Astronomers have observed a small, massive object at the center of our milky way galaxy. a ring of material orbits this massive object; the ring has a diameter of about 16 light-years and an orbital speed of about 130 km/s. for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of black hole calculations.
determine the mass m of the massive object at the center of the milky way galaxy. take the distance of one light year to be 9.461 x 1015m. express your answer in kilograms.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants