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How to calculate the speed of a satellite around the sun.

  1. Apr 2, 2015 #1
    Hi guys,
    I'm currently doing a little project an I need to calculate the speed of a satellite around the sun! I'm currently trying with the Earth, but i have some problem.
    When i'm using this formula : (2*Pi*a*Sqrt(1-e2))/T(1±e)
    I get an answer in km/s which seams pretty good. (29,75 km/s)
    But when i'm using this one : Sqrt(G*M*(2/r)-(1/a)) i'm getting 1,32*1017
    I don't really know how I can transform that answer into something in km/s

    If i'm not clear enough, feel free to ask me questions!

    Thanks!
     
  2. jcsd
  3. Apr 2, 2015 #2

    Drakkith

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    Staff: Mentor

  4. Apr 2, 2015 #3
    Yeah, i'm using the equation listed above but i'm gonna link you different image where it's clearly listed ! Thank you very much for helping me !

    Eq1 : http://i.imgur.com/GYaHMLJ.png
    Where Vp is Speed,
    a is the length of the semi-major axis of the elliptical orbit
    e is the eccentricity
    Eq2 : http://upload.wikimedia.org/math/6/6/d/66dd08fa58f176503e2f0b6603769f4d.png
    Where V is Speed,
    μ is the standard gravitational parameter,
    r is the distance at which the speed is to be calculated
    a is the length of the semi-major axis of the elliptical orbit
    Image 3 : http://i.imgur.com/zzmlLKQ.png
    Here is my project so far, as you can see, my answers aren't good when it comes to the second equation!
     
    Last edited: Apr 2, 2015
  5. Apr 2, 2015 #4

    Bandersnatch

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  6. Apr 2, 2015 #5
    Thanks you ! But it's worse now... I'm getting : upload_2015-4-2_16-30-38.png
    What's the unit of this? How can I convert it to km/s ?

    Thanks!
     
  7. Apr 2, 2015 #6

    Bandersnatch

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    Gold Member

    See the wikipedia link. They do the exact same calculation you're doing as an example, with numbers and units. The ##\mu## in their equation is just the same as ##GM##.
     
  8. Apr 2, 2015 #7

    mfb

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    2016 Award

    Staff: Mentor

    If you get 1016 it is a calculation error. Do you square the product instead of taking the square root?

    Quick estimate using SI units: G is 10-10, M is 1030 , r and a are 1011 so 2/r is 10-11 and 1/a is half that value.
    That means the product is about 108 and the square root is 10000 with units m/s, or 10km/s - which is the right order of magnitude.
     
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