latitude
lines do NOT come together. This means that a person pointing in any
direction except the cardinal points (N, S, E, W) will cause the 'take-off'
direction from the immediate locality to be one angle, the intermediate
angles at any particular place to be constantly changing as the circular
path passes by their locality, and the 'reception' angle to be something
quite different again. The direction from your QTH will always cause you
confusion because you are inevitably looking at a FLAT PROJECTION of a
SPHERE.

Consider an example: Find a Globe, use a piece of cotton to mark out two
points in opposite hemispheres and about 1/3 of a rotation apart. Look at
the angles between the cotton and the Longs and Lats along the cotton. Your
eye will show that these change. (The effect is most marked if one point is
near a pole. And, observe how the trend of the angles 'reverses' as you
cross the Equator.) 


WHAT ABOUT SATELLITES?

There is another spherical calculation that you need to make with a
satellite. It is, after all, not on the earth-sphere, but on another surface
joning you and the satellite (which might be a straight line if you
can/could see the satellite!)

If you **can** see the satellite, fine. Point at it! Be my guest! 
Oohhhh, you can't actually **see** it, but the computer **knowns** where it
is! 

As it happens, the satellite is over a place on the surface. We **can** work
out this sub-satellite point on the surface and then do the spherical
calculation from your to there (called the 'azimuth'); and, we also
calculate the apparent height of the satellite above a virtual horizon
(called the 'elevation'). NOW, we can point the antenna, along a line
described by the combination of a **spherical** angle and an elevation from
a point (your QTH) on the surface of the sphere.

And, that's how it's done! 

So, to answer your question, the signal between the satellite and the earth
station follows a straight line (for VHF+) but its 'apparent' path is along
a great circle from its sub-satellite point.

As I said, the direction from your QTH will always cause you confusion
because you are inevitably looking at a FLAT PROJECTION of a SPHERE.


I hope it makes SOME sense.

Peter R. Ellis
VK1KEP
(A VK Navy man)

		-----Original Message-----
		From:	Jon Ogden [mailto:jono@enteract.com]
		Sent:	Wednesday, 19 January 2000 13:55
		To:	amsat-bb@amsat.org
		Subject:	[amsat-bb] Beam Headings for the Birds

		OK

		Here's a question perplexing me for some time:

		Does the RF signal path to and from the birds follow a
"Great Circle" route
		or not?  For example. when I see a bird south of Hawaii my
tracking program
		says to point the antennas West.  This would be pretty much
akin to a great
		circle route from my location (Chicago), yet drawing on a
map, west is not
		in a straight line to the bird.

		I understand the concept of the great circle routes for HF
propagation.  But
		a satellite is above the surface of the earth so why would
the signal still
		follow the great circle route?

		Any comments?

		73,

		Jon
		KE9NA 

		-------------------------------------
		Jon Ogden
		KE9NA

		Member:  ARRL, AMSAT, DXCC, NRA

		http://www.qsl.net/ke9na

		"A life lived in fear is a life half lived."

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