I know!
It's either Cygnus, Pegasus, Perseus, Cassiopeia, Andromeda, Auriga, Ursa Major or Ursa Minor!
Usual miserable murky skies last night. No chance of seeing the comet. Saved me shivering on the seafront after sunset...
First, the Subaru camera quiz answer:
I thought Capella because the brightest star is yellow, but it turns out to be Kochab and Polaris we are looking at:
I got a glimpse of Jupiter and its moons last night, but the Full Moon reduced my exposure time by a factor of 4.
I am wondering if can glimpse Europa since it is in the news with the Clipper space probe.
This is what I got on October 3, Ganymede and darker Callisto:
With a bit of luck, Europa might be doable on Sunday AM 20 Oct:
The very limit of the camera, Callisto is about 10 arcminutes max. Europa about 4 arcminutes at around magnitude 5, I think. Should be fun. Chance of the comet too. Maybe even the wretched Nova.
I have plans for Saturn and Titan too. But Titan is about magnitude 9 at 7 arcminutes.
The rings are quite closed at the moment, and it varies:
But below my camera resolution at 1 arcminute anyway.
https://skyandtelescope.org/observing/interactive-sky-watching-tools/
This will be a stretch.
First, the Subaru camera quiz answer:
I thought Capella because the brightest star is yellow, but it turns out to be Kochab and Polaris we are looking at:
I got a glimpse of Jupiter and its moons last night, but the Full Moon reduced my exposure time by a factor of 4.
I am wondering if can glimpse Europa since it is in the news with the Clipper space probe.
This is what I got on October 3, Ganymede and darker Callisto:
With a bit of luck, Europa might be doable on Sunday AM 20 Oct:
The very limit of the camera, Callisto is about 10 arcminutes max. Europa about 4 arcminutes at around magnitude 5, I think. Should be fun. Chance of the comet too. Maybe even the wretched Nova.
I have plans for Saturn and Titan too. But Titan is about magnitude 9 at 7 arcminutes.
The rings are quite closed at the moment, and it varies:
But below my camera resolution at 1 arcminute anyway.
https://skyandtelescope.org/observing/interactive-sky-watching-tools/
This will be a stretch.
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By Sunday, Oct. 20, the moon won't be a factor. That's just in time and should help make sure Sunday provides one of the darkest skies yet in which to see comet Tsuchinshan-ATLAS with the naked eye. It could be the final time...
I read it here: https://www.space.com/comet-tsuchinshan-atlas-visible-how-long
Comet Tsuchinshan-ATLAS seen over Whippoorwill Hill, in Bloomington, Indiana on Oct. 16, 2024.(Image credit: Josh Dinner/Future)
With a bit of luck....
https://www.yr.no/en/forecast/hourl...en/Stockholm/Värmdö Municipality/Hovnoret?i=1
//
https://www.yr.no/en/forecast/hourl...en/Stockholm/Värmdö Municipality/Hovnoret?i=1
//
What rubbish! To the LEFT of Arcturus, more like.
I think tonight might give a slim fighting chance in Portsmouth, UK. 20% cloud predicted at 20.00 Hrs BST.
This is the site the PROFESSIONALS use:
https://www.ventusky.com/
Looks like Ascot will be a wet bog today. Iresine (FR) will be champing at the bit in the 15.55.. 😀
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Very nice piece here from Ethan on time and space-time
https://bigthink.com/starts-with-a-...swab&utm_content=10/19/24+SWAB&rjnrid=1y4BlkP
https://bigthink.com/starts-with-a-...swab&utm_content=10/19/24+SWAB&rjnrid=1y4BlkP
The information in the article will be familiar to followers of this thread, but it's nice to have it all in the one place. 😎
In fact, we explored the term "spacetime interval" quite recently (page 230):
Minkowski proposed that the spacetime interval, s, is related to space and time by Pythagoras' theorem in four dimensions:
Where i is an imaginary unit (the square root of -1), c is a constant (the speed of light), and t is the time interval spanned by the space-time interval, s.
Now i squared is equal to minus one, so the spacetime interval is given by:
In the above equation, the 'second' becomes just another unit of length.
It's all quite a study really. I have downloaded some of Einstein's publications from Project Gutenberg:
https://www.gutenberg.org/ebooks/bookshelf/103
They are hard to read, black print on white, but actually it's mostly all there even back in the day.
I get on better with Motion Mountain Vol. 2 on Relativity, Special and General in PDF Dark Mode:
The 4-matrix can usually be simplified to a 2 matrix (x and t) in straightforward cases.
I have forgotten most of the Matrix stuff, bit I know the determinant of 1 is all important for a Conservation Law:
That's pretty much it with Special Relativity, with is in an inertial or non-accelerating frame. General Relativity is much deeper.
COMET NEWS!!!
I have got it.
I got the focus wrong, it wasn't where I expected. Higher in fact. It was faint in the twilight.
Those stars are in the Indiana Oct 16 picture too, and well to the left and higher than orange Arcturus:
The cloud rolled in and cut off my poorish efforts. But it looks quite an easy object now. Weather permitting....
https://www.gutenberg.org/ebooks/bookshelf/103
They are hard to read, black print on white, but actually it's mostly all there even back in the day.
I get on better with Motion Mountain Vol. 2 on Relativity, Special and General in PDF Dark Mode:
The 4-matrix can usually be simplified to a 2 matrix (x and t) in straightforward cases.
I have forgotten most of the Matrix stuff, bit I know the determinant of 1 is all important for a Conservation Law:
That's pretty much it with Special Relativity, with is in an inertial or non-accelerating frame. General Relativity is much deeper.
COMET NEWS!!!
I have got it.
I got the focus wrong, it wasn't where I expected. Higher in fact. It was faint in the twilight.
Those stars are in the Indiana Oct 16 picture too, and well to the left and higher than orange Arcturus:
The cloud rolled in and cut off my poorish efforts. But it looks quite an easy object now. Weather permitting....
Here's more on time and spacetime since Bonsai has reintroduced the topic:
In his theory of special relativity, Einstein told us that space and time can not be treated independently. Rather, they are "converted" into each other in such a way as to keep the speed of light constant for all observers.
However, the conclusion that space and time could be seen as components of a single four-dimensional spacetime came from Hermann Minkowski.
As Minkowski summed it up: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality".
Einstein initially dismissed Minkowski's four-dimensional interpretation of his theory, but changed his mind quickly as the language of spacetime proved to be essential in deriving his theory of general relativity.
P.S. I have distilled the above information from the work of others to provide a summary that is hopefully easy to follow.
In his theory of special relativity, Einstein told us that space and time can not be treated independently. Rather, they are "converted" into each other in such a way as to keep the speed of light constant for all observers.
However, the conclusion that space and time could be seen as components of a single four-dimensional spacetime came from Hermann Minkowski.
As Minkowski summed it up: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality".
Einstein initially dismissed Minkowski's four-dimensional interpretation of his theory, but changed his mind quickly as the language of spacetime proved to be essential in deriving his theory of general relativity.
P.S. I have distilled the above information from the work of others to provide a summary that is hopefully easy to follow.
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For some reason, the quote flag did not appear after I highlighted the following words:
COMET NEWS!!!
I have got it.
Well done Steve!
COMET NEWS!!!
I have got it.
Well done Steve!
Speaking of which ...
I follow the photographer on Twitter, he got a nice catch by his pic being the magazine's cover. https://x.com/johnkrausphotos
I follow the photographer on Twitter, he got a nice catch by his pic being the magazine's cover. https://x.com/johnkrausphotos
As a self-appointed Eco-warrior in my dotage, I have to notice that my learned friend @benb is profligate with huge 2.2Mb images. Surely this is wasteful in terms of CO2 emissions from electricity at diy's server farm?
Mr. M*sk seems similarly unconcerned with littering space with tens of thousands of St*rlink satellites which will be annoying Astronomers for centuries to come. And while his huge booster returned to Earth, the second stage is sleeping with the fishes or still up in space for all I know. Huge CO2 emissions from his cheap boosters too. Jeff Bezos' rockets just leave water as residue.
He should give huge amounts of dollars to politicians to support his efforts with electric cars and his rockets... Oh wait... HE DOES!
In this fearful age, our great consolation, as the great Hendrik Lorentz said, is advances in Physics.
https://www.gutenberg.org/ebooks/11335
Quite. He also mentions the existence of a fourth dimension, which, interestingly being the great Mathematician that he was, he considers to be wrong thinking:
You are probably familiar with the way Special Relativity explained the true meaning of Maxwell's Equations. of electromagnetism.
General Relativity predicted the accurate precession of the perihelion of Mecury, the bending of starlight in eclipses, and red shift in spectra from stars due to their beng down a gravitational well which was difficult back then.
He opened by repeating that amusing statement that, in his day, only 12 people understood Relativity.
Increasingly, I think that Matrix mechanics is a better way to do things than those tired old differential equations that were popular back in the day. And I sure am tired of hearing about a,b and c, Anne, Bob and Carol flashing torches at each other from their rockets whilst using a stopwatch. Relativity is self-evidently how the Universe works. No need to keep proving it with all those daft and boring thought experiments, IMO.
Mr. M*sk seems similarly unconcerned with littering space with tens of thousands of St*rlink satellites which will be annoying Astronomers for centuries to come. And while his huge booster returned to Earth, the second stage is sleeping with the fishes or still up in space for all I know. Huge CO2 emissions from his cheap boosters too. Jeff Bezos' rockets just leave water as residue.
He should give huge amounts of dollars to politicians to support his efforts with electric cars and his rockets... Oh wait... HE DOES!
In this fearful age, our great consolation, as the great Hendrik Lorentz said, is advances in Physics.
https://www.gutenberg.org/ebooks/11335
Quite. He also mentions the existence of a fourth dimension, which, interestingly being the great Mathematician that he was, he considers to be wrong thinking:
You are probably familiar with the way Special Relativity explained the true meaning of Maxwell's Equations. of electromagnetism.
General Relativity predicted the accurate precession of the perihelion of Mecury, the bending of starlight in eclipses, and red shift in spectra from stars due to their beng down a gravitational well which was difficult back then.
He opened by repeating that amusing statement that, in his day, only 12 people understood Relativity.
Increasingly, I think that Matrix mechanics is a better way to do things than those tired old differential equations that were popular back in the day. And I sure am tired of hearing about a,b and c, Anne, Bob and Carol flashing torches at each other from their rockets whilst using a stopwatch. Relativity is self-evidently how the Universe works. No need to keep proving it with all those daft and boring thought experiments, IMO.
Application of Einstein’s theory to Maxwell’s theory showed that electric and magnetic forces are not separate but are different manifestations of the same thing - the electromagnetic force.
The origin of the electromagnetic force exerted by a current-carrying conductor is the difference in charge density within the conductor caused by the relativistic Lorentz contraction of the moving electrons, even though their velocities are only millimeters per second!
I tried to explain it all on page 62!
As far as I know, Einstein worked all his stuff out from two principles:
1) The Speed of Light is the same for all observers,
2) The Laws of Physics are the same for all observers.
Learned Caltech Professor in Episode 43 shows how with a metal coil and a fixed magnet, you can either move the magnet while keeping the coil stationary, or move the coil while keeping the magnet stationary.
You get either an electric field E or a changing magnetic field B explanation for the force, which is pure Michael Faraday. But the real invariant is the 4-vector potential, and that is a Special Relativity thing.
Episode 42 is a treasure for Special Relativity:
Considerably better Comet A3 picture tonight:
I could not see a thing with my eyes except Arcturus and Vega, and conditions were terrible, but the camera cut through it. About 20 degrees high so quite easy.
Focussing was near guesswork in the gloom, but I repeated the shots several times.
I attach the full 30 x 20 degree picture if you want a close look. Attractive orange/blue double near the top. I think it is Beta Ophiucus, but not sure. The distinctive butterfly shaped head of Serpens Caput top right in the full image.
Enjoy the rare gap in the clouds! 😎
1) The Speed of Light is the same for all observers,
2) The Laws of Physics are the same for all observers.
Learned Caltech Professor in Episode 43 shows how with a metal coil and a fixed magnet, you can either move the magnet while keeping the coil stationary, or move the coil while keeping the magnet stationary.
You get either an electric field E or a changing magnetic field B explanation for the force, which is pure Michael Faraday. But the real invariant is the 4-vector potential, and that is a Special Relativity thing.
Episode 42 is a treasure for Special Relativity:
Considerably better Comet A3 picture tonight:
I could not see a thing with my eyes except Arcturus and Vega, and conditions were terrible, but the camera cut through it. About 20 degrees high so quite easy.
Focussing was near guesswork in the gloom, but I repeated the shots several times.
I attach the full 30 x 20 degree picture if you want a close look. Attractive orange/blue double near the top. I think it is Beta Ophiucus, but not sure. The distinctive butterfly shaped head of Serpens Caput top right in the full image.
Enjoy the rare gap in the clouds! 😎
Attachments
You always leave me wanting more, Steve!
Entry level:
The electromagnetic four-potential is a concept in physics that combines the electric and magnetic fields into a single four-dimensional vector. It is used in the theory of electromagnetism to describe the electromagnetic interactions between charged particles and fields. The four-potential provides a unified framework for understanding the behavior of electric and magnetic fields in a relativistic context.
Advanced level:
In the context of special relativity, electromagnetic four-potential is a joining together of the magnetic vector potential* and the (scalar) electrical potential. Since the electromagnetic four-potential is a mathematical four-vector, standard four-vector Lorentz transformation rules apply. Therefore, if the electric and magnetic potentials are known in one inertial reference frame, they can be simply calculated in any other inertial reference frame.
*As an illustration, the above diagram shows the magnetic field (top) and the magnetic vector potential (bottom) of a solenoid.
Attached is some mathematics. I just need one of your 10 year old child prodigies to explain it to me!
(Credit: multiple sources.)
Attachments
That orange star at the top of my comet picture is red giant Kappa Ophuici, magnitude 3.2!
https://en.wikipedia.org/wiki/Kappa_Ophiuchi
I detest Vectors. Horrible things. And all that algebra, which is even worse. We should have stuck with Quaternions (which do not commute, so are ideal for Quantum Mechanics) and Matrices!
Untangling the Electromagnetic four potential, which has a scalar electric part phi, and a vector magnetic part A identified by the arrow above:
https://en.wikipedia.org/wiki/Electromagnetic_four-potential
What the heck is that triangle thing? Divergence or its differential, I think. The upside down V thing is the horrible Vector Cross Product X.
(Horrible because it invents a third dimension to a two dimensional problem.)
We have just seen the same equation:
The Matrix part is easy. It is just the 4-Matrix of the simpler 2-Matrix with a Lorentz factor Gamma, and a velocity factor Beta of v/c.
So when sage Paul Dirac was baffling and alarming young whippersnapper Dick Feynman about his QED theory by asking "Is it Covariant?", he was really just asking if his new fangled theory was Lorentz covariant.
https://en.wikipedia.org/wiki/Lorentz_covariance
Sort of thing a child of ten would ask, IMO. Otherwise its simply not going to work! 🤣
https://en.wikipedia.org/wiki/Kappa_Ophiuchi
I detest Vectors. Horrible things. And all that algebra, which is even worse. We should have stuck with Quaternions (which do not commute, so are ideal for Quantum Mechanics) and Matrices!
Untangling the Electromagnetic four potential, which has a scalar electric part phi, and a vector magnetic part A identified by the arrow above:
https://en.wikipedia.org/wiki/Electromagnetic_four-potential
What the heck is that triangle thing? Divergence or its differential, I think. The upside down V thing is the horrible Vector Cross Product X.
(Horrible because it invents a third dimension to a two dimensional problem.)
We have just seen the same equation:
The Matrix part is easy. It is just the 4-Matrix of the simpler 2-Matrix with a Lorentz factor Gamma, and a velocity factor Beta of v/c.
So when sage Paul Dirac was baffling and alarming young whippersnapper Dick Feynman about his QED theory by asking "Is it Covariant?", he was really just asking if his new fangled theory was Lorentz covariant.
https://en.wikipedia.org/wiki/Lorentz_covariance
Sort of thing a child of ten would ask, IMO. Otherwise its simply not going to work! 🤣
Perhaps we should take a step (leap?) back and explain what 'transformations' are all about.
Suppose we occupy a frame of reference (S) where the spatial coordinates and time are denoted by x, y, z, and t.
How would these coordinates transform to another frame of reference (S') that is moving at a velocity, v, relative to ours?
For simplicity, assume that this relative velocity is along the x-axis.
In Newtonian mechanics the transformations are simple: y, z, and t remain the same, but x' = (x - vt).
Hence:
x' = (x - vt)
y' = y
z' = z
t' = t
In Einsteinian mechanics, however, we have to take into consideration x contraction and t dilation by applying Lorentz transformations:
And here are the Lorentz transformations being converted into matrix form:
I was never too hot on matrices, but understand they have been used in computer graphics to represent rotations and other transformations of images.
Suppose we occupy a frame of reference (S) where the spatial coordinates and time are denoted by x, y, z, and t.
How would these coordinates transform to another frame of reference (S') that is moving at a velocity, v, relative to ours?
For simplicity, assume that this relative velocity is along the x-axis.
In Newtonian mechanics the transformations are simple: y, z, and t remain the same, but x' = (x - vt).
Hence:
x' = (x - vt)
y' = y
z' = z
t' = t
In Einsteinian mechanics, however, we have to take into consideration x contraction and t dilation by applying Lorentz transformations:
And here are the Lorentz transformations being converted into matrix form:
I was never too hot on matrices, but understand they have been used in computer graphics to represent rotations and other transformations of images.
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