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Circular to elliptical path

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data
    A satellite is at an altitude of 3R (R- Radius of the planet) circulating around the planet with a velocity v. In order to make its path elliptical the velocity is changed from v to βv. What should be maximum value of β such that the satellite doesn't collide with the planet?


    2. Relevant equations
    First the expression of V is the orbital velocity and
    Initial energy = final energy.( in terms of Gravitation)
    I cant remember any other equation.

    3. The attempt at a solution
    I tried but i didn't get the right answer.. The answer is sqrt(2/5)..Thanks in advance for help..
     
  2. jcsd
  3. Apr 13, 2013 #2

    mfb

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    I think you are looking for a minimal value.
    Consider the case where the satellite is just "touching" the surface: There are two ways to calculate its velocity, based on two conserved quantities of orbits. They both have to give the same result for a real orbit, this allows to calculate β.
     
  4. Apr 13, 2013 #3
    Please tell your calculation.. i have also taken the consideration of just touching the surface. .
     
  5. Apr 13, 2013 #4

    mfb

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    It is your homework problem, not mine. I know how to do it, I don't have to learn that any more.
     
  6. Apr 13, 2013 #5
    Is the answer coming?
     
  7. Apr 13, 2013 #6

    mfb

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    I helped you to get the answer yourself.

    If you show your work here, I might look for mistakes.
     
  8. Apr 15, 2013 #7
    I have done the following things:
    0.5mv^2=GMm/4R.
    Then 0.5 Mβ^2V^2-GMm/4R=-GmM/R.
    What's the mistake here?
     
  9. Apr 15, 2013 #8

    mfb

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    Where does this come from? It is wrong by a constant factor.
    Why do you have M (instead of m) in the first term? Again, where does the "4" come from? What happened to the velocity at the lowest point of the elliptical orbit?
     
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