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Earth orbit -- geosynchronous orbit calculation

  1. Sep 22, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-9-21_22-36-1.png

    2. Relevant equations

    ε= r_max - r_min / r_max + r_min
    = r*v2 / gRE

    3. The attempt at a solution
    I first find that 1 revolution is 2π rad , the angular velocity ω = 2π rad / 24h = π/43200 rad /s
    so v = rω where r is the unknown
    ε = 0 (circular orbit)

    r*(rω)2 / g RE = 0


    Correct route?
     
  2. jcsd
  3. Sep 22, 2016 #2

    kuruman

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    Your approach is incorrect. You need to use Newton's 2nd law to find a relation between speed and radius in a circular orbit.
     
  4. Sep 22, 2016 #3
    st
    start with F= ma, then integrate?
     
  5. Sep 22, 2016 #4

    kuruman

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    No need for integration. Remember that the acceleration here is centripetal. What is an expression for F?
     
  6. Sep 22, 2016 #5
    F=ma then a is gravity?
     
  7. Sep 22, 2016 #6

    kuruman

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    No, a is the centripetal acceleration. What is an expression for it? F is the force of gravitational attraction between two masses according to Newton's law of gravitational attraction.
     
  8. Sep 22, 2016 #7
    GmM/ r2
     
  9. Sep 22, 2016 #8

    kuruman

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    That's F. What about a on the other side of the equation?
     
  10. Sep 22, 2016 #9
    m (r'' + rω) cuz it is the angular movement ?
     
  11. Sep 22, 2016 #10

    kuruman

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    Centripetal acceleration is ω2r, not ωr. Also, what is r'' for a satellite in a circular orbit?
     
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