Martin Brown wrote:
On 24/08/2017 00:01, Michael Moroney wrote:
Jeff-Relf.Me @. writes:
Sagittarius A* is THOUGHT to be the location of a supermassive black
hole
https://en.wikipedia.org/wiki/Sagittarius_A*
"Thought", not "known".
"Thought" to a rather high degree of certainty.
Orbits of multiple stars are tracked orbiting "something"
with a mass of about 4.1 million solar masses but a radius of less than
45 AU (otherwise the star S14 would collide with it).
https://upload.wikimedia.org/wikiped...tre_orbits.svg
Wiki
The name is of the source is _Wikipedia_. Instead, “wiki” is now an
umbrella term for a live-editable community-maintained online source
(from “wiki”, the Hawaiian word for “quick”).
claims Sgr A
The name of the astronomical object is obviously S(a)g(itta)r(ius) A_*_
(emphasis mine).
has Rs ~ 1.3x10^10 M which I make to be about 80AU
What are you talking about?
The symbol for radius is usually a lowercase “r”.
The symbol for the SI unit of metre (or meter) is “m”, not “M”. [“M” is
reserved as the unit prefix for “mega”, from greek «μ*γας» /megas/ „great“,
meaning one million times the unit.]
The SI unit prefix “k” (for “kilo”, from Greek «χίλιοι» /kh*lioi/ „a
thousand“) means 1000 times the unit:
1 km = 1000 m.
So
1.3 × 10¹⁰ m = 1.3 × 10⁷ km
which is *much less* than
1 AU ≈ 150'000'000 km = 150 × 10⁸ km = 1.5 × 10¹⁰ km.
(1 AU is the average distance Terra–Sol.)
(in the section on Schwarzchild radii
(Karl) _Schwarzschild_
- which is suspect is out of date)
It is not. The Schwarzschild radius of a non-rotating, uncharged
(Schwarzschild) black hole (BH) is
rₛ = 2 G M∕c²,
where G is Newton’s gravitational constant, and M is the mass of the black
hole. A mass of
M = 4.1 × 10⁶ M☉ ≈ 8.153 × 10³⁶ kg,
where the mass of Sol (or solar masses) is
M☉ ≈ 1.988435 × 10³⁰ kg,
corresponds to a Schwarzschild radius of
rₛ ≈ 1.211 × 10¹⁰ m = 1.211 × 10⁷ km ≈ 0.08094 AU
The is very close to the aforementioned 1.3 × 10¹⁰ m.
See also:
http://www.wolframalpha.com/input/?i=Schwarzschild+radius&dataset=
(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*).
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.
--
PointedEars
Twitter: @PointedEars2
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