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The identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 17.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo's craft travels steadily at 0.970c, and Goslo's travels at 0.750c. Calculate the age difference between the twins after Goslo's spacecraft lands on Planet X.   answer in y please

The identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 17.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo's craft travels steadily at 0.970c, and Goslo's travels at 0.750c. Calculate the age difference between the twins after Goslo's spacecraft lands on Planet X.   answer in y please

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The identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 17.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo's craft travels steadily at 0.970c, and Goslo's travels at 0.750c. Calculate the age difference between the twins after Goslo's spacecraft lands on Planet X.
  answer in y please 

Expert Solution
Step 1

According to the Earth's frame,

Speedo's trip lasts for a time  

                                         ∆t=∆xv∆t=17.0 ly0.970 ly/yr∆t=17.53 yr

Speedo's age increase only by proper time interval during his trip.

                                        ∆tp=∆tγ∆tp=17.53 yr×1-0.970c2c2∆tp=4.26 yr

Step 2

Similarly for Goslo,

                                       ∆tp=∆tγ1-v2c2∆tp=17.0 ly0.750 ly/yr×1-0.750c2c2∆tp=15.46 yr

When Speedo has landed on the planet X, he ages by

                                            17.0 ly0.750 ly/yr-17.0 ly0.970 ly/yr=5.30 yr

 

 

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