[Since I have temporarily disengaged my killfile anyway …]

Michael Moroney amok-crossposted to 3 newsgroups, *despite* F’up2 being
already set:

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.

No, if the "central" body’s radius would be _that size or larger_, the
"orbiting" S14 would collide with it, assuming that the description that S14
comes as close to that body’s *center of mass* as 45 AU is correct.

So "it" must be smaller than 45 AU radius.

That much is true. And I have just *calculated* how small or large "it"
*really* must be if it is a black hole, given this mass: about 0.08 AU,
which is *much* smaller than 45 AU. (Can you not read?)

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.

Not even wrong. Rather, *any* object can have a radius of *45 AU* and a
total mass of about 4.1 million solar masses. (Homework assignment: Look up
statistics of celestial objects to find at least one such object.)

And an object that has either a mass of 4.1 million solar masses *and* a
radius of about 0.08 AU or less, or a radius of 45 AU and a mass of

rₛ = 2 G M∕c²

M = c² rₛ∕(2 G)

M(r = 45 AU) ≈ 4.533 × 10³⁹ kg ≈ 2.28 × 10⁹ M☉ [thanks, Wolfram|Alpha]

(2.28 *billion* solar masses, short scale) or *more*, must be a black hole.

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.

You don’t say!

However it is close enough to likely have interesting relativistic
effects.

You probably mean “cause”, not “have”.

Another star (S0-102) gets within 260 AU and reaches over 1% of
the speed of light.

The *special*-relativistic effects (and *those* are concerned when it comes
to relative speeds) at 0.01 c (≈ 30'000 km∕s; according to Wolfram|Alpha,
the typical CRT electron speed) are *negligibly small*:

γ(0.01 c) ≈ 1∕√(1 − 0.01²) ≈ 1.00005 ∎

As a rule of thumb, as far as relative speeds are concerned, things get
interesting at and over about 0.42 c (42 % c), where γ makes a difference
in lengths and times of 10 % or more of the rest frame values.

S14 must be really booking.

I do not know that idiom, but I presume it refers to high (orbital) speed
(as in bets on horse racing). If so, you would probably be correct _in the
≤ 45 AU vicinity of Sgr A*_.

However, sadly, you have no clue what you are talking about.


F’up2 news:sci.astro

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PointedEars

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