Question

The black hole at the center of the Milky Way has a mass of 4 million solar masses and is located at a distance of 8 kpc from Earth. What is the Schwarzschild radius of this black hole? What angle would its diameter span on the sky, measured in milliarcseconds (mas). b) 10 points Suppose an object on the surface of the Moon (distance 4 × 108 m from Earth) covered the same angle as the black hole at Milky Way’s center. What would the physical size of this object be, in meters?

Answer 1

(a) The Schwarzschild radius is given by,

Substituting values we get, (All units are converted to SI)

The angle subtended can be calculated by, (r is the distance to the object and l is the arc length)

Substituting values we get, (here arc length is the diameter and distance to the object is given)(All units are converted to SI)

(b) Now here we have to calculate l value, the angle subtended is the same as the above part, and the distance to the object is given. Hence we can write,

Substituting values we get.