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According to density wave theorem, some other questions here [and my basic understanding from it] the spiral arms of an spiral galaxy are fixed regions of space around it with higher gravity, where the "passing stars" undergo a higher gravitation between themselves and somehow slow down; just like some galactic speed bumps for stars. As the stars and matter pass through this speed bumps, they slow down, bust some new stars and after passing it, gonna speed up again.

The question however is, when a known observed star or sky region which is in front of us, passes through this arms, the distance between us decreases considerably because they are slowed down and we are not, and the observed sky region would seem distorted significantly. Since it takes 230 million earth years to have one orbit around milky way, the milky way has about 4~6 arms, the observable distance of sky for us is far enough, the chances of this phenomenon is quite high while in reality, we don't see distortions like this.

milky way arms

Here is a simple drawing to present my question. The red dots are earth and an observed star: My awful drawing Which part of my simple modelling is wrong?

I'm an amateur cosmology Wikipedia article-jumper, so forgive me if I get things wrong.

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    $\begingroup$ Perhaps the answer is "this happens, but it takes millions of years" So you don't see distortions from day to day... I can probably expand that into an answer if you think it is useful. $\endgroup$
    – James K
    Commented Dec 16, 2022 at 21:12
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    $\begingroup$ @JamesK I'll be thankful. Well the chances seem to be high, since there are a lot of this over-dense locations, and in the inner orbits of the milky way there seem to be more over-dense regions than "normal" regions. If we are able to see an star on the inner orbit, on the edge of entering an over-dense region, the observed phenomenon would be more present. does it happen to be more frequent than millions of years? $\endgroup$ Commented Dec 17, 2022 at 7:49

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The picture isn't quite right. The spiral arms are gravitational waves, the orbits of stars speed up as they approach (due to gravitational attraction of the matter in the arm) and slow down as they leave.

The scale of this picture is huge. Pretty much all the stars that we can see as stars are in the Orion spur (and under the circle marking the sun), and all are moving along with us. When we leave an arm we slow down but they will be slowing down too.

There are stars that are currently on the edge of an arm and are being accelerated or decelarated by the mass in the arm, but such stars will be very distant. And the acceleration takes millions of years.

It is a statistical acceleration of stars. If you take an individual star it may be affected gravitationally by its local gravitational field, but if you average out the accelerations of a large number of stars on the edge of an arm, their average acceleration will be towards the arm, due to the excess of matter in the spiral arm.

Observing these accelerations would be most challenging. The changes in velocity would only be noticeable over the millions of years it takes for a star to enter an arm. This is why the mechanism for the formation of spiral arms was discovered theoretically, not directly observed.

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It is believed that there are betwween one hundred billion and four hundred billion stars in our galaxy.

The Gaia space observatory is expected to have detected and measured the directions to about one billion stars, or about 0.25 to 1.0 percent of all the stars in the galaxy. Some of the stars detected by Gaia may be as far away as the galactic center, about 26,000 light years from Earth. But Gaia clearly has not detcected all the stars within a sphere with radius of 26,000 light years from Earth, since there would be tens of billons of stars within that radius.

Astronomers have detected individual stars much farther away than 26,000 light years, including stars millions of light years distant in other galaxies. As a science fiction fan and amateur astronomer I am very fmailiar with "the great and glorius S Doradus" in the Large Magellanic Clud, for example, which was considereed to be themost lumious star known for several decades.

In 2022 the most distant individual star observed was discovered to be about 28 billion years from Earth, and it was named Earendel. Of course only very rare circumstances would enable us to detect a star at such a great distance.

https://www.smithsonianmag.com/smart-news/astronomers-spot-the-most-distant-individual-star-ever-detected-in-outer-space-180979847/

If the question is asking about the stars visible fromEarth without opitcal aid, and the visible asterism and constellations in Earth's sky, there are only a few thousand stars luminous and/or close enough to Earth to be seen with unaided or "naked" eye. How many stars can be seen depends of the viewing conditions at the time and and place, and the abilities of the viewer's eyes.

Considering all the stars visible in all directions around Earth, the upper end on the estimates seems to be about 10,000 visible stars. Other estimates place the number of stars visible to the eye alone – surrounding the entire Earth – at more like 5,000. At any given time, half of Earth is in daylight. So only half the estimated number – say, between 5,000 and 2,500 stars – would be visible from Earth’s night side.

Plus, another fraction of those visible stars would be lost in the haze all around your horizon. That could bring you down to around 2,000, the number commonly used for these estimates. Just know that it varies depending on a number of factors.

https://earthsky.org/astronomy-essentials/how-many-stars-could-you-see-on-a-clear-moonless-night/

Each star has an actual luminosity or brighness, called its absolute magnitude, and an appranet brightness as seen with the naked eye or telescopes from Earth, called its apaprent magnitude. The apparent magnitude of a star is determined by its absolute magnitude, which varies greatly between stars, and by its distance from Earth, which also differs greatly.

The magnitude scale is such that higher magnitudes are less bright than lower magnitudes.

There is no distance so close to Earth that all the stars within that distance (not counting the Sun) are close and bright enough to be seen with the naked eye from Earth. Proxima Centauri, or Alpha Centauri C, is the closest star (except the Sun)to the solar system. It has an absolute magnitude 15.60, and an apparent magnitude of 10.43 to 11.11

https://en.wikipedia.org/wiki/Proxima_Centauri

But the farther from the Sun, the lower the percentage of the stars that will be visible with the naked eye from Earth, until at a distance of a few thousand light years even the brightest stars will not be visbile with the naked eye from Earth.

Here is a link to a list of the 92s tars not countngtheSun which appear brightest from Earth.

https://en.wikipedia.org/wiki/List_of_brightest_stars

They have apparent magnitudes between the brightest, sirius at -1.46 to the least bright on the list, Acrab, at plus 2.50. Higher magnitudes are dimmer. Their distances vary between the closest, Alpha Centauri A & B, at about 4.4 light years, to the most distant, Deneb, at about 2,600 light years.

And there is a similar distance distrubtion for the naked eye stars with higher apparent magnitudes.

A number of naked eye stars are probably much farther than Deneb.

The answers to this question discuss a number of candidates.

https://physics.stackexchange.com/questions/45759/what-is-the-farthest-away-star-visible-to-the-naked-eye

The variable star Rho Cassiopeaie is believed to be about 8,200 light years away,and is sometimes visible to the naked eye, which might make it the most distant naked eye star.

The very unusual Eta Carinae might be the most distant naked eye star. It is about 2,300 parsecs or about 7,500 light years from Earth. It is a multiple star and variable. at the present time it is brighter than apaprent magnitude 4.4 andthus anaked eye star. In 1886 it faded bleo wnaked eye sivisibity for a number of decades. And during the Great Eruption of 1837-1845 it greatly incresed in brightness, reaching -0.8 in 1843.

V762 Cassiopeaie is often claimed to be the most distant naked eye star. https://www.universeguide.com/star/5926/v762cassiopeiae

SN 1885 A was a supernova in the Andromeda Galaxy about 2,600,00 light years from Earth which reached an apparent magnitude of 5.85 on 21 August 1885 and dimmed to magnitude 14 6 months later. That is a little brighter than usual naked eye limit of about 6.5.

Anyway all of the few thousnd naked eye stars are within a few hundred or a few thousand light years from Earth, mixed in with millions of stars not luminous enough to be visible from Earth.

So I have to wonder how many of the naked stars that are in the same direction as the nearest spiral arm are closer to Earth than that spiral arm, and how many are in that spiral arm, and how many are farther away than that spiral arm. Naked eye stars in the opposite direction from the nearest spiral arm might not have their motions affected by it.

Here is a thought experiement. There are many asteroids in the asteroid belt in our solar system.

Nonetheless, hundreds of thousands of asteroids are currently known, and the total number ranges in the millions or more, depending on the lower size cutoff. Over 200 asteroids are known to be larger than 100 km,[46] and a survey in the infrared wavelengths has shown that the asteroid belt has between 700,000 and 1.7 million asteroids with a diameter of 1 km or more.[47]

https://en.wikipedia.org/wiki/Asteroid#Asteroid_belt

Suppose that people installed giant lamps on every asteroid so that it could be seen for tens of millions of miles, including from other asteroids passing nearby. As the asteroids orbited the Sun at different distances, speeds, etc. the "constellations" and "star" patterns formed by asteroid ights seen on the surfaces of other asteroids would sslowing change.

For example if one asteroid had an orbital period twice as long as a asteroid with an inner orbit, after the inner asteroid made on full orbit and was back in its original position, the other asteroid would have made only half an orbit and would be on the other side of the Sun from where it was one period of the innenr asteroid earlier.

Thus the directions to the various asteroids, and the "constellations" they made in the sky of one asteroid, would be constantly changing over the course of one orbital period of the viewing asteroid, and that orbital period would be only a few Earth years long.

And that is a similar situation to the orbits of the stars in our galaxy. The distances between stars and the directions between them change slowly as they orbit the center of the galaxy with different orbits. Thus the apprent constellations in the sky of the Earth are constantly slowly changing.

Here is a link to a list of stars which have passed within 5 light years of Earth within the last iive million years or will do so within the next five million years, as computed from their positions in 3 D space and their velocities toward or away from Earth and their sideways movements.

https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs#Distant_future_and_past_encounters

Nine of those stars have passed or will pass less than 2 light years from Earth. And three others have passed or will pass less than 1 light year from Earth. And those close encounters will change the orbits of both stars as they pass, including changing their orbital speed around the center of the galaxy.

At the Sun's distance from the center of the Galaxy, where a single orbit takes about two hundred and fity million years, a star is likely to spend 50 million or 100 million years between close encounters with a spiral arm that may change its orbital speed. And during that time it is likely to have tens, maybe hundreds, of close encounters with other stars which will change its orbital speed.

Since those stars are also moving sideways as seen from Earth (proper motion) they not only get brighter or dimmer but also seem to move relative to other stars. Thus the shapes of asterisms and constellatins change slowly over time until they are no longer recognizeable.

Here is a link to an article with an animation of the changes in the Big Dipper between 100,000 years in the past and 100,000 years in the future.

https://www.popularmechanics.com/space/deep-space/a20347/how-the-big-dipper-has-changedand-will-changeover-200000-years/

And here is a link to a video showing changes in Orion over hundreds of thousands of years.

https://www.space.com/37148-orion-constellation-changes-over-450000-years.html

And I think that unlessthe gravitational pull of spiral armsis very strong it will have a minor effect in changing stellar orbital speeds and the shapes of constellations compared to close encounters between orbiting stars.

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