Suppose astronomers find a small "satellite" galaxy that is orbiting NGC 5055 at a distance of 60 kpc (kpc = kilo-parsec) from the galaxy's center. The small galaxy is orbiting NGC 5055 with a velocity of 200 km/s.

a. Is thesatellitegalaxy's velocitythe same or different than what you would expect based on NGC 5055's rotation curve? Why?

b. What is the total mass of NGC 5055 within theorbit of the satellite galaxy in kg and in solar masses? Remember to convert your distanceunits to meters before you calculate this mass.

c. Assuming the mass of the stars andgaswithin NGC 5055 is 8x10¹⁰Solar Masses, what is the percentage of dark matterin the galaxy?