Question

What is the Schwarzschild radius of the black hole at the center of the Milky Way? What

      is the ratio of the gravitational acceleration the Sun feels from this black hole to the

      gravitational acceleration the Sun feels from the entire Milky Way? Comment on the

      gravitational significance the black hole has on our Solar System.

Answer 1

The schwarzschild radius can be determined only when the mass of the star is known. It is not possible to determine the radius for this black hole mathematically as there are a wide variety of estimate which change rapidly. How ever,a star of 1 solar mass (the sun) needs to be crushed down to 3 KM across or a radius of 1.5 KM for it to become a black hole. stars with a larger solar mass will have a larger schwarzschild radius.

In 1916, Karl Schwarzschild obtained an exact solution^[2][3] to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition , the solution contained a term of the form ; where the value of making this term singular has come to be known as theSchwarzschild radius. The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century.

Parameters

The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi) while the Earth's is only about 9.0 mm, the size of a peanut. The observable universe's mass has a Schwarzschild radius of approximately 10 billion light years.

	(m)	(g/cm3)
Universe	4.46