Astronomers believe that there is a massive black hole at the center of the Milk

Question

Astronomers believe that there is a massive black hole at the center of the Milky Way galaxy. What evidence is there for that?

A group of astronomers have observed a star "S2" in a 15.2-year orbit around the center of the galaxy. They measured the period of revolution T = 15.2 years, the eccentricity of the elliptical orbit e = 0.87, and the semimajor axis of the orbit a = 4.62 mpc. [The unit: mpc = milli-parsec = 0.001 parsec.]

(A) Calculate the mass of the compact object about which S2 is revolving.

(B) Compare the mass to the mass of the sun.

(C) Compare the radius of the orbit of S2, to the size of our solar system.

Explanation / Answer

(a) T=2(a3/GM) -->M=42a3/GT2 = (4*(3.14159^2)*(4.62*10^-3*3.0856*10^16)^3)/(6.67*10^-11*(479665275^2))

Hence M=7.45249022 × 1036 kg

(b)M/Msun = 3.747*10^6, the compact object is 3.747*10^6 times more massive than the sun

(c)Not sure what it means by radius but i list 3 meaningful distances

size of solar system(at the edge of the Oort cloud) ~ 100AU=1.49598*10^13 m

a:semi-major axis= 4.62*10^-3*3.0856*10^16= 1.4255472 × 1014 m

perihelion=a(1-e)=  1.4255472*10^14*91-0.87) = 1.85321136 × 1013

aphelion=a(1+e)= 2.66577326 × 1014

as calculateed the size of the orbit is a little larger than the size of the solar system, during perihelion the orbits are about the same sized.

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