Question

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.

Observations of stars, as well as theories of the structure of stars, suggest that it is impossible for a single star to have a mass of more than about 50 solar masses. Can this massive object be a single, ordinary star?

Answer 1

Answer: Yes, it can be a single, ordinary star.

Explanation: To determine a mass of a star, we use the orbital speed formula, given by: v =
`\sqrt{(GM)/(R) }`, where

v is the speed;

G is a constant: G = 6.67*
`10^(-11)`
`(m^(3) )/(kg.s^(2) )`

M is mass of a massive object;

R is the distance between the object orbiting and the massive object;

The formula can be rewritten as:

`M = (v^(2).R )/(G)`

First, we change R from light years to km:

1km=1.057*
`10^(-13)`

R=
`(15)/(2*1.057.10^(-13) )`

Calculating mass:

M =
`(2^(2)*10^(4)*14.2*10^(13) )/(6.67*10^(-11) )`

M = 4.25*
`10^(28)` kg

A solar mass is the standard unit of mass. It is approximately 2*
`10^(30)`Kg and can be used for comparison: A single star cannot be more than 50 solar masses.

50 solar masses = 50*2*
`10^(30)` =
`10^(32)` kg

Comparing the mass of the object with this parameter, we have

`(10^(32) )/(4.25.10^(28) )` = 0.235.
`10^(4)` = 2.35.
`10^(3)`

From this, we know that 50 solar masses is greater than the small, massive object found. So, this object can be a single, ordinary star.