FYKOS Year 36 Series 3 Problem 4 — escape to Tau Ceti · FYKOS 36 #36.3.4

Physics · mechanics

Problem

Since our Sun will explode one day, it will be necessary to organize the construction of an evacuation spacecraft, in which at least

0.000~001\,\mathrm{\%}

of humanity can escape. To escape, people choose the star Tau Ceti which is

12\,\mathrm{ly}

away at that time. They build engines that accelerate the spacecraft to a cruising speed of

v = 0.75 c

in very little time. Unfortunately, at half a distance to their destination, they observe both the Sun's and Tau Ceti's explosions. How long before the observation the explosions happened in an inertial coordinate frame of the spacecraft? And when in the coordinate system fixed with the stars? Presume that the Sun and Tau Ceti are static relative to each other.

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