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GPS Satellites' height

 
 
TiTaN_pi8
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      03-04-2006, 06:45 PM

Hellow

On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h)

But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result

Here is the calculation

v= sqrt(G* mA/(rA+h)

where v = velocity (speed
G = 6.67*10^-11 (N*m)/kg
mA= the earth's mass = 59.8*10^23 k
rA= the earth's radius = 6.37*10^6

after filling in these numbers

v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6)
v = 3871.61 m/
v = 13938 km/

why is the result so much off from the data on the websites? Am I doing something wrong

Thanks a lot!

--
TiTaN_pi8

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Phil Wheeler
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      03-05-2006, 02:22 AM
Something odd here:

> v = sqrt(3.99*1014/(6.37*106+20,240*106))




TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>
> But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>
> Here is the calculation:
>
> v= sqrt(G* mA/(rA+h))
>
> where v = velocity (speed)
> G = 6.67*10^-11 (N*m)/kg
> mA= the earth's mass = 59.8*10^23 kg
> rA= the earth's radius = 6.37*10^6 m
>
> after filling in these numbers:
>
> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
> v = 3871.61 m/s
> v = 13938 km/s
>
> why is the result so much off from the data on the websites? Am I doing something wrong?
>
> Thanks a lot!!
>
>

 
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DingBAT
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Posts: n/a
 
      03-05-2006, 04:17 AM

"Phil Wheeler" <(E-Mail Removed)> wrote in message
news:TXrOf.2946$(E-Mail Removed)...
> Something odd here:
>
>> v = sqrt(3.99*1014/(6.37*106+20,240*106))

>
>
>
> TiTaN_pi8 wrote:
>> Hellow,
>>
>> On most webpages I find that the speed of the GPS satellites is about
>> 11000 km/h (some also say 12000 km/h).
>>
>> But if I calculate the speed that a satellite must have in order to stay
>> in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>>
>> Here is the calculation:
>>
>> v= sqrt(G* mA/(rA+h))
>>
>> where v = velocity (speed)
>> G = 6.67*10^-11 (N*m)/kg
>> mA= the earth's mass = 59.8*10^23 kg
>> rA= the earth's radius = 6.37*10^6 m
>>
>> after filling in these numbers:
>>
>> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
>> v = 3871.61 m/s
>> v = 13938 km/s
>>
>> why is the result so much off from the data on the websites? Am I doing
>> something wrong?
>>
>> Thanks a lot!!
>>


YES


 
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Sam Wormley
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      03-05-2006, 04:21 AM
TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>
> But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>
> Here is the calculation:
>
> v= sqrt(G* mA/(rA+h))
>
> where v = velocity (speed)
> G = 6.67*10^-11 (N*m)/kg
> mA= the earth's mass = 59.8*10^23 kg
> rA= the earth's radius = 6.37*10^6 m
>
> after filling in these numbers:
>
> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
> v = 3871.61 m/s
> v = 13938 km/s
>
> why is the result so much off from the data on the websites? Am I doing something wrong?
>
> Thanks a lot!!
>
>


Take a look at the figure you are using for rA+h.

You can get the square root of the semimajor axis for each satellite
from the YUMA data
http://www.navcen.uscg.gov/ftp/GPS/a...ma/yuma341.txt
http://www.navcen.uscg.gov/ftp/GPS/almanacs/yuma/
http://www.navcen.uscg.gov/gps/almanacs.htm

Regards,
-Sam

 
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Sam Wormley
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      03-05-2006, 04:30 AM
TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>
> But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>
> Here is the calculation:
>
> v= sqrt(G* mA/(rA+h))
>
> where v = velocity (speed)
> G = 6.67*10^-11 (N*m)/kg
> mA= the earth's mass = 59.8*10^23 kg
> rA= the earth's radius = 6.37*10^6 m
>
> after filling in these numbers:




where does this 3.99 come from and 20240*10^6 ??

> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
> v = 3871.61 m/s
> v = 13938 km/s
>
> why is the result so much off from the data on the websites? Am I doing something wrong?
>
> Thanks a lot!!
>
>

 
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Sam Wormley
Guest
Posts: n/a
 
      03-05-2006, 04:39 AM
TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>
> But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>
> Here is the calculation:
>
> v= sqrt(G* mA/(rA+h))
>
> where v = velocity (speed)
> G = 6.67*10^-11 (N*m)/kg
> mA= the earth's mass = 59.8*10^23 kg
> rA= the earth's radius = 6.37*10^6 m
>
> after filling in these numbers:
>
> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
> v = 3871.61 m/s
> v = 13938 km/s
>
> why is the result so much off from the data on the websites? Am I doing something wrong?
>
> Thanks a lot!!
>
>


I get
http://www.google.com/search?q=sqrt%...10%5E7+m%29%29
based on the radius of a satellite from YUMA data.
 
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Phil Wheeler
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      03-05-2006, 05:20 AM
Where did you read 11,000 km/hr for a GPS sat? Are you sure that is not
for GEO?

Phil

TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>
> But if I calculate the speed that a satellite must have in order to stay in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>
> Here is the calculation:
>
> v= sqrt(G* mA/(rA+h))
>
> where v = velocity (speed)
> G = 6.67*10^-11 (N*m)/kg
> mA= the earth's mass = 59.8*10^23 kg
> rA= the earth's radius = 6.37*10^6 m
>
> after filling in these numbers:
>
> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
> v = 3871.61 m/s
> v = 13938 km/s
>
> why is the result so much off from the data on the websites? Am I doing something wrong?
>
> Thanks a lot!!
>
>

 
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Andy H
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Posts: n/a
 
      03-05-2006, 08:39 AM

"Phil Wheeler" <(E-Mail Removed)> wrote in message
news:gyuOf.1277$(E-Mail Removed)...
> Where did you read 11,000 km/hr for a GPS sat? Are you sure that is not
> for GEO?
>
> Phil
>
> TiTaN_pi8 wrote:
>> Hellow,
>>
>> On most webpages I find that the speed of the GPS satellites is about
>> 11000 km/h (some also say 12000 km/h).
>>
>> But if I calculate the speed that a satellite must have in order to stay
>> in it's orbit at a height of 20240 km, I find 13938 km/h as the result.
>>
>> Here is the calculation:
>>
>> v= sqrt(G* mA/(rA+h))
>>
>> where v = velocity (speed)
>> G = 6.67*10^-11 (N*m)/kg
>> mA= the earth's mass = 59.8*10^23 kg
>> rA= the earth's radius = 6.37*10^6 m
>>
>> after filling in these numbers:
>>
>> v = sqrt(3.99*10^14/(6.37*10^6+20,240*10^6))
>> v = 3871.61 m/s
>> v = 13938 km/s
>>
>> why is the result so much off from the data on the websites? Am I doing
>> something wrong?
>>
>> Thanks a lot!!
>>

Isn't it 12K Miles?


 
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Phil Wheeler
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      03-05-2006, 03:18 PM
TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about 11000 km/h (some also say 12000 km/h).
>


What websites would those be?

Phil
 
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Phil Wheeler
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      03-05-2006, 03:40 PM
TiTaN_pi8 wrote:
> Hellow,
>
> On most webpages I find that the speed of the GPS satellites is about
> 11000 km/h (some also say 12000 km/h).
>


From one website:

> The satellites orbit the earth with a speed of 3.9 km per second and
> have a circulation time of 12 h sidereal time, corresponding to 11 h
> 58 min earth time. This means that the same satellite reaches a
> certain position about 4 minutes earlier each day. The mean distance
> from the middle of the earth is 26560 km. With a mean earth radius of
> 6360 km, the height of the orbits is then about 20200 km. Orbits in
> this height are referred to as MEO medium earth orbit. In
> comparison, geostationary satellites like ASTRA or Meteosat
> satellites orbit the earth at 42300 km, which is about twice the
> distance of GPS satellites.


From another:

> The current GPS configuration consists of a network of 24 satellites
> in high orbits around the Earth. Each satellite in the GPS
> constellation orbits at an altitude of about 20,000 km from the
> ground, and has an orbital speed of about 14,000 km/hour (the orbital
> period is roughly 12 hours - contrary to popular belief, GPS
> satellites are not in geosynchronous or geostationary orbits).


So your calculation is not all that bad.

Phil
 
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