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Total mechanical energy of orbiting satellite

  1. Nov 9, 2012 #1
    1. The problem statement, all variables and given/known data
    what would be the total mechanical energy of a 200 kg satellite in a geosynchronous orbit around the earth? The only known data is the radius of the earth and mass of the earth the mass of the satellite, m=200 kg, it would have a period of T=24h, but i do not know the radius of the orbit.

    2. Relevant equations

    WNC=E2-E1

    Fc=mac

    3. The attempt at a solution

    I don't know how to get an answer with out knowing the radius of the orbit. I tried to make use of the period however i would still need the radius as the velocity is dependent on the radius of the orbit.

    I would appreciate any help.
     
  2. jcsd
  3. Nov 9, 2012 #2
    If F=ma is used for the satellite and the value of G is given then the radius of the orbit can be found.
     
  4. Nov 9, 2012 #3
    how would the gravitational constant help?

    F=ma
    GMEm=mv2
    r2 r

    the only thing i can think of would be

    v2=GME
    r

    but then i have two unknowns the v and r.
     
  5. Nov 9, 2012 #4
    Note that v = rω

    and ω = 2π/T where the value of T is known.
     
  6. Nov 9, 2012 #5

    PeterO

    User Avatar
    Homework Helper

    You can look up the Radius of the moon's orbit, and the Period of the Moon, then apply R3/T2 to find the radius of the orbit with a period of 24 hours [1 day].
     
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