If we intercept an electron having total energy 1533 MeV that came from Vega, which is 26 ly from us, how far in light-years was the trip in the rest frame of the electron? (Answer: 8.7*10^-3 ly)

Answer 1

rest energy of electron m₀c²=0.512 MeV
E=mc²=1533 MeV
mc² =m₀c²/sqrt(1-β²)... (1)
τ=τ₀/sqrt(1-β²) …..(2)
Divide (1) by (2)
mc²/τ= m₀c²/τ₀
τ₀=τ• m₀c²/mc²= 26•0.512/1533=0.00868 ly

Answer 2

Thank you so much!