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Satellite in orbit

  1. Mar 25, 2017 #1
    1. The problem statement, all variables and given/known data
    Satellite m=3 000kg, circular orbit at the height h = 300km above the Earth´s surface.

    a/ calculate energy ( work ) for delivering satellites into orbit ?

    b/ during 1 month the satellite approached the Earth of Δh=13,8 km. Prove that the radial component of velocity in comparison with the tangential component is insignificant.

    c/ What the average resistance force is applied to the satellite during flight?

    2. Relevant equations
    I know: RE = 6 370 km.....radius of the Earth
    ME = 5,98 .1024 kg...mass of the Earth
    G = 6,67 . 10 -11 Nm2kg-2...gravitational constant

    3. The attempt at a solution
    a/

    W = Ep1 - Ep0
    W = - (G*ME* m) / 2( RE + h) - (- (G*ME* m) / RE
    W = G*ME* m * (( RE+2h)/ 2RE( RE +h))

    with numbers: W = 9,81 . 1010 J
     
  2. jcsd
  3. Mar 25, 2017 #2

    gneill

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    Okay. Did you consider the satellite's initial kinetic energy associated with the rotation of the Earth at the time of the satellite launch? Did you have a reason to ignore it?

    You should have listed the equations you used to calculate the energies in the relevant equations section.
     
  4. Mar 25, 2017 #3
    yes.......
    W = ΔEp + ΔEk
    ΔEk = 1/2 mv2 - 0
     
  5. Mar 25, 2017 #4

    gneill

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    So the Earth is not rotating?
     
  6. Mar 25, 2017 #5
    Yes, the Earth moves, but I think -change in kinetic energy can be ignored due to the small mass of the satellite in comparison to the Earth ?
     
  7. Mar 25, 2017 #6

    gneill

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    Probably something you should verify. What's the KE of the satellite while resting on the Earth's surface? Assume a launch from the equator.
     
  8. Mar 25, 2017 #7
    a circuit the earth s = 40 000 km
    time......24 hour
    v = s/t = 40 000/24 = 1667 km/hour = 463 m/s

    Ek = 0,5 * 3000 * 4632 = 321,5 MJ
     
  9. Mar 25, 2017 #8

    gneill

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    Okay. Does that represent a significant contribution to the work done? If not then you are justified in ignoring it.
     
  10. Mar 25, 2017 #9
    comparison ........ 9,81.107 MJ x 321,5 MJ....yes, I can ignore ΔEk
     
  11. Mar 25, 2017 #10

    gneill

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    Good!
     
  12. Mar 25, 2017 #11
    super :-) so it is a/ , but I dont know how prove b/
    radial velocity of the satellite is the centripetal force ?
     
  13. Mar 25, 2017 #12

    gneill

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    Velocity is not force.

    It's not clear to me what the import is of the Δh. The problem doesn't say whether this is due to the satellite's orbit becoming elliptical or if it remains circular but is shrinking in size over time. Looking at part (c) I'm leaning towards the latter, the orbital radius is shrinking over time due to some frictional force eating away at the KE of the orbit.

    For (b) I suppose you could look at the definition of velocity since you have the radial displacement and the time period over which it occurred.
     
  14. Mar 25, 2017 #13
    maybe calculate the tangent to the path that the satellite executed for one month ... as a circuit track * time and compare it with the Δh?

    path is circular....h = 300 km, RE = 6 370 km.....radius of the Earth, circumference = 2π( R+h)
    in 1 month....s=t*circumference.......but I dont know t :-( that way probably is not the way :-(
     
  15. Mar 25, 2017 #14
    v = √G*M/r
     
  16. Mar 25, 2017 #15

    gneill

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    The satellite's R changed by Δh over one month. What average velocity does that give you?

    What's the satellite's on-orbit velocity?
     
  17. Mar 25, 2017 #16
    v = √ 6,67.10-11 * 5,98 . 1024 / 6 370 000 + 300 000 = 7739 m/s
     
  18. Mar 26, 2017 #17
    vector v = vector radial component of velocity vr + vector tangential component of velocity vt
    image114.png
    the numerical value........ image115.png
     
    Last edited by a moderator: May 9, 2017
  19. Mar 27, 2017 #18
    What should be the next steps, please?
     
  20. Mar 27, 2017 #19

    gneill

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    What precisely are you trying to determine?
     
  21. Mar 27, 2017 #20
    that radial component of the velocity is in proportion to the tangential insignificant...

    during 1 month the satellite approached the Earth of Δh=13,8 km

    can I compare flew a distance s = v*t with Δh?
     
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