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Gravitation - change of orbit

  1. Jul 13, 2015 #1
    1. The problem statement, all variables and given/known data
    A spaceship is in a circular orbit of radius ##r_0## about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship's speed by 50%. This causes the spaceship to move into an elliptical orbit.
    a) What is the spaceship's, just after the rocket burn is completed, in terms of M, G and ##r_0##?
    b) In terms of ##r_0##, what are the spaceship's minimum and maximum distance from the planet in its new orbit?

    2. Relevant equations


    3. The attempt at a solution
    Let's look at part a first. This is an even numbered problem and I'm not sure about the answer.
    Let ##v_i = 2v_f## and the mass of the ship be m
    Just after firing, the movement can still be considered circular and the ship experiences a centripetal acceleration of
    ##a_r = \frac{F}{m}##, leading to
    ##\frac{GmM}{r_0^2} = m\frac{(2v_f)^2}{r_0}##
    ##v_f = \sqrt{\frac{GM}{4r_0}}##
    Is this correct?
     
  2. jcsd
  3. Jul 13, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    This statement is a bit misleading. Just calculate the initial velocity in terms of M, G and r0, then you don't need assumptions about the orbit (you know the initial orbit) to find vf.

    The answer is right.
     
  4. Jul 14, 2015 #3
    Looking at now I can see just how obvious and simple it is. But that's what happens when doing physics problems as the time approaches midnight. Thanks for the input.
     
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