The identical twins Speedo and Gosto 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 momento different spacecraft. Speedo's spacecraft travels steadily at 0.930c and Goslo's at 0.715c. (a) Calculate the age difference between the twins after Goslo's spacecraft lands on Planet X 5434 X 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. y (b) Which twin is older?

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klefenz klefenz · Answer 1 · 2019-09-10T19:00:26+02:00

Answer:

The age difference will be 11.35 years

Explanation:

From the point of view of Earth, Speedo's ship travelled 19.5 ly at 0.930c, thus it took it 19.5/0.930 = 20.97 years to arrive.

From the point of view of Earth, Goslo's ship travelled 19.5 ly at 0.715c, thus it took it 19.5/0.715 = 27.27 years to arrive.

But from Speedo's point of view it took him a different time to get to Planet X. This is calculated by the inverse of the time dilation transform:

[tex]T0 = T * \sqrt{1-\frac{v^2}{c^2}}[/tex]

[tex]T0 = 20.97 * \sqrt{1-\frac{0.93c^2}{c^2}} = 7.708 years[/tex]

And for Goslo:

[tex]T0 = 22.27 * \sqrt{1-\frac{0.715c^2}{c^2}} = 19.06 years[/tex]

The age difference will be 19.06 - 7.708 = 11.35 years