Question

Galaxies contain both stars and dark matter. The mass M of a galaxy that is located within a certain star's orbit is given by where v is the velocity of the star, r is the distance from the galaxy's center to the star, and G is Newton's gravitational constant, 6.673 x 10- N m/kg Stars near the edge of a particular galaxy have velocities of 259 km/s. The radius of the galaxy is 53 kpc. How much mass is in the galaxy? galaxy = kg If luminous matter makes up 7.0% of the mass in the galaxy. how much mass is in the luminous matter? luminous matter kg The rest of the mass is dark matter. How much dark matter does this galaxy contain? dark matter kg

Answer 1

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Mass of galaxy M = v^2 r/G G = 6.673 times 10^-11 N m^2/kg^2 V = 259 times 10^3 m/s r = 53 kpc = 1.635 times 10^21 m so M = (259 times 10^3)^2 (1.635 times 10^21)/6.673 times 10^-11 = 16436.001 times 10^38 M = 1.64 times 10^42 kg luminous matter mass = (7%) M = 7/100 times 1.64 times 10^42 m = 11.5 times 10^40 kg so dark matter Mass = M - m = (1.64 - 0.115) times 10^42 kg = 1.5 times 10^42 kg