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 15 light-years and an orbital speed of about 200 km/s.
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.

M = 42.553· kg

Explanation: A orbit where a body remains traveling around a gravitating mass at constant radius is called Circular Orbit. Although in reality the orbit is more like an ellipse, the circular orbit is a good approximation to the real one.

In that system, it is possible to determine the velocity needed to maintain the orbit. The formula is:  v = , where:

v is velocity;

G is the gravitational constant( = 6.67·)

M is the mass of the gravitating mass;

r is the distance between the center of the massive object and the orbiting object;

But, this question is asking for the mass M, so, rearraging:

Transforming light-years in metres and dividing by 2 to find the radius:

r = (15.9.461 x 10¹⁵)· = 70.9575

M =

M = 42.553.kg

The mass of the massive object at the center of the ring is 42.553.kg.

i think its

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.