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Lorentz factor = 10^6, solving for Beta

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle moves such that its relativistic factor γ equals one million. Find β (=v/c).
    Give answer in the form β = 0.999..., with correct number of nines before first non-nine digit. Do not use a calculator

    2. Relevant equations

    (1-β^2)^(-1/2) = 10^6


    3. The attempt at a solution

    I've messed around algebraically in a few ways, and tried the binomial approximation, but can't seem to find a way to deal with the β^2 without a calculator.
     
  2. jcsd
  3. Sep 17, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    Try to manipulate γ = 106 into an expression for β2 of the form β2 = 1-ε where ε is a very small number that you will determine.

    Then β = [itex]\sqrt{1-ε}[/itex]. Expand this to first order in ε.
     
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