[Since I have temporarily disengaged my killfile anyway …]
Michael Moroney amok-crossposted to 3 newsgroups, *despite* F’up2 being
already set:
> Thomas 'PointedEars' Lahn <
Point...@web.de> 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>