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Orbits Q

  1. May 16, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    A comet in a circular orbit around the Sun has speed v0 and radius r0 = aRE ,
    where RE is the radius of the Earth’s orbit and α is a constant > 1. The comet has its
    velocity reduced by Δv in a collision that does not change its initial direction. Show
    that the minimum value of Δv required to move the comet into an orbit which intersects
    the Earth’s orbit is given by

    delta v min = vo[1- root(2/(1+a))]

    2. Relevant equations



    3. The attempt at a solution

    Not sure what the neatest way to proceed is?

    Im guessing we look at energy and angular momentum..

    after the collision, total energy is 1/2 m(vo - delta v)^2 - PE (which is unchanged)..

    But when i put this into the Ellipse equation for energy i.e. E = 1/2m(dr/dt)^2 + J^2/... etc

    and set dr/dt = 0 and J = mRe(vo-deltav)..i get everything cancelling out and leaving vo^2 = GM/Re..

    not sure what im meant to do basically!
     
  2. jcsd
  3. May 17, 2010 #2

    bon

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    anyone?
     
  4. May 17, 2010 #3
    Classic Hohmann transfer orbit. You're trying to get what's known as the vis-visa orbit. Here's an example that will help, but not give you the answer. :)

    http://en.wikipedia.org/wiki/Hohmann_transfer_orbit
     
  5. May 18, 2010 #4

    bon

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    Thanks..this was useful - but it lacked a derivation of the delta v expressions...

    how can i work this out using conservation of energy and momentum?

    Thanks
     
  6. May 18, 2010 #5
    Right, that's the question, how can you work that out using conservation laws? :p

    I hate to be so hard up for information, but maybe you could post some more work so I could tell you where you went wrong.
     
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