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Homework Help: Help with proving this Kepler's laws based theorem

  1. May 10, 2009 #1
    the proposition is that if r(t) has a constant length (//r(t)// is constant), then prove that r(t) is perpendicular to dr/dt at all t.

    I was thinking that if r(t) is just a function of the radius and its magnitude //r// is constant, then its basically talking about a circle? and by saying prove that r is perpendicular to dr/dt is basically asking to prove that the radius vector is always orthogonal to the velocity v(t) vector? I need a mathematical proof of this proposition using vectors. Thank, you
  2. jcsd
  3. May 11, 2009 #2
    What is d/dt(r.r)?

    BTW Kepler hasn't got much to do with it.
    Any wiggly path on the surface of a sphere has constant r.

    Last edited: May 11, 2009
  4. May 11, 2009 #3
    I'm not sure what your asking. this is a general proof so i dont know what d/dt(r.r) is. all the information i have is posted.
    Last edited: May 11, 2009
  5. May 11, 2009 #4
    i got an idea... would the //x(t)// be equal to the length of the curve of x(t) and therefore //x(t)//=integral(x(t).dx/dt) and since //x(t)// is constant the indefinite integral can only=c if the x(t).dx/dt=0 and so they are perpendicular. Can someone plz tell me if all this makes sense?
  6. May 11, 2009 #5
    r^2 is constant:

    0 = d/dt r^2 = 2 r dot dr/dt
  7. May 11, 2009 #6
    oh ok so you're saying that since //r(t)// is constant then //r(t)//^2 is constant which means (r.r) is constant and that derivative which is a dot product is 0. yeah this was easier than i thought my integral solution also works i think
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