GPS Satellites' height

Discussion in 'General GPS' started by TiTaN_pi8, Mar 4, 2006.

  1. TiTaN_pi8

    TiTaN_pi8 Guest

    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*m²)/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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    TiTaN_pi8, Mar 4, 2006
    #1
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  2. TiTaN_pi8

    Phil Wheeler Guest

    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*m²)/kg²
    > 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!!
    >
    >
     
    Phil Wheeler, Mar 5, 2006
    #2
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  3. TiTaN_pi8

    DingBAT Guest

    "Phil Wheeler" <> wrote in message
    news:TXrOf.2946$...
    > 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*m²)/kg²
    >> 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
     
    DingBAT, Mar 5, 2006
    #3
  4. TiTaN_pi8

    Sam Wormley Guest

    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*m²)/kg²
    > 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/almanacs/yuma/yuma341.txt
    http://www.navcen.uscg.gov/ftp/GPS/almanacs/yuma/
    http://www.navcen.uscg.gov/gps/almanacs.htm

    Regards,
    -Sam
     
    Sam Wormley, Mar 5, 2006
    #4
  5. TiTaN_pi8

    Sam Wormley Guest

    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*m²)/kg²
    > 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!!
    >
    >
     
    Sam Wormley, Mar 5, 2006
    #5
  6. TiTaN_pi8

    Sam Wormley Guest

    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*m²)/kg²
    > 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((G*6*10^24+kg)/(2.65596*10^7+m))
    based on the radius of a satellite from YUMA data.
     
    Sam Wormley, Mar 5, 2006
    #6
  7. TiTaN_pi8

    Phil Wheeler Guest

    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*m²)/kg²
    > 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!!
    >
    >
     
    Phil Wheeler, Mar 5, 2006
    #7
  8. TiTaN_pi8

    Andy H Guest

    "Phil Wheeler" <> wrote in message
    news:gyuOf.1277$...
    > 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*m²)/kg²
    >> 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?
     
    Andy H, Mar 5, 2006
    #8
  9. TiTaN_pi8

    Phil Wheeler Guest

    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
     
    Phil Wheeler, Mar 5, 2006
    #9
  10. TiTaN_pi8

    Phil Wheeler Guest

    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
     
    Phil Wheeler, Mar 5, 2006
    #10
  11. TiTaN_pi8

    Guest

    You can confirm this yourself using the latest TLEs. For example, I'll
    choose NAVSTAR 54 because it travels quite close to 20,240 km above the
    earth's surface. Assume that you are observing from the equator.
    Assuming circular motion (e = 0.0033732; just 179 m between apogee and
    perigee, so this is reasonable).

    The mean motion is 2.00575858, so it orbits every 43075.97179 secs.
    Rearranging the standard equation: r^3 = t^2 * GM / 4 pi^2

    This gives me a radius of 26,554,726 and a satellite height of
    20,176,589. I can ignore the earth's oblateness for my assumed
    position. At the point the body passes over the equator, it is
    travelling at 13,947.6 kilometres per hour.

    This is almost exactly what you got.

    To confirm, you would need to do this for a few SVs in the
    constellation and adjust for eccentric anomaly and build in the
    flattening factor at your location, but clearly you've got the picture.

    To be fair to the web sites you mention, I suspect they're just trying
    to show casual users that a satellite travels at a very high velocity
    indeed.
     
    , Mar 7, 2006
    #11
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