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Physics/time paradoz, I think

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Question
I am having difficulty understanding this question. Any help would be greatly appreciated. I think the problem has to do with time paradox, I am not sure.

Two identical twins Stephanie and Tracy join a migration from Earth to Planet X, 20.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same moment on different spacecraft. Stephanie’s spacecraft travels steadily at 0.95c and Tracy’s at 0.75c.
a) Calculate the age difference between the twins after Tracy’s craft lands on planet X.
b) Which twin is older?

Answer
As an object (or person in this case) moves closer to the speed of light relative to an observer at rest, the rate of time passage in the moving system versus the rate of time passage in the rest frame decreases according to:
T=To*sqrt(1-v^2/c^2)
If Stephanie is moving at 0.95c the relativistic factor B1 for her [again, relative to the rest frame] becomes:
B1=sqrt(1-.95^2)=0.312=31.2%
Now the time for Stephanie to get to the star in the rest frame is calculated normally:
T1=d/v1=20cyr/0.95c=21.1yr
Using the time dilation factor for Stephanie B1 the time t1 for Stephanie becomes:
t1=T1*0.312=21.1yr*0.312=6.58yrs
Repeating the same calculations for Tracy at 0.75c:
B2=sqrt(1-0.75^2)=0.661=66.1%
T2=d/v2=20cyr/0.75c=26.7yr
t2=T2*0.661=17.6yrs
So it has taken Stephanie 6.58 years to get to the destinations while it has taken Tracy 17.6 years to get there.
When Tracy arrives she will have aged by 17.6 years.
While Stephanie has taken 6.57 years to get there, she then has to await Tracy's arrival. In the rest frame Stephanie arrives T2-T1 years:
T2-T1=26.7-21.1=5.6yrs
Since Stephanie aged 6.58 years on her trip to her destination and then had to wait 5.6 years for Tracy to arrive she has aged:
6.58+5.60=12.18yrs
Therefore, when Tracy arrives at the destination she has aged 17.6 years while Stephanie has aged 12.2 years. Tracy is older by 17.6-12.2=5.6 years.

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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