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Energy transfer from x altitude to geosynchrous altitlude

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data

    INTRO TO THE PROBLEM :For a circular orbit around a massive gravitating body, the speed depends on the radius according to the equation V = sqrt (GM/r) ; for elliptical orbits, the speed varies according to the equation v^2 = 2GM([ 1/r - 1/(2a), where r is the distance from the massive body and a is the semimajor axis of the ellipse (i.e., half the sum of the closest and farthest distances). A satellite can be transferred from one circular orbit (at radius r1) to a higher orbit (at radius r1) by boosting the circular speed v1 at v2 to the appropriate speed for an elliptical orbit whose distance varies between r1 and r2 , and then boosting the speed in the elliptical orbit at r2 to the circular speed v2. This is called a Hohmann transfer.

    THE PROBLEM STATEMENT :
    How much energy is required for the first boost in such a transfer to take a 280kg satellite from a circular orbit at a 400 km altitude to the altitude of a geosynchronous orbit?

    change in K_1 = _________J

    2. Relevant equations


    stated above in the intro

    3. The attempt at a solution

    clueless?
     
  2. jcsd
  3. Mar 17, 2009 #2

    LowlyPion

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    The conservation of energy still works doesn't it?

    (Potential + Kinetic) before + Energy = (Potential + Kinetic) after?
     
  4. Mar 17, 2009 #3
    so,

    1/2mv^2 - GMm/r = 1/2mv^2 - GMm/r

    ?
     
  5. Mar 17, 2009 #4

    LowlyPion

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    The Δ anyway. Mustn't that be the additional energy?
     
  6. Mar 17, 2009 #5
    I'm sorry i am confused
     
  7. Mar 17, 2009 #6

    LowlyPion

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    You have initial potential energy and kinetic energy in lower orbit.

    You add energy.

    You get a higher orbit with kinetic energy and potential energy.
     
  8. Mar 17, 2009 #7
    how about saying it mathematically. can you start me off?
     
  9. Mar 17, 2009 #8

    LowlyPion

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    You have the equation below. I'm sure you can do it.

    Besides if it comes up on a quiz, I won't be there to start you off. It's good practice.
     
  10. Mar 17, 2009 #9
    So whats the formula to delta k ?
     
  11. Mar 17, 2009 #10

    LowlyPion

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    Don't they give you the formulas for how to calculate the v2's
     
  12. Mar 17, 2009 #11
    ok. r is the radius of the earth + 400km and a is ? And that formula above v^2 =...
    is delta K ?
     
  13. Mar 17, 2009 #12

    LowlyPion

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    Well that's a good part of it, but strictly speaking you want to be working with ½mv² for KE. so use the v² 's that you find to determine your ½mv² 's.
     
  14. Mar 17, 2009 #13
    How would I represent (a) as? in the equation above?
     
  15. Mar 18, 2009 #14

    LowlyPion

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    Don't look now, but they tell you how to determine a in the problem. If your ellipse is to vary between r1 and r2, what is the semi-major axis?
     
  16. Mar 19, 2009 #15
    (r1+r2) / 2
     
  17. Mar 20, 2009 #16

    LowlyPion

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    That would seem so.

    So plug 'em in and get'er done.
     
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