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Lorentz factor = 10^6, solving for Beta

  • Thread starter demoncore
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  • #1
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Homework Statement


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

Homework Equations



(1-β^2)^(-1/2) = 10^6


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.
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
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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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