1) The observed period of the binary system Cygnus X-1, presumed to be binary system consisting...

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1) The observed period of the binary system Cygnus X-1, presumed to be binary system consisting of a bright star and a black hole, is 5.6 days. The mass of the visible component is 20 solar masses and the black hole has a mass of 16 solar masses. a) Show that the semimajor axis of the orbit of the black hole relative to the visible star is roughly one-fifth of the distance from Earth to the Sun. b) Find the semimajor axes of the orbit of the two masses around the centre of mass. c) Estimate the orbital speed of the star relative to the black hole. Clearly state the as- sumptions used in your estimate. 1) The observed period of the binary system Cygnus X-1, presumed to be binary system consisting of a bright star and a black hole, is 5.6 days. The mass of the visible component is 20 solar masses and the black hole has a mass of 16 solar masses. a) Show that the semimajor axis of the orbit of the black hole relative to the visible star is roughly one-fifth of the distance from Earth to the Sun. b) Find the semimajor axes of the orbit of the two masses around the centre of mass. c) Estimate the orbital speed of the star relative to the black hole. Clearly state the as- sumptions used in your estimate.