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

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