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GPS Satellite Transits — Observable?

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#1 JoeInMN

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Posted 14 August 2019 - 08:03 PM

I had Stellarium Mobile open on my tablet at work today, and noticed that (if the simulation was accurate) a satellite identified as GPS BIIRM-8 (PRN 05) was going to transit the Sun. I took a screenshot from Stellarium Desktop when I came home. Location is downtown Minneapolis, MN. Cropped, so ignore the FOV figure. Would this thing have been big enough to be visible in, say, a 102mm scope at high enough power? I'm guessing it would have been a very tiny speck, but these satellites move so slowly that it would have spent something like forty-five seconds in front of the Sun, and might have made an interesting video target.

 

190814_gps_transit.jpg

 

I've had my Baader film for months, but with the Sun the way it is currently, I haven't been much motivated to make a filter before this November's Mercury transit. I guess I really should get on that, just in case something else interesting comes up. Not that it would have done me much good today, when I was at work...


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#2 Eddgie

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Posted 15 August 2019 - 08:13 AM

I have a doubt that it could be seen.

 

These are much smaller than the ISS, but more importantly, they are in medium earth orbit at about 20,000 km (12,000 miles).  The ISS is by comparison orbits at 350 km. 

 

Still, I would not rule it out for a ground based instrument, though I think you would need more aperture than 100mm.  

 

Each solar panel on a Block III satellite is about 5m, so if you added the entire width of the panels and bus, you would probably get an angular size of 30m, so at 20,000 km, the angular size would be a little over 5 arc minutes.

 

The height of the panes is also about 5m, so in the other aspect, the angular size would only be about .52 arc seconds.

 

The problem though is that these figures are for a "solid" surface, and the configuration is two panels to a side with the bus between.   

 

For this reason, we would probably be better as taking the size of a pair of panels, and these are about 5m by 12m. Now we have about .52 arc seconds by about 104 arc seconds and at this size, I think that it would be beyond detection in a 100mm scope.

 

There is also this.    Not only is the size small, but the first rule of contrast transfer is that a bright line against a dark background will appear wider than it is, but a dark line against a bright background will appear narrower than it is.

 

If we consider the two panels to be a small "Dash" that is .52 arc seconds wide when stood on end, we can see that diffraction of the aperture is going to make the .52 arc second height (now called the width) diminish to something far less than this.

 

Now I think it would be possible to image with an amateur size instrument, but I think you would need to be imaging, and I think you would need to be several times the aperture you have. 

 

But I am after all just guessing.  I have never tried to see it with a 100mm instrument, or any size instrument to be perfectly fair about it.  


Edited by Eddgie, 15 August 2019 - 08:16 AM.

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#3 SkipW

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Posted 15 August 2019 - 11:29 AM

I can't vouch for the accuracy of the transit prediction, but they sure got the sunspots wrong!

 

 

Each solar panel on a Block III satellite is about 5m, so if you added the entire width of the panels and bus, you would probably get an angular size of 30m, so at 20,000 km, the angular size would be a little over 5 arc minutes.

You might want to check your math. The angular size of 30 meters at 20,000,000 meters is a fraction of an arc second. But, hey... what's three orders of magnitude among friends, right? tongue2.gif

 

But you're right: it's not going to be visible.



#4 JoeInMN

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Posted 15 August 2019 - 01:04 PM

I can't vouch for the accuracy of the transit prediction, but they sure got the sunspots wrong!

Heh... Yeah, it's just a generic Sun image. A plugin that would replace the default image with a real-time one fetched from somewhere on the wwweb would be interesting.

 


There is also this.    Not only is the size small, but the first rule of contrast transfer is that a bright line against a dark background will appear wider than it is, but a dark line against a bright background will appear narrower than it is.

No wonder I have so much trouble seeing the canals on Mars rolleyes.gif 

 

Thanks to all for the info!



#5 Eddgie

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Posted 15 August 2019 - 04:57 PM

Well, Calculator says 5 arc minutes....

 

size.jpg

 

If the internet is wrong and you have the correct figure, I would appreciate having it.


Edited by Eddgie, 15 August 2019 - 04:59 PM.


#6 Spectral Joe

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Posted 15 August 2019 - 06:51 PM

For 20000 kilometers distance it should be .03 kilometers size, not 30.

 

0.309 arcsec.


Edited by Spectral Joe, 15 August 2019 - 06:53 PM.


#7 SkipW

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Posted 15 August 2019 - 07:00 PM

Well, Calculator says 5 arc minutes....

It sure does.

 

Unfortunately you're specifying distance = 20,000 meters and size = 30 meters -or- 20,000 km and 30 km. Both of these must be in the same units, so you need to convert the distance to 20,000,000 meters (or leave distance alone and convert size to 0.030 km).

 

 

Small angle approximation:

 

Angle (radians) = size / distance = 30m / 20,000 km = 30m / 20,000,000m = 0.0000015

 

Converting from radians to degrees and then to minutes and to seconds of arc:

 

0.0000015 * 180° / pi = 0.0000015 * 57.3° = 0.000086°

 

0.000086° * 60 arcmin / 1° = .0052 arcmin

 

0.0052 arcmin * 60 arcsec / 1 arcmin = 0.31 arcsec

 

 

For any angle:

 

Angle= 2 * arctan( (size / 2) / distance)= 2 * arctan(15m / 20,000,000m) = 0.0000859°

 

Again, size and distance have to be the same units for this to work.


Edited by SkipW, 15 August 2019 - 07:01 PM.


#8 Eddgie

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Posted 15 August 2019 - 09:25 PM

apologies for my mistake.  I did not think he would be able to see it anyway.



#9 SkipW

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Posted 16 August 2019 - 10:01 AM

No worries. In the end, you were right about it not being visible... you were just more right than you thought!



#10 Spectral Joe

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Posted 16 August 2019 - 11:15 AM

At 5 arcmin you couldn't miss it, the sun is 30 arcmin wide.




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