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Homework Help: Angular Momentum vs Latus Rectum

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    There is a shuttle following a circular orbit around a planet. At some point P in the orbit, the shuttle fires thrusters causing the speed at that point to increase. I am supposed to a) find the angular momentum, gravitational force at the point P, centripetal acceleration at the point P, and the radius of curvature at point P. Part B is to say whether the latus rectum of my new orbit is smaller, larger, or equal to that of the circular orbit.

    2. Relevant equations

    I used L=R x P, a=v^2/r, and F=Gmm/r^2.

    3. The attempt at a solution

    I didn't have much problem with part A. The velocity perpendicular to the radius changed, so the cross product for L increased, making L larger. The gravitational force stayed the same at the point, since that only depended on the radius. The centripetal acceleration increased, since v increased, while r remained the same. And lastly, the radius of curvature at the point didn't change, because the radius didn't change instantaneously.

    My problem is that, it is known that L, the angular momentum, is directly proportional to the latus rectum, c. But for the ellipse just made, the latus rectum is smaller than that for the circle. Thus my new L should be SMALLER than my first L for the circular orbit. But the velocity increase tells me something different! In other words, when analyzing two different aspects of this orbit, I get both an increase and a decrease in angular momentum, depending on whether I look at the velocity or the latus rectum. What am I missing here?

    EDIT: Also, my professor gives a hint that this point P will lie along the semi-major axis of the newly elliptical orbit. But he has drawn the point at a 3' o clock location on the circular orbit. If the thrusters went off here, I would expect the point to lie along the semi-minor axis because the shuttle should move further now in this direction than it has previously! Perhaps this is just a typo?
    Last edited: Nov 22, 2008
  2. jcsd
  3. Nov 23, 2008 #2
    No, centripental acceleration does not change, because the force of gravity does not change.
  4. Nov 23, 2008 #3
    Major axis/minor axis are determined based on the orientation of the
    elliptical orbit, so they are not necessarily alligned to your coordinate sistem.
  5. Nov 23, 2008 #4
    You have the "particle" moving in a circle so that its instantaneous velocity is tangential to the circle and it experiences a centripetal acceleration towards the center of the circle (due to gravity).

    I might be mistaken, but it doesn't seem like you have considered the directionality of the thruster's acceleration compared to that of the centripetal force correctly in your logic - but I apologize if I'm wrong in this interpretation!
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