Answer to Question #201890 in Astronomy | Astrophysics for Syed Abdullah

Question

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:   ct x y z   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 ≤ ϕ < 2π):   ct 0 sin ϕ cos ϕ   (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 (

Answer 1

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