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: 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 = [tex]\sqrt{\frac{GM}{R} }[/tex], where
v is the speed;
G is a constant: G = 6.67*[tex]10^{-11}[/tex][tex]\frac{m^{3} }{kg.s^{2} }[/tex]
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:
[tex]M = \frac{v^{2}.R }{G}[/tex]
First, we change R from light years to km:
1km=1.057*[tex]10^{-13}[/tex]
R= [tex]\frac{15}{2*1.057.10^{-13} }[/tex]
Calculating mass:
M = [tex]\frac{2^{2}*10^{4}*14.2*10^{13} }{6.67*10^{-11} }[/tex]
M = 4.25*[tex]10^{28}[/tex] kg
A solar mass is the standard unit of mass. It is approximately 2*[tex]10^{30}[/tex]Kg and can be used for comparison: A single star cannot be more than 50 solar masses.
50 solar masses = 50*2*[tex]10^{30}[/tex] = [tex]10^{32}[/tex] kg
Comparing the mass of the object with this parameter, we have
[tex]\frac{10^{32} }{4.25.10^{28} }[/tex] = 0.235.[tex]10^{4}[/tex] = 2.35.[tex]10^{3}[/tex]
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.