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{"ops":[{"insert":"Space and time are interconnected according to special relativity. Because of that, coordinates\nhave four components (three position coordinates x, y, z, one time coordinate t ) and can be ex-\npressed as a vector with four rows as such:\n\uf8eb\n\uf8ec\uf8ec\uf8ec\uf8ed\nct\nx\ny\nz\n\uf8f6\n\uf8f7\uf8f7\uf8f7\uf8f8\nThe spaceship from problem A.4 (Special Relativity - Part I) travels away from the Earth into the\ndeep space outside of our Milky Way. The Milky Way has a very circular shape and can be ex-\npressed as all vectors of the following form (for all 0 \u2264 \u03d5 < 2\u03c0):\n\uf8eb\n\uf8ec\uf8ec\uf8ec\uf8ed\nct\n0\nsin \u03d5\ncos \u03d5\n\uf8f6\n\uf8f7\uf8f7\uf8f7\uf8f8\n(a) How does the shape of the Milky Way look like for the astronauts in the fast-moving space-\nship? To answer this question, apply the Lorentz transformation matrix (see A.4) on the circular\nshape to get the vectors (ct0\n, x0\n, y0\n, z0\n) of the shape from the perspective of the moving spaceship.\n(b) Draw the shape of the Milky Way for a spaceship with a velocity of 20%, 50%, and 90% of the\nspeed of light in the figure below (Note: The ring shape for a resting spaceship is already drawn.):\n"}]}

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