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Universal Gravitation problem - Satellite Orbit

  1. Dec 23, 2015 #1
    1. The problem statement, all variables and given/known data
    http://prntscr.com/9huihp
    Given,
    Mass of the Earth = 6*1024
    Mass of Satellite = 45 kg
    Radius of Satellite's orbit = 4.2*107
    G = 6.67*10-11
    Find the velocity of the satellite.

    2. Relevant equations
    Gravitational Force Fg = (G*Me*Ms)/(Rs2)
    Newton's second law:
    Fg = Ms*a where a = v2/Rs due to uniform circular motion.

    3. The attempt at a solution
    http://prntscr.com/9huloh
    http://prntscr.com/9hulwt

    I feel like I'm being thrown off either by the units being in km/s or by not accounting for the fact that the acceleration vector points in the -x direction, but I don't see why that would affect the magnitude of the velocity. Can anyone point me in the right direction as to what I may be neglecting, because these problems are usually pretty easy for me.
    *ps. sorry if my writing is not legible enough to read!
     
  2. jcsd
  3. Dec 23, 2015 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Well, you have the correct formula for the orbital speed of the satellite. Did you check your arithmetic? That's a good place to start.

    I checked your calculations, and I come up with a different result.
     
  4. Dec 23, 2015 #3
    WOW.

    Last time I did this problem I remembered making sure to take the square root of my answer but I still ended up not getting the correct answer, but now I did. Forgot to do the last step! Thank you.
     
  5. Dec 23, 2015 #4
    Hi windyfan:

    I confess that I do have trouble with the illegibility.

    Re http://prntscr.com/9huloh
    The equation that you derive looks OK.

    Re http://prntscr.com/9hulwt
    There is a need to keep track of units. I can't tell if you are doing that right or not since you don't include the units in your work. You are also not mentioning in section (1) the units for G and Rs. I suggest you do the work again writing all the units for each expression.

    Hope this helps.

    Regards,
    Buzz
     
  6. Dec 23, 2015 #5
    Thank you, because I realized it was because of the unorganized way I did my work that I forgot to complete the arithmetic!

    This thread can be closed. Thank you guys for pointing my errors out!
     
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