I wasn't aware until today that NASA had launched an experimental solar sail spacecraft into orbit.
The solar sail has an area equal to half that of a tennis court and is orbiting at twice the altitude of the ISS.
Its mission is to test out the technology in advance of the development of larger solar propulsion spacecraft.
Note to budding astrophotographer Steve:
The solar sail could appear as bright as Sirius in the night sky, although an app is required to locate it.
https://www.space.com/nasa-solar-sail-how-to-see-night-sky
The solar sail has an area equal to half that of a tennis court and is orbiting at twice the altitude of the ISS.
Its mission is to test out the technology in advance of the development of larger solar propulsion spacecraft.
Note to budding astrophotographer Steve:
The solar sail could appear as bright as Sirius in the night sky, although an app is required to locate it.
https://www.space.com/nasa-solar-sail-how-to-see-night-sky
Sounds like more Space Junk to me. Don't balloons always blow downwind? How are you going to get it back against the light pressure, even with some gravitational slingshot along "The Interplanetary Highway" of Lagrange points?
With all the fuss about Einstein and General Relativity, it has to be said that there is little money in it.
NO. Einstein, Shmeinstein. THE MAN is Claude Shannon. Nobody's ever heard of him, but your mobile phone wouldn't work without him:
Even this picture is compressed threefold to a jpg using his theories.
What it boils down to is the amount of information in a signal or channel is the sampling rate x the bit depth with error correction. Or in analog, the bandwidth x the signal to noise ratio.
This leads to a remarkable conclusion. No matter how rubbish your channel is, by repeating the message umpteen times you can achieve 100% accuracy!
So this astrophotographer might be feeling quite smug about his picture of Andromeda taken with better equipment than mine, a 200mm lens and a star tracker for 1.5 hours:
And my first 4 second effort may look puny at this stage:
But I know that if I stitch, say, 256 pictures together, work on signal to noise ratio via darker nights, I might rival him.
As a matter of interest, here is a visualisation of where we are in relation to Andromeda currently.
In fact the rest of the Universe will have pretty much run away when we hit Andromeda. This is because we seem to live in a De Sitter solution of General Relativity, where distant space actually has a repulsive force on us and hence moves away
https://en.wikipedia.org/wiki/De_Sitter_invariant_special_relativity
In fact Willem De Sitter was all buddy-buddy with Albert Einstein in the 1930's as they puzzled over a mathematical construction of Spacetime allowing for an expanding Universe. The idea is still being explored to explain the acceleration.
With all the fuss about Einstein and General Relativity, it has to be said that there is little money in it.
NO. Einstein, Shmeinstein. THE MAN is Claude Shannon. Nobody's ever heard of him, but your mobile phone wouldn't work without him:
Even this picture is compressed threefold to a jpg using his theories.
What it boils down to is the amount of information in a signal or channel is the sampling rate x the bit depth with error correction. Or in analog, the bandwidth x the signal to noise ratio.
This leads to a remarkable conclusion. No matter how rubbish your channel is, by repeating the message umpteen times you can achieve 100% accuracy!
So this astrophotographer might be feeling quite smug about his picture of Andromeda taken with better equipment than mine, a 200mm lens and a star tracker for 1.5 hours:
And my first 4 second effort may look puny at this stage:
But I know that if I stitch, say, 256 pictures together, work on signal to noise ratio via darker nights, I might rival him.
As a matter of interest, here is a visualisation of where we are in relation to Andromeda currently.
In fact the rest of the Universe will have pretty much run away when we hit Andromeda. This is because we seem to live in a De Sitter solution of General Relativity, where distant space actually has a repulsive force on us and hence moves away
https://en.wikipedia.org/wiki/De_Sitter_invariant_special_relativity
In fact Willem De Sitter was all buddy-buddy with Albert Einstein in the 1930's as they puzzled over a mathematical construction of Spacetime allowing for an expanding Universe. The idea is still being explored to explain the acceleration.
Solar sails would facilitate future low-cost deep space missions.
Over time, the small but continual thrust from sunlight can accelerate a spacecraft to very high speeds.
Such spacecraft would not be required to return to Earth!
De Sitter came up with the idea of a universe dominated by a positive cosmological constant (Λ) and no other matter sources.
However, cosmologists are not interested in pure de Sitter space because they know that there is other matter in the universe.
Modern cosmological theory is based on the Friedmann - Lemaitre - Robertson - Walker (FLRW) metric.
I therefore disagree that we currently live in a de Sitter universe, but it could be the universe that will exist in the distant future.
I thought the idea and big problem of String Theory is it works in an AdS (Anti De Sitter) Space, and we live in a dS (De Sitter) Space of positive scalar curvature... but I'll leave that to the FLRW experts. 🤣
Let me remind you of the Corona Borealis constellation, currently about 15 degrees high 2 hours after sunset, wherein we hope and expect to see the new Nova star shortly near Epsilon:
Imagine my consternation last night on finding 3 unidentified flying objects in it. 🙁
I took another picture just over a minute later:
By my estimates the smudge immediately above delta CrB is moving 3mm or 0.3 degrees in 2 seconds. Dividing 0.15 degrees per second into 360 degrees gives an orbital period of 2400s or 40 minutes.
This is vary bad maths indeed except as a ballpark guess. But interestingly, satellites in low earth orbit (< 800km) take about 90 minutes to orbit.
So I strongly suspect I have spotted Starlink satellites in the twilight!
Elon at SpaceX is planning around 6,000 of these things, as are many other players. Happily at this orbit they fall down after 5 years without further boosts.
This will bring Internet to the World via your Starlink dish, and it will be difficult for Governments to stop it, though threats to shoot them down have already been made by some..
Who'd have thought the future is Space Invaders?
I'll stop there. 🙂
Let me remind you of the Corona Borealis constellation, currently about 15 degrees high 2 hours after sunset, wherein we hope and expect to see the new Nova star shortly near Epsilon:
Imagine my consternation last night on finding 3 unidentified flying objects in it. 🙁
I took another picture just over a minute later:
By my estimates the smudge immediately above delta CrB is moving 3mm or 0.3 degrees in 2 seconds. Dividing 0.15 degrees per second into 360 degrees gives an orbital period of 2400s or 40 minutes.
This is vary bad maths indeed except as a ballpark guess. But interestingly, satellites in low earth orbit (< 800km) take about 90 minutes to orbit.
So I strongly suspect I have spotted Starlink satellites in the twilight!
Elon at SpaceX is planning around 6,000 of these things, as are many other players. Happily at this orbit they fall down after 5 years without further boosts.
This will bring Internet to the World via your Starlink dish, and it will be difficult for Governments to stop it, though threats to shoot them down have already been made by some..
Who'd have thought the future is Space Invaders?
I'll stop there. 🙂
We hear that our universe is flat (or so close to flat we can’t tell the difference), but then become confused when we hear that we live in a de Sitter universe, that is curved
The key to understanding this is that in 4D spacetime our universe is curved, but for the 3 dimensions of space it is flat.
It's not easy to understand, but the boffins say we can have a curved 4D spacetime with a flat 3D space embedded within it.
Cosmologists are using the FLRW model when they say 3D space is flat.
When we speak of de Sitter space, we really mean de Sitter spacetime.
A positive value of the cosmological constant Λ leads to positive 4D curvature, and to an accelerating expansion of spacetime - that's de Sitter space.
De Sitter space (correctly spacetime) is defined as being empty and devoid of matter (ordinary or dark). Its positive cosmological constant leads to the positive curvature that produces an accelerating expansion of spacetime.
However, because de Sitter space has no matter in it, but our universe does, one should not really say ours is a de Sitter universe.
Remember we have to take into account that the combination of ordinary and dark matter density opposes the acceleration from the cosmological constant. Whichever of these is stronger dictates whether the expansion of spacetime is accelerating or decelerating.
As the universe ages, matter will become so diluted that its effect on curvature will approach zero, and the cosmological constant will dominate. In effect, we are moving towards a de Sitter universe.
The growing number of low-Earth-orbit satellites is making observations from the world's telescopes more difficult.
The above image, taken by the ESO (European Southern Observatory), is of the 434 light-years distant star, Albireo.
Very nice article on Ramanujan
https://www.quantamagazine.org/srin.../?utm_source=flipboard&utm_content=topic/math
https://www.quantamagazine.org/srin.../?utm_source=flipboard&utm_content=topic/math
There's mention of 'Monstrous Moonshine' in that article!
Apparently 'Groups' underpin modern mathematics.
The 'Monster Group' has more than 8 x 10^54 elements and represents geometric rotations in a space with nearly 200,000 dimensions.
That's just plain crazy!
OK, I'm out of here. Call me a taxi! 😉
Apparently 'Groups' underpin modern mathematics.
The 'Monster Group' has more than 8 x 10^54 elements and represents geometric rotations in a space with nearly 200,000 dimensions.
That's just plain crazy!
OK, I'm out of here. Call me a taxi! 😉
Well, my Cox internet services has had four outages so far this year... short ones, true, but Telco equipment is designed to be 99.99999% available... so this is poor maintenance by Cox -ie: CHEAP ***.
So, I've decided to get Starlink.
Musk is my man.
I read that SpaceX currently operates more than 6,400 Starlink spacecraft in low Earth orbit (LEO).
About 250 of them are direct-to-cell (DTC) satellites.
(Smartphones in areas without cell coverage can route the phone signal to terrestrial networks via a DTC satellite.)
About 250 of them are direct-to-cell (DTC) satellites.
(Smartphones in areas without cell coverage can route the phone signal to terrestrial networks via a DTC satellite.)
I enjoyed that. I am not sure that continued fractions and partitions are exactly my bag. Ramanujan worked with what he had in a few old textbooks. And Prime Numbers are endlessly interesting. I still use the memorable Taxicab Number 1729 as part of my Internet Security...'nuff said. Hackers are everywhere. 🙁
I was hoping one of you Citizen Scientists would provide a more precise solution to my observations of Starlink satellites. Seems I have to do EVERYTHING round here... 🙄
I am mulling over an extremely clever Felix Klein type Projective Geometry solution to this.
I think I must calculate the familiar Cross-Ratio here, an INVARIANT in perspective:
https://en.wikipedia.org/wiki/Cross-ratio
See it is good to get away from local co-ordinate systems and look at the invariants. Quadratic equations may look different from your perspective, but they are all parabolas in the end:
I was always impressed with Felix Klein's book in the University library. which was called something like "Elementary Mathematics from a Higher Standpoint".
Why be a grub-like ground dweller crawling around, when you can soar like an eagle over the mathematical landscape. 🤣
I read that Starlink’s satellites remain in their train-like position in an intermediate (400 km) orbit for a few months after which they each go their separate ways.
Those that have already departed to their higher operational (550 km) orbit leave behind 'holes' in the trains, meaning the distance between each satellite isn’t equal.
Your a taxi yore a taxi!
At my first visit to Irland and leaving the local company office, this was the loud shear I heard from the lovely girl at the fornt desk ;.)
Took me a minute to figure it out :-D
//
In a moment between races at Horse Club in the Lord Palmerston Pub yesterday, I decided to enter "Pistol Pete" who claims to be a retired Maths Teacher into our Quiz for Pub MASTERMIND!
First Question on your specialist subject of mathematics, Pete:
What is the significance of 1729 in mathematics history?
Err, PASS...
Name three prime factors of 1729.
Er, PASS...
Why is the number 186,883 important?
Err, PASS...
Why is the j-invariant considered important in number theory:
https://en.wikipedia.org/wiki/J-invariant
Er, PASS.
What is the smallest number that is the sum of two squares two ways?
Err, PASS...
It is, of course, 50, known as the Clapham Omnibus number.
We now move onto General Knowledge. Who won the Sussex Stakes at Goodwood in 2024?
Er, PASS.
It was of course, Notable Speech. Running on Saturday in the Breeder's Cup.
Which Horse won the Grand National 3 times and name was "Murder" Backwards?
Er, Red Rum. 🙂
Congratulations, Pistol Pete, you have scored one point. Next weeks contender is Steve aka system7, who has chosen Horse Racing as his specialist subject. 🤣
First Question on your specialist subject of mathematics, Pete:
What is the significance of 1729 in mathematics history?
Err, PASS...
Name three prime factors of 1729.
Er, PASS...
Why is the number 186,883 important?
Err, PASS...
Why is the j-invariant considered important in number theory:
https://en.wikipedia.org/wiki/J-invariant
Er, PASS.
What is the smallest number that is the sum of two squares two ways?
Err, PASS...
It is, of course, 50, known as the Clapham Omnibus number.
We now move onto General Knowledge. Who won the Sussex Stakes at Goodwood in 2024?
Er, PASS.
It was of course, Notable Speech. Running on Saturday in the Breeder's Cup.
Which Horse won the Grand National 3 times and name was "Murder" Backwards?
Er, Red Rum. 🙂
Congratulations, Pistol Pete, you have scored one point. Next weeks contender is Steve aka system7, who has chosen Horse Racing as his specialist subject. 🤣
In nuclear physics, 50 is a 'Magic Number'.
The other most widely recognised magic numbers are 2, 8, 20, 28, 82, and 126.
There's a hypothetical element of atomic number 126. It's temporarily called Unbihexium (Ubh) until someone actually confirms its existence!
It all goes back to the Manhattan Project, closed nuclear shells and German physicist Maria Mayer.
Magic numbers were the bedrock of the nuclear shell model for which Mayer shared the 1963 Nobel prize in Physics.
https://en.wikipedia.org/wiki/Nuclear_shell_model