440 RelativityP39.15(a)Since your ship is identical to his, and you are at rest with respect to your own ship, itslength is 20 0.m.(b)His ship is in motion relative to you, so you measure its length contracted to 19 0.m.(c)We haveLLvcp=−122from whichLLvcp===−19 00 950122..m20.0 mand vc=0 312..*P39.16In the Earth frame, Speedo’s trip lasts for a time∆∆txv===20 021 05..ly0.950 ly yryr .Speedo’s age advances only by the proper time interval∆∆ttp==−=γ21 056 574..yr10.95yr2during his trip.Similarly for Goslo,∆∆txvvcp=−=−=120 010 7517 64222...ly0.750 ly yryr .While Speedo has landed on Planet X and is waiting for his brother, he ages by20 020 05 614...ly0.750 ly yrly0.950 ly yryr−=.Then Gosloends up older by 17 646 574
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