Answer to Question #202955 in Astronomy | Astrophysics for Ema

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 ex-

pressed 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 ex-

pressed as all vectors of the following form (for all 0 ≤ ϕ < 2π):





ct

sin ϕ

cos ϕ





(a) How does the shape of the Milky Way look like for the astronauts in the fast-moving space-

ship? 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 (Note: The ring shape for a resting spaceship is already drawn.):

Answer 1

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