The Gap in the Sats
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The Gap in the Sats
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Wildlifewriter
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PostPosted: Fri Oct 28, 2005 11:34 am    Post subject: The Gap in the Sats Reply with quote

Do you ever look look at the "Sky View" display on your GPS?

Most units have a section which shows the signal strength from various satellites in view - and some have a little "chart" which shows where the sats are in the sky, relative to your current position. Have you noticed something strange about it?

I have.

Now, most GPS users just take all of this satellite stuff for granted. They're up there, we're down here, this shows the position. Hike completed, or cache found - job done. But it's not that simple...

There are thirty American nav satellites in operation at the moment. (Plus some which are out of service, under test or just loafing around.) On the GPS display, the positions of these seem to be random. They change from hour to hour, but - seen from one place - there's no obvious pattern

The pattern IS there. These GPS satellites are in orbit around the Earth, at an altitude of some 20,500 Km. (10,900 Nautical miles). The orbits are inclined to the equator at an angle of 55º. Like this...



Of course, that diagram doesn't help much because the Earth is a sphere. If we look at the orbits on a projected map, the whole system looks something like...



Notice something interesting: each satellite track (in a rather fetching pink) passes over a different part of the surface - but none of them pass over the North or South Poles. This is a result of the inclined orbits - and it means that none of the satellites are overhead at much more than 60º North, or South.

I don't know about you, but I'm still having some difficulty in visualizing what all this means , as seen from the ground. To help, I set a little program running on my PDA, which records the track of each GPS satellite over a 12-hour period. (Because the sats orbit twice in one day, it gives a picture of the whole constellation as it's seen from here.) This is the result...



... which is kinda interesting. The tracks show that in our part of the world (my latitude is 54º 33' N) there is an area of the sky where GPS satellites are NEVER seen.

I didn't know that...

... And I'll bet YOU didn't, either. Smile


-Wlw.
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HighlandNick
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PostPosted: Fri Oct 28, 2005 7:05 pm    Post subject: Reply with quote

The recorded track that your last PDA pic gives indicates the actual track that the satellite takes. If you could see it, looking up, (a bit like a contrail left by a jet) then that would show its path.
That doesn't mean that the satellite isn't in view, as it can "see" a large patch of the ground from where it is but from the side slightly.

Presumably the orbits of the satellites (as set by the US military) allows them to concentrate their view of the surface for military purposes, rather than civil ones. Perhaps, due to the "Special Relationship" they don't need to look at us (UK and NI) too closely as they won't have cruise missiles targeted on Belfast?? Twisted Evil Twisted Evil

In any case, there doesn't seem to be much point in having too many satellites orbiting over the poles, as there is little need for them here. Even with the 55 degree inclined orbit, there will still be at least four satellites visible (but lower on the horizon) even at the poles. In this way, satellite coverage is maximised in areas of high population, below say 60 degrees north / south.
There is a good webpage - http://www.kowoma.de/en/gps/orbits.htm that shows some GPS satellite orbits, and from here, you can go to a Java applet on the NASA site that shows the J - orbital path that satellites take. This applet can be speeded up to show the path of any satellite.
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Wildlifewriter
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PostPosted: Fri Oct 28, 2005 7:44 pm    Post subject: Reply with quote

HighlandNick wrote:
The recorded track that your last PDA pic gives indicates the actual track that the satellite takes. If you could see it, looking up, (a bit like a contrail left by a jet) then that would show its path.
That doesn't mean that the satellite isn't in view, as it can "see" a large patch of the ground from where it is but from the side slightly.

I didn't say that it wasn't in view - only that no satellite crosses that particular patch of sky.


Quote:
Even with the 55 degree inclined orbit, there will still be at least four satellites visible (but lower on the horizon) even at the poles. In this way, satellite coverage is maximised in areas of high population, below say 60 degrees north / south.

Using Trimble's simulator, with a 10º horizon mask, it seems that there are (on average) rather MORE satellites visible from the North pole at any given hour, than from the equator - but they are, as you rightly point out, lower in the sky.

This is slightly counter-intuitive and I'm not mathematician enough to work out the geometry of why it happens.

-Wlw.
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HighlandNick
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PostPosted: Fri Oct 28, 2005 8:16 pm    Post subject: Reply with quote

Wildlifewriter wrote:

I didn't say that it wasn't in view - only that no satellite crosses that particular patch of sky.

I take your point, I misinterpreted what you intended!!


Quote:
(Nick) Even with the 55 degree inclined orbit, there will still be at least four satellites visible (but lower on the horizon) even at the poles. In this way, satellite coverage is maximised in areas of high population, below say 60 degrees north / south.

Quote:
(wlw) Using Trimble's simulator, with a 10º horizon mask, it seems that there are (on average) rather MORE satellites visible from the North pole at any given hour, than from the equator - but they are, as you rightly point out, lower in the sky.

This is slightly counter-intuitive and I'm not mathematician enough to work out the geometry of why it happens.

-Wlw.


Why you should see more? I would have to ponder this one a bit longer!!

Anyway, with the 55 degree maximum angle from the equator, it leaves a nice little hole - do you remember the Spirograph?? This was a nice way of looking at advancing "orbital" paths in a simple manner. Repetitive circles overlapping and precessing give a circular area with no coverage.
There will be a similar size hole over the south pole as well, as the satellite orbits are also inclined at 55 degrees south.

On a slightly different tack, but no doubt connected somehow, have you had a look at the polar coverage using Google Earth??
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Billy Twigger
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PostPosted: Fri Oct 28, 2005 10:40 pm    Post subject: Reply with quote

You guys need to stay in more! Shocked
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Naefearjustbeer
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PostPosted: Sat Oct 29, 2005 8:47 am    Post subject: Reply with quote

I managed to glean Blah Blah Blah GPS Blah Blah PDA Blah Blah SKY Blah GAP Blah Blah Blah from that lot Puzzled Very Happy Very Happy Wink Question Idea
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Wildlifewriter
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PostPosted: Sat Oct 29, 2005 11:02 am    Post subject: Reply with quote

Naefearjustbeer wrote:
I managed to glean Blah Blah Blah GPS Blah Blah PDA Blah Blah SKY Blah GAP Blah Blah Blah from that lot Puzzled Very Happy Very Happy Wink Question Idea

Well don't try to read technical articles while the baby's crying, then.

-Wlw.
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HighlandNick
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PostPosted: Sat Oct 29, 2005 7:37 pm    Post subject: Reply with quote

A couple of Spirograph images that show the same hole from precessing curves:

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Billy Twigger
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PostPosted: Sat Oct 29, 2005 10:18 pm    Post subject: Reply with quote

HighlandNick wrote:
A couple of Spirograph images that show the same hole from precessing curves:


Results
precessing was not found in the Cambridge Advanced Learner's Dictionary

Did you spell it correctly? Here are some alternatives:

parishes
.
(First and last elements of unreasonably long list - Admin)
.
pursues

I think I know what you meant! and admin censored it ! (it was prozac)


Last edited by Billy Twigger on Sat Oct 29, 2005 11:38 pm; edited 1 time in total
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HighlandNick
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PostPosted: Sat Oct 29, 2005 10:25 pm    Post subject: Reply with quote

Hah Hah
Try Googling for:

gyroscope precessing
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PostPosted: Sun Oct 30, 2005 8:13 am    Post subject: Reply with quote

A satellite directly overhead (90 degrees elevation) is completely useless for navigation as one of the major error components in the system is directly proportional to the tangent (tan) of the angle of elevation, since tan 90 = infinity you get infinate positional error. Running alongside each satellite orbit are large strips of the earth's surface where the signal is usable so the strips of a satellite orbiting at 60 degrees latitude extend to the poles.
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Billy Twigger
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PostPosted: Sun Oct 30, 2005 8:50 am    Post subject: Reply with quote

Billy Twigger wrote:
You guys need to stay in more! Shocked


I apologise for being so flipant Embarassed - this is a really interesting thread.
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HighlandNick
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PostPosted: Sun Oct 30, 2005 9:39 am    Post subject: Reply with quote

Billy Twigger wrote:


I apologise for being so flipant


Well I looked up "flipant" in the dictionary and couldn't find it Very Happy Very Happy Very Happy
It suggested i tried:

flip ant
flip-ant
flippant
.. (That's quite enough. For a forum where pointless off-topic posts are welcomed - nay, encouraged - please go HERE -GxAdmin)


Apologies to the admin man who will probably have to delete this list (and me) as well.
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Wildlifewriter
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PostPosted: Sun Oct 30, 2005 10:06 am    Post subject: Reply with quote

mckryton wrote:
A satellite directly overhead (90 degrees elevation) is completely useless for navigation as one of the major error components in the system is directly proportional to the tangent (tan) of the angle of elevation, since tan 90 = infinity you get infinate positional error.

Nonsense.

A satellite directly overhead still contributes an element to the computed 3-D positional solution. Since the solution is based on ranging (not "angles") this contribution is as valid as any other.

Because a minimum of four ranging signals is required for a 3-D solution, there could only be an "infinate (sic) positional error" if all FOUR satellites were to be directly overhead at the same instant.

This cannot happen, therefore such an error cannot occur.

-Wlw.
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HighlandNick
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PostPosted: Sun Oct 30, 2005 1:00 pm    Post subject: Reply with quote

Quote:
.. (That's quite enough. For a forum where pointless off-topic posts are welcomed - nay, encouraged - please go HERE -GxAdmin)


Yes, go on, click on the link. I did - it's pure dead brilliant Laughing Laughing Laughing
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