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Oribtal Radius

  1. Feb 2, 2005 #1
    I need to find the orbital radius of a satilite, while only knowing its orbital period.


    i tried..

    a = 4π²r/T²
    Fnet = Fg
    a = Gm/r²

    Gm/r² = 4π²r/T²
    r = cuberoot(T²Gm/4π²)

    didnt work out..
     
  2. jcsd
  3. Feb 2, 2005 #2

    dextercioby

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    What??What are u saying by "didn't work out" ?Your formula is okay for a circular orbit...

    Daniel.
     
  4. Feb 2, 2005 #3
    Hmm..i keep getting 3.19x10^7

    but the answer is 6.95x10^6
     
  5. Feb 2, 2005 #4
    Try this:
    From the period, find the speed (simple calculation). Then, use this formula to find the radius:

    [tex]v=\sqrt{\frac{Gm_E}{r}}[/tex]
     
  6. Feb 2, 2005 #5
    hmm, in order to find the speed dont you need the radius?

    like v = 2πr/T ?
     
  7. Feb 2, 2005 #6

    Gokul43201

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    I see nothing wrong with your approach. Why don't you post the numbers given (actually just the value of T), so we can check the calculation ?
     
  8. Feb 2, 2005 #7
    Oh yeah. Just give me a second to think about this...
     
  9. Feb 2, 2005 #8
    i guess that would help lol..

    A satilite has an orbital period of T = 5760 s. What is the average orbital radius of its orbit?
     
    Last edited: Feb 2, 2005
  10. Feb 2, 2005 #9

    dextercioby

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    Please post the initial text of the problem...

    Daniel.
     
  11. Feb 2, 2005 #10

    Gokul43201

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    I get 6.95 * 10^6 m.

    You must have made a calculation error. Show us your working, and we'll show you what's wrong.
     
  12. Feb 2, 2005 #11
    I did exactly that and got 6.95 x 10^6 m. Maybe you punched in the numbers wrong...
     
  13. Feb 2, 2005 #12
    well isnt this anoying..
    k i put the cube root of..

    ( (5760²)(6.67x10^(-11)(5.98x10^24) ) / 4π²
     
  14. Feb 2, 2005 #13
    wait...i see a missing bracket, one sec lol

    damn didnt make a difference...wut am i doin wrong?
     
    Last edited: Feb 2, 2005
  15. Feb 2, 2005 #14

    dextercioby

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    Without using the calculator i could show that the result is
    [tex] 6\cdot 10^{6} <r<7\cdot 10^{6} [/tex]

    :wink:

    So how about pluggng in the numbers properly...

    Daniel.
     
  16. Feb 2, 2005 #15
    yeah, you're missing a bracket. :tongue2:
     
  17. Feb 2, 2005 #16
    ive done this like 10 times now and added the brackets...still gettin 3.2x10^7 lol
     
  18. Feb 2, 2005 #17
    OK, show me exactly what you typed into you calculator.
     
  19. Feb 2, 2005 #18

    Gokul43201

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  20. Feb 2, 2005 #19

    dextercioby

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    Okay:U need to take 3-rd order root from:
    [tex]\frac{(5.76)^{2}\cdot 1000^{2}\cdot 6.67\cdot 10^{-11}\cdot 5.98\cdot 10^{-24}}{4\pi^{2}} \simeq 300\cdot 10^{18} [/tex]

    Daniel.
     
  21. Feb 2, 2005 #20
    ok i got it to work haha, thx for the help guys
     
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