The identical twins Speedo and Goslo join a migration from the Earth to Planet X

Question

The identical twins Speedo and Goslo join a migration from the Earth to Planet X, 19.5 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. Speedo's spacecraft travels steadily at 0.965c and Goslo's at 0.755c.

(a) Calculate the age difference between the twins after Goslo's spacecraft lands on Planet X.

5.62 Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. yr

Explanation / Answer

Their time difference is computed by the formula:
T1=T/sqrt1-V^2/C^2.
Speedo's time to planet X is 20.207 years.
Goslo's time to planet X is 25.828 years.
For 20.207 years, Speedo's time dilation is 80.2%.
For 25.828 years, Goslow's time dilation is 38.3%
Speedo = 16.206 yrs.
Goslo = 9.892 yrs.
The difference is 6.314 yrs.

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