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Thread: Question Regarding The Speed of Satellites

  1. #1 Question Regarding The Speed of Satellites 
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    I wonder how fast a GPS satellite is traveling. I imagine pretty fast. Anyone have a fairly official number?


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  3. #2  
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    It shouldn't be to hard to calculate the exact speed. All GPS satellites are geosynchronous, which means they fly at an altitude of 22,300 miles (35,786 km) above the Earth's surface, and make one orbit every sidereal day (23hr 56 min).

    When you do the simple calculation, remember to add the Earth's radius to the altitude. Then you have it.


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  4. #3  
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    Actually, GPS satellites are not in geosychronous orbits. They orbit at an altitude of about 20,179 km and have periods of 1/2 a sidereal day.

    This gives them an orbital speed of about 3873 m/s
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    Yeah, I read they orbit twice a sidereal day on Wikipedia. It says they orbit at an altitude around 20,200 km. I thought they were geosynchronous too, though.

    But let's say I am trying to calculate the speed of a geosynchronous satellite using Steve's numbers. I know it's a simple calculation for you guys, but not so much for me. I did this:

    35,786 km + 6,378 km (about Earth's radius, right?) = 42,164 km.

    42,164 / 1436 minutes (sidereal day) = 29.36 km per minute... right?

    Okay, I'm just going to go out on a limb here and guess that I am not right in the slightest.
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  7. #6  
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    Quote Originally Posted by GrantG
    Yeah, I read they orbit twice a sidereal day on Wikipedia. It says they orbit at an altitude around 20,200 km. I thought they were geosynchronous too, though.

    But let's say I am trying to calculate the speed of a geosynchronous satellite using Steve's numbers. I know it's a simple calculation for you guys, but not so much for me. I did this:

    35,786 km + 6,378 km (about Earth's radius, right?) = 42,164 km.

    42,164 / 1436 minutes (sidereal day) = 29.36 km per minute... right?

    Okay, I'm just going to go out on a limb here and guess that I am not right in the slightest.
    Close, but you forgot to multiply the radius by 2 pi to get the circumference.
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    Wow, I am just embarrassingly bad at this kind of stuff. Sorry if I'm being annoying right now, but I have little confidence in my math abilities.

    So. 6,378 X 2 X 3.14?

    I get 40,053.84 km.

    Then I'm going to add that to 35,786 (altitude in km) for 75,839.84 km.

    75,839.84 / 1436 minutes = 52.81 km per minute or, uh, roughly 3,169 km per second (which is about 1969 miles per second) for a geosynchronous orbit at an altitude of 35,786km.

    Now to butcher Janus's answer, which is what I really wanted to know:

    40,053 + 20,200 (altitude) = 60253

    /1436 = 41.96 km per minute or 2517.53 km per second OR roughly 1564 miles per second times 2 (on account that they orbit twice in sidereal day) for 3,128 miles per second.

    3,128 miles per second for a GPS satellite at an altitude of Wikipedia's 20,200 km estimate.

    I know I used a number slightly different than Janus did (the altitude), but I thought my answer would be closer.
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  9. #8  
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    Quote Originally Posted by GrantG
    Wow, I am just embarrassingly bad at this kind of stuff.

    3,128 miles per second for a GPS satellite at an altitude of Wikipedia's 20,200 km estimate.
    Yes, and no.

    At 3,128 miles per second at any height above the earth's surface the satellite would leave orbit and never bee seen or heard of again.
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  10. #9  
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    lol Janus's answer is meters per second, isn't it? All this time I thought it was miles.

    Oh, man...
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  11. #10  
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    So. 6,378 X 2 X 3.14?
    I think you messed up at the very beginning.

    you added the altitude to the circumference of the earth.

    you probably meant

    (6378+35786) x 2 x Pi
    ^^^^^^
    That is the radius from the center of the earth to the sattellite.

    You get the circumference of the oribit which is what I think you were trying to do. Correct me if I am wrong.
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  12. #11  
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    with my numbers I get

    total circumference = 42164 add three zeros to get to circumference in meters 42164000 divided by seconds in half a sidereal day

    42164000/43082


    speed in Meters/seconds = 978.6

    but thats only to orbit once around the earth if the earth was standing still so you have to find the speed of the rotation of the earth which would be

    6378 x 2 x 3.14/ 86164 = 464 m/s so from the angular portion of physics I need to some how convert these angular speeds into tangential velocity. So lets see.

    V=rW where V is tangential speed r is radius from center of rotation and w is omega or angular speed. So eureka I just multiply by radius and I will have the right answer I think.

    crap. I need to convert to radians I don't know if this is going to come out right. 2pi/43082 this is coming out to 6.14


    Someone tell me where I went wrong I know that 978 is probably right but I messed up when Radians got involved.
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    Grant, if you would have just taken your first answer and multiplied by 2 pi, you would have had it. 3.1 km/s, the same as Wikipedia
    http://en.wikipedia.org/wiki/Geocentric_orbit
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  14. #13  
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    3km/s is for one rotation everyday. The gps satellites orbit at twice that rate. But I still don't see what I did wrong. I too was at first getting 3100m/s and then I did it a different way because somebody was using minutes instead of seconds on the forum. You have to multiply the minutes by 60 to get seconds.
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  15. #14  
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    Quote Originally Posted by GenerationE
    with my numbers I get

    total circumference = 42164 add three zeros to get to circumference in meters 42164000 divided by seconds in half a sidereal day
    Whoops, that 42164 is radius not circumference. circumference would be 42164000 x 2pi = 264924225.3 meters.

    42164000/43082
    Also, since you are trying to find the orbital speed for a geosynchronous satellite, you do not use half a sidereal day but a full one, so you get

    264924225.3/86164

    speed in Meters/seconds = 978.6
    =3074.6 meters/sec

    which agrees quite nicely with the 3073.8 meters/sec you get by using the formula for orbital velocity:

    V = sqrt(GM/r)

    Using the mass of the Earth for M and 42164000 meters for r.

    but thats only to orbit once around the earth if the earth was standing still so you have to find the speed of the rotation of the earth which would be

    6378 x 2 x 3.14/ 86164 = 464 m/s so from the angular portion of physics I need to some how convert these angular speeds into tangential velocity. So lets see.
    You don't need to worry about the rotation of the Earth at all. Orbital speed is measured relative to the center of the Earth.

    V=rW where V is tangential speed r is radius from center of rotation and w is omega or angular speed. So eureka I just multiply by radius and I will have the right answer I think.

    crap. I need to convert to radians I don't know if this is going to come out right. 2pi/43082 this is coming out to 6.14


    Someone tell me where I went wrong I know that 978 is probably right but I messed up when Radians got involved.
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  16. #15  
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    ugh I always use one number wrong. So I was accidently multiplying by the radius still. Ok got it.
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