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Deriving taylor series for v/c and gamma

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    The velocity of a proton relative to
    our galaxy is vp/c = 1-(0.5*10^20), i.e. almost one. Such protons are actually observed.

    When velocity it very nearly one [tex]\gamma[/tex] is very large. 1/[tex]\gamma[/tex]
    is very small. Use Taylor series to show that for v almost one we have

    v/c[tex]\approx[/tex]1-(1/2)(1/[tex]\gamma^{2}[/tex])....

    2. Relevant equations



    3. The attempt at a solution

    I haven't done Taylor series for about a year now, and I don't quite remember how to do it. The teacher gives us some basic info on the mathematics needed to do the homework, but I can't seem to figure out a relationship. I've also looked for explanations of taylor series relevant to my question, but I havent found anything
     
  2. jcsd
  3. Sep 12, 2010 #2

    vela

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    First, express v/c as a function of 1/γ2. Then expand that function as a Taylor series about 1/γ2=0.

    f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + ...
     
  4. Sep 13, 2010 #3
    I imagine that you could also just do a taylor expansion on gamma and it would give you similar results, though I have to admit I haven't looked into it. This is just what's normally done.
     
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