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.

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explanation:

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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