Question Details: If astronauts could travel at 0.825 to Alpha Centauri, 6.27 lt

Question

Question Details: If astronauts could travel at 0.825 to Alpha Centauri, 6.27 lt yraway, we on Earth would say it takes t=6.27 lt yr/0.825=7.6 yearsto reach Alpha Centauri. The astronauts disagree. a) How much time passes on the astronauts' clocks? Answer in unitsof y. b) What distance to Alpha Centauri do the astronauts measure?Answer in units of lt yr. Question Details: If astronauts could travel at 0.825 to Alpha Centauri, 6.27 lt yraway, we on Earth would say it takes t=6.27 lt yr/0.825=7.6 yearsto reach Alpha Centauri. The astronauts disagree. a) How much time passes on the astronauts' clocks? Answer in unitsof y. b) What distance to Alpha Centauri do the astronauts measure?Answer in units of lt yr. Question Details: If astronauts could travel at 0.825 to Alpha Centauri, 6.27 lt yraway, we on Earth would say it takes t=6.27 lt yr/0.825=7.6 yearsto reach Alpha Centauri. The astronauts disagree. a) How much time passes on the astronauts' clocks? Answer in unitsof y. b) What distance to Alpha Centauri do the astronauts measure?Answer in units of lt yr.

Explanation / Answer

   a.   Time is dilatedas      t   =   t0 / {1 -(v/c)2}   =   7.6 /{ 1 - (0.825c / c)2}          t   =   13.448   years    b.   Length will becontractedas   L   =   L0* {1 -(v/c)2}   =   6.27 *{ 1 - (0.825c /c)2}   =   3.5434   ly

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