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 = $\sqrt{\frac{GM}{R} }$, where

v is the speed;

G is a constant: G = 6.67*$10^{-11}$$\frac{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:

$M = \frac{v^{2}.R }{G}$

First, we change R from light years to km:

1km=1.057*$10^{-13}$

R= $\frac{15}{2*1.057.10^{-13} }$

Calculating mass:

M = $\frac{2^{2}*10^{4}*14.2*10^{13} }{6.67*10^{-11} }$

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

$\frac{10^{32} }{4.25.10^{28} }$ = 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.