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Change orbit from circle to parabola

  1. Nov 23, 2012 #1

    1(a) The problem statement, all variables and given/known data

    A space ship travels in a circular orbit around a planet. It applies a sudden
    thrust and increases its speed by a factor f . If the goal is to change the
    orbit from a circle to a parabola, what should f be if the thrust points in the tangential direction?

    1(b) Is your answer any different if the thrust points
    in some other direction? What is the distance of closest approach if the
    thrust points in the radial direction?


    2. Relevant equations
    Kepler’s laws


    3. The attempt at a solution
    We know that for circle, ε=0; for parabola ε=1
    We also know that [itex]ε=\sqrt{1+\frac{2EL^{2}}{m\alpha^{2}}}[/itex]
    So [itex]E=-\frac{m\alpha^{2}}{2L^{2}}[/itex] for ε=0
    [itex]E=0[/itex] for ε=1

    But I don't know what to do next in order to find the increased factor f
     
  2. jcsd
  3. Nov 23, 2012 #2

    TSny

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    Hello. Could you please define the symbols ##\alpha## and ##L##?

    Can you express the kinetic energy of the ship in terms of ##m##, ##\alpha## and ##L## before and after the thrust?
     
    Last edited: Nov 23, 2012
  4. Nov 23, 2012 #3
    [itex]V(r)=-\frac{\alpha}{r}[/itex]
    So [itex]\alpha=GMm[/itex]

    [itex]L[/itex] is angular momentum.

    I think it is possible to express KE in terms of m and L but not [itex]\alpha[/itex].
    But what should I do next?
     
  5. Nov 23, 2012 #4

    TSny

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    ok. Express kinetic energy in terms of ##\alpha## and ##r## using E= KE + V
    You can assume ##r## remains constant during the thrust. So you should be able to relate initial and final speeds since you know how E changes. Instead of expressing E in terms of L, try to express E in terms of r for a circular orbit.
     
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