;-)
Then also you agree with me that we must introduce another, a further mathematical constant: A matter-space-time-interwoven-constant. Because "collapsing space-time" "swallows" "matter", is "interwoven", but "expanding space-time" does not "take along" "matter", is not "interwoven"-).
Let's fix the size of this constant approximately at: Little boys, whom the "expanding space-time" inflates their costume to adult size out of gratitude for their belief in it, and: "scientific institutes" popping up in space-time-holes, where these little boys can be dropped off by their parents or their thigh-knocking girlfriends by day, so that they know everytime where they can call or pick them up;-)
Here's the Titius-Bode relation plotted against the actual distances of planets from the Sun.
The relation comes from starting with a simple arithmetic progression of numbers:
0, 3, 6, 12, 24, 48, 96, 192, 384.
Note that each number is twice the previous. Then, by adding 4 to each number and dividing the result by 10, this yields a sequence of numbers that roughly corresponds to the spacing of planets in our solar system out to Uranus (in AU).
https://astrobites.org/2014/05/19/t...racteristics with any extrasolar counterparts.
The relation comes from starting with a simple arithmetic progression of numbers:
0, 3, 6, 12, 24, 48, 96, 192, 384.
Note that each number is twice the previous. Then, by adding 4 to each number and dividing the result by 10, this yields a sequence of numbers that roughly corresponds to the spacing of planets in our solar system out to Uranus (in AU).
https://astrobites.org/2014/05/19/t...racteristics with any extrasolar counterparts.
I seem to have recovered from a temporary mind warp caused by @cumbb and his relentless bombardment of junk "Electric Universe" science! I realised the Photon is massless, so Stephen J. Crothers really doesn't know much about escape speed. Phew! 🙂
Bode's Law is of course mere NUMEROLOGY. Kepler wasted much time on "The Music of the Spheres" which attempted to find the pattern of our Solar System planets before finding his true metier in Elliptical orbits.
My current interest is just how BIG can Black Holes get?
Very big indeed it seems.
This pair are substantial at approx. 1.8 x 10^10 Solar masses for the Primary. That is an extremely large number.
This one, Abell 1201 BCG is even bigger at around 3 x 10^10 Solar masses:
https://www.bbc.co.uk/news/uk-england-tyne-65109663
https://en.wikipedia.org/wiki/Abell_1201_BCG
https://en.wikipedia.org/wiki/List_of_most_massive_black_holes
There may be some sort of ultimate limit on size around this figure, but essentially these things have as much mass as our entire Milky Way Galaxy.
It does not surprise me that these things have huge electromagnetic fields leading to jets and all sorts of radio noise when you consider the accretion disk rotating around it at near light-speed.
In fact the Maths must be similar to what goes on in the Hydrogen Atom's spherical harmonics:
Which pretty much explains the Periodic Table of Elements.
A subject important in Chemistry which I used to enjoy before discovering Physics. I set out to obtain as many of them as possible for my home laboratory, but found certain of them hard to get, especially Plutonium 239.
I didn't know why at the time... 😕
Bode's Law is of course mere NUMEROLOGY. Kepler wasted much time on "The Music of the Spheres" which attempted to find the pattern of our Solar System planets before finding his true metier in Elliptical orbits.
My current interest is just how BIG can Black Holes get?
Very big indeed it seems.
This pair are substantial at approx. 1.8 x 10^10 Solar masses for the Primary. That is an extremely large number.
This one, Abell 1201 BCG is even bigger at around 3 x 10^10 Solar masses:
https://www.bbc.co.uk/news/uk-england-tyne-65109663
https://en.wikipedia.org/wiki/Abell_1201_BCG
https://en.wikipedia.org/wiki/List_of_most_massive_black_holes
There may be some sort of ultimate limit on size around this figure, but essentially these things have as much mass as our entire Milky Way Galaxy.
It does not surprise me that these things have huge electromagnetic fields leading to jets and all sorts of radio noise when you consider the accretion disk rotating around it at near light-speed.
In fact the Maths must be similar to what goes on in the Hydrogen Atom's spherical harmonics:
Which pretty much explains the Periodic Table of Elements.
A subject important in Chemistry which I used to enjoy before discovering Physics. I set out to obtain as many of them as possible for my home laboratory, but found certain of them hard to get, especially Plutonium 239.
I didn't know why at the time... 😕
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The supermassive black hole at the heart of the Milky Way has a mass of four millions times that of the Sun.
Its mass is still very small compared to the 200 billion solar masses of our galaxy.
A billion solar mass black hole would have an event horizon 3 billion km in radius, roughly the distance of Neptune to the Sun.
The resulting density would be roughly 1/1000 of a gram per cc - and that’s the density of air!
So, if you were to enclose the solar system out past Neptune in a giant sphere and fill it with air, would it be a black hole?
I read it here: https://www.discovermagazine.com/the-sciences/ten-things-you-dont-know-about-black-holes
Its mass is still very small compared to the 200 billion solar masses of our galaxy.
A billion solar mass black hole would have an event horizon 3 billion km in radius, roughly the distance of Neptune to the Sun.
The resulting density would be roughly 1/1000 of a gram per cc - and that’s the density of air!
So, if you were to enclose the solar system out past Neptune in a giant sphere and fill it with air, would it be a black hole?
I read it here: https://www.discovermagazine.com/the-sciences/ten-things-you-dont-know-about-black-holes
I do actually listen to you, Galu. You seem to have a pretty sharp Scientific Mind... unlike some others I could mention. 🙄
It surprises me how undense extremely large Black Holes are.
I noted your previous remarks that large ones are very insubstantial in terms of Mass density, or as I generally prefer to call it, Energy or Information density.
https://en.wikipedia.org/wiki/Information_theory
As thin as air.
I am currently still awaiting my intended primer on General Relativity, because eBay is occasionally slow in supplying the goods:
Much as I liked the glamour of Quantum Mechanics, I think I neglected the more mundane Classical General Relativity.
A worthy topic, IMO. Many subtleties lie within. I am not even sure I see the need for a Quantum Theory of Gravity.
It surprises me how undense extremely large Black Holes are.
I noted your previous remarks that large ones are very insubstantial in terms of Mass density, or as I generally prefer to call it, Energy or Information density.
https://en.wikipedia.org/wiki/Information_theory
As thin as air.
I am currently still awaiting my intended primer on General Relativity, because eBay is occasionally slow in supplying the goods:
Much as I liked the glamour of Quantum Mechanics, I think I neglected the more mundane Classical General Relativity.
A worthy topic, IMO. Many subtleties lie within. I am not even sure I see the need for a Quantum Theory of Gravity.
How BIG can a "Black Holes" get?
As a rule, "black holes" assume the size of the skulls of believers. And even the shapes;-)
Aside: Is there a "scientific"!!! proof for "photons" as physical phenomenon or are also here misinterpretations of (mis)observations on the way? And how would the "photon" run through bended "space-time" look like. Even an exact observation and exact description of dented rubber blankets would allow statements about this;-) But for this you would had to understand "space" and "time";-)
As a rule, "black holes" assume the size of the skulls of believers. And even the shapes;-)
Aside: Is there a "scientific"!!! proof for "photons" as physical phenomenon or are also here misinterpretations of (mis)observations on the way? And how would the "photon" run through bended "space-time" look like. Even an exact observation and exact description of dented rubber blankets would allow statements about this;-) But for this you would had to understand "space" and "time";-)
... that helps to "see" "1" "phenomenon", that we interpret as ""1 Photon".
Like this picture of a "phenomenon" which we interpret as a "black hole".
... want,
... simply state;-)
Without pointing out further conceivable interpretations.
Without mentioning the high technical effort to "construct" this "image" (-ination). Without mentioning all our ignorance and speculations, circular reasoning, disregarding logic, allowing contradictions, methodological errors, omitting further observations, limiting observation and more;-)
What is assured scientific statement: once in the heads you do not get it out;-)
Like this picture of a "phenomenon" which we interpret as a "black hole".
... want,
... simply state;-)
Without pointing out further conceivable interpretations.
Without mentioning the high technical effort to "construct" this "image" (-ination). Without mentioning all our ignorance and speculations, circular reasoning, disregarding logic, allowing contradictions, methodological errors, omitting further observations, limiting observation and more;-)
What is assured scientific statement: once in the heads you do not get it out;-)
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Some posts seem to be forgetting that things currently don't tie up so new unknown substances and energies are being looked for.
There is another factors as well. I mentioned an astronomer that lost his funding looking at aspects that don't fit.
There is also another bloke that aught to be pretty famous for the work he did but questions big bang ideas. Actually he seems to be the person that gave rise to the term trying to explain it to the public. Far bit of reading
https://en.wikipedia.org/wiki/Fred_Hoyle
https://en.wikipedia.org/wiki/Nucleosynthesis
Notice what happened when the accolades were handed out. He wasn't keen on the big bang and developed another theory eventually. Bad news for him, some don't want those questions kicking around. I've read some of his books the one on relativistic maths proved too much. He's even done work in that area. Some quotes in the wiki are very probably out of context especially anthropic aspects.
This wouldn't be the first time this area of science has worked itself into a cul-de-sac. If that is the case it can be extremely difficult to get out.
As mentioned earlier in the thread, the term "Big Bang" was an expression coined by Fred Hoyle to belittle a theory he very much disliked.
He totally rejected the "Big Bang" theory and believed instead in the "Steady-State" theory of the universe.
https://www.thoughtco.com/steady-state-theory-2699310
In 1964, he wrote prophetically:
"More and more the professions will cross over into the entertainment field. Those of us who are not employed directly in industry will come to realize that what we are really in is 'show biz'."
The evidence for the Big Bang lies in the presence of the cosmic microwave background radiation (CMBR).
The initial flash of light created by the Big Bang in our region of space is still spreading out into distant space.
By the same token, light that was created by the Big Bang in distant regions of space is currently travelling towards us.
Due to the expansion of the universe this light reaches us, not as visible light, but stretched out in wavelength to become microwave radiation - the CMBR.
So, in whatever direction we look, we see the remnants of the light from the Big Bang.
This is consistent with the idea that the Big Bang took place everywhere at the same time and not just at a single point in space.
This is a deeply touching moment in the History of Mathematics;
I am very fond of the late John Horton Conway. I consider him absolutely the Tops in recent Mathematics, even if he really could cure himself of scratching his face.
If you don't understand the j-invariant and the Monster Group, well, you really don't know what is going on!
https://en.wikipedia.org/wiki/J-invariant
https://en.wikipedia.org/wiki/Monster_group
So could we move on to productive Science here? I am well-known for concise solutions to Mathematical problems. And so should you be.
Just sayin'. After all, Life is Short. So let's get focussed on stuff that matters. 🙂
I am very fond of the late John Horton Conway. I consider him absolutely the Tops in recent Mathematics, even if he really could cure himself of scratching his face.
If you don't understand the j-invariant and the Monster Group, well, you really don't know what is going on!
https://en.wikipedia.org/wiki/J-invariant
https://en.wikipedia.org/wiki/Monster_group
So could we move on to productive Science here? I am well-known for concise solutions to Mathematical problems. And so should you be.
Just sayin'. After all, Life is Short. So let's get focussed on stuff that matters. 🙂
Yes, as Black Holes become more massive, their density decreases.
The mathematics says that N times the mass drops the density by a factor of N squared, e.g., 10 times the mass results in 1/100th of the density.
A Black Hole of three times the Sun’s mass will have an event horizon radius of about 9 km. That means it has a huge density, about two quadrillion grams per cubic cm (2 x 10^15).
Mathematics, the science of structure, order and relation (according to Britannica).
Yes, we could do with some structure around here! 😀
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I’m wondering if Bode’s law applies to planets that form naturally out of an accretion disk around a proto star. Might be if planets are captured or later have their orbits perturbed, the law doesn’t cover that.
Prof Cox speaks about how either Jupiter or Saturn (can’t recall) appears to have spent time in what is now the inner planet orbits before moving out to their present location. Interestingly, you’d expect the gas giants to be closer to their host star because that’s where generally there’s more material to form large planets early in a solar system’s history. Exonplanet observations Seem to bare this out - not 100% but in many cases gas giants are located close to their host stars.
Prof Cox speaks about how either Jupiter or Saturn (can’t recall) appears to have spent time in what is now the inner planet orbits before moving out to their present location. Interestingly, you’d expect the gas giants to be closer to their host star because that’s where generally there’s more material to form large planets early in a solar system’s history. Exonplanet observations Seem to bare this out - not 100% but in many cases gas giants are located close to their host stars.