Thomas 'PointedEars' Lahn writes:

Martin Brown wrote:

(although the page on Sgr A itself says 4.1M sun and about 45AU)

You are confusing the radius of the region surrounding the assumed black
hole with the Schwarzschild radius of the black hole, whereas the former is
much larger. Note that for such a BH, the Schwarzschild radius is the
radius beyond which we can have *no* information instead (as it *is* the
radius of the *event horizon*).

The "45AU" size is the maximum radius of whatever "it" is, if it was any
larger, Star S14 would collide with it. So "it" must be smaller than 45
AU radius.

Since we know of no physics that allows for an object of 45 AU radius and a
mass of 4.1M sun, other than a black hole or something rapidly collapsing
into a black hole, this is excellent evidence of a black hole there.

Star S14 must be getting awfully close to grazing the event horizon.

That is possible, but not based on your argument, but based on the diagram.

For a Schwarzschild BH, the outer event horizon is the surface of a sphere
that has the Schwarzschild radius as its radius. 45 AU, the radius of the
space in which S14 is described to be orbiting, is not anywhere near
0.08 AU.

About 560 times the event horizon radius. However it is close enough to
likely have interesting relativistic effects. Another star (S0-102) gets
within 260 AU and reaches over 1% of the speed of light. S14 must be
really booking.