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Gravitation and Gravitational Fields

  1. Aug 11, 2015 #1
    1. The problem statement, all variables and given/known data

    A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5 N/kg.

    a) Calculate the distance above the surface of Earth at which the satellite must orbit

    b) Assuming the orbit is circular, calculate the acceleration of the satellite and its direction

    c) At what speed must the satellite travel in order to maintain this orbit?

    2. Relevant equations

    F=G(m1)(m2)/(r)^2

    v= √(G)(m) / (r)

    3. The attempt at a solution

    a)
    G=6.67 x 10^-11 N•m^2/kg^2
    m=5.98 x 10^24 kg
    F=4.5 N/kg

    F=G(m1)(m2)/(r)^2

    r^2=G(m1)(m2) / (F)

    r^2=(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (4.5 N/kg)
    r=^2√8.863688889 x 10^13
    r=2.98 x 10^13m

    ∴The distance above the surface of the Earth that the satellite must orbit is 2.98 x 10^13m or 2.98 x 10^10km


    b)

    v= √(G)(m) / (r)

    v=√(6.67 x 10^-11 N•m^2/kg^2)(5.98 x 10^24 kg) / (2.98 x 10^13m)
    v=√(9.98866 x 10^14) / (2.98 x 10^13m)
    v=3.66 m/s

    I don't think that its possible that this could be correct, after looking up a little bit about satellites I found that satellites have a much greater orbital velocity than this. I also don't understand how I am supposed to calculate the direction of the satellite with the information that has been given.

    c) And finally, for c) wouldn't my answer just be the same as part b) ? Since I am only maintaining orbit I don't think I need to be concerned about an escape velocity.



    Help with these would be really appreciated. Thank you.
     
  2. jcsd
  3. Aug 11, 2015 #2
    The second part asks you to find acceleration , not velocity .
    This is incorrect . Check the formula for ' v ' once again .

    Hope this helps .
     
  4. Aug 11, 2015 #3
    I can't find any other formulas related to acceleration to solve this type of problem. Would it work if I solve for velocity and then divide velocity by time? Although, with this question I don't know if that would work either. Was part a) correct?
     
  5. Aug 11, 2015 #4
    Do you know circular motion ?

    Part A is fine .
     
  6. Aug 11, 2015 #5
    Would a formula for planet/celestial orbit work for part c? Such as K=G(m1+m2) / (4π^2)
     
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