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. Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. Remember that one twin will have arrived first and you must account for that time on the planet as well

Explanation / Answer

To solve, determine the distance between planets. Then, determine the time it takes each twin to travel that distance and find the difference.

Using c = 299,792,458 m/s (you may want to change to the more common value
c = 3 x 10^8 m/s);

To find distance:
convert 22 light years to seconds
(365days/yr) x (24hr/day) x (60min/hr) x
(60s/min) = 31,536,000 s/yr
(19.5 light yrs) x (31536000 s/yr) = 614,952,000 s
now, multiply by c to find distance
(614,952,000 s) x (299,792,458 m/s) = 1.84358 x 10^17 m

Find the time it takes each twin to travel:
Speedo velocity =
0.965 x (299,792,458 m/s) = 289,299,722 m/s
(divide distance between planets by Speedo's velocity to find travel time)
(1.84358 x 10^17 m) / (289,299,722 m/s) = 637,256,056.6 s

Goslo's velocity =
0.755 x (299,792,458 m/s) = 226,343,305.8 m/s
(again, divide distance by Goslo's velocity)
(1.84358 x 10^17 m) / (226,343,305.8 m/s) = 814,506,085.6 s

The difference in time for the twin to reach Planet X:
(814,506,085.6 s) - (637,256,056.6 s) = 177,250,029.3 s
convert to yrs, dividing by the seconds/yr calculated above
(177,250,029.3 s) / (31,536,000 s/yr) = 5.62 years

That's your answer - the age difference will be 5.62 years.

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