B Where Are the To-Scale Diagrams of Alpha Centauri's Orbits?

[Warp]

I sometimes get surprised by things that do not seem to exist in this world. For example, as far as I know, nobody has ever, during the entire history of photography, made a photographic time-lapse of lunar libration. There are plenty of computer renderings, but no photographic time-lapse showing the real thing. One would think that it's a topic interesting enough for at least someone to attempt, but apparently not. (If such a time-lapse exists, I have not found it.)

Ok, maybe getting good-quality photographs of the Moon every night for an entire month is too difficult. However, sometimes things don't seem to exist that should be much, much simpler.

Alpha Centauri is a rather interesting star system in that it's a triple star system, with two of the stars orbiting each other relatively close, and the third one orbiting them really, really far away. In order to get an idea of how far away, I would like to see a to-scale orbit diagram of the Alpha Centauri triple star system.

If such a picture exists, I have been unable to find it. It baffles my mind a bit why not. Is our closest stellar neighbor being a triple star system such a boring subject that nobody has bothered even just drawing a diagram (at least one that's to-scale)?

Well, considering how hard it is to find a diagram of the solar system orbits to-scale (they exist, but they seem to be quite a rarity) I suppose I shouldn't be that surprised.

 

[Baluncore]

It is only 5 years since the three Centauri were shown to be gravitationally bound.
https://en.wikipedia.org/wiki/Alpha_Centauri#Orbital_properties

 

[Vanadium 50]

As @Baluncore points out, it's only very recently that it has been determined that Proxima Centauri even has an orbit. But let's work some numbers. If Proxima's radius is one pixel, it's orbit is about 12 million pixels. So you need a 3000K monitor to display it. Not 3K. 3000K. 150 trillion pixels.

Not going to happen any time soon.

 

[Orodruin]

Having personally travelled* between the A and B stars and Proxima Centauri, I can tell you that it is faaaar and takes almost an hour even when flying a fictional superluminal spaceship.

* The computer game Elite: Dangerous takes place in a 1:1 procedurally generated replica of the galaxy. While most star systems are the results of a procedural engine, a good chunk of real systems have been placed in the game by hand (particularly of course the Sol system and other relatively nearby systems). One of those systems is Alpha Centauri so that is a pretty accurate to-scale rendition of that system. The A and B stars are not really distinguishable from the background when you are at Proxima.

In-game trivia:
The long trek from the A and B stars to Proxima is known as the Hutton run after a small orbital outpost Hutton orbital at Proxima. Making the Hutton run is considered a bit of a rite of initiation and there is a standing prank to try to convince new players that you can obtain one of the game’s most expensive ships for free at Hutton orbital.

 

[Ibix]

Vanadium 50's approach is a good one for this kind of diagram. Set a sensible size for the image of the smallest thing and see how big the largest thing is. Weakening his assumptions slightly and allowing that you're only interested in the orbits and not the stars, the Wiki page provided above says that A and B are between 11 and 35 AU apart and C is 13,000 AU away. Let's say we draw A and B's orbit as a 1mm × 3.5mm ellipse (and note that Pluto's orbit is comparable to this size). Then C is about 1.18m away on that scale. So that diagram is an ellipse a man could fit inside with a large grain of salt in the middle somewhere.

And that's why you don't see diagrams to scale. The ratios between the sizes of things of interest are crazy.

 

[Drakkith]

Alpha Centauri is a rather interesting star system in that it's a triple star system, with two of the stars orbiting each other relatively close, and the third one orbiting them really, really far away. In order to get an idea of how far away, I would like to see a to-scale orbit diagram of the Alpha Centauri triple star system.

What exactly do you want drawn on your diagram? Just their orbits? Their orbits compared to their sizes? Their orbits compared to the distance between the Sun and the other 3 stars?

 

[Tom.G]

As another relative example, using a common desktop screen resolution of 100 pixels-per-inch:

If the Earth is one pixel in size and you wish to show its complete orbit around the Sun, the screen size would be about 9 feet, or 2.75 meters, square.

If printed at 600 PPI, the paper would be 1.5 feet, or .46 meters square.

The above numbers assume a circular orbit of 93,000,000 miles diameter, however our orbit is about 1.6% eccentric, so add 1.6% to the above estimates.

So... you would have to remove your picture window to get the screen into the living room, and maybe raise your ceiling. If you use a 'rule-of-thumb' viewing distance being the screen diagonal, you would be 12.75 feet, 3.9 meters, away. That gives the angular size of that 1-pixel Earth being 0.22 arcseconds. Since the human eye can resolve around 0.7 to 1 arcsecond, you would not be able to see that Earth.

That's why to-scale orbital diagrams are somewhat scarce.

(As you may guess, I was getting bored and looking for something to do. )

 

[snorkack]

* The computer game Elite: Dangerous takes place in a 1:1 procedurally generated replica of the galaxy. While most star systems are the results of a procedural engine, a good chunk of real systems have been placed in the game by hand (particularly of course the Sol system and other relatively nearby systems). One of those systems is Alpha Centauri so that is a pretty accurate to-scale rendition of that system. The A and B stars are not really distinguishable from the background when you are at Proxima.

And that´s inaccurate.
Proxima is approximately 20 times closer to AB than Sun is.
https://en.wikipedia.org/wiki/Alpha...n,_Alpha_Centauri_AB_and_Proxima_Centauri.png
Note some nasty errors here. No proper error bars for the Proxima-AB distance. And I doubt that the Sun-Proxima-AB angle is known to minutes, let alone seconds!
In terms of magnitude, AB is about 6,5 magnitudes brighter from Proxima than Sun. A is about -6,5, B is -5,2. Both are brighter than Venus from Earth (-4,4). They are also far brighter than the fixed stars - the brightest fixed star from Proxima is Sirius, too, but at -1,2 dimmer than from Sun. Sun is +0,5 - conspicuous but comparable to Betelgeuse, Procyon or Beta Centauri. In the sky of Proxima b, Alpha Centauri AB are by far the brightest objects after Proxima and Proxima d

In terms of separation from each other... From Sun, AB true maximum separation is 26 seconds, but due to inclination and argument of apsides, the apparent maximum is just about 22 seconds and apparent minimum 1,7 seconds. What precisely is AB-s apparent orbit as viewed from Proxima - inclination, maximum and minimum separation, epochs? A separation in the region of 7...8 minutes would be easy for naked eye! It is quarter the width of full Moon.

 

[Orodruin]

And that´s inaccurate.
Proxima is approximately 20 times closer to AB than Sun is.
https://en.wikipedia.org/wiki/Alpha...n,_Alpha_Centauri_AB_and_Proxima_Centauri.png
Note some nasty errors here. No proper error bars for the Proxima-AB distance. And I doubt that the Sun-Proxima-AB angle is known to minutes, let alone seconds!
In terms of magnitude, AB is about 6,5 magnitudes brighter from Proxima than Sun. A is about -6,5, B is -5,2. Both are brighter than Venus from Earth (-4,4). They are also far brighter than the fixed stars - the brightest fixed star from Proxima is Sirius, too, but at -1,2 dimmer than from Sun. Sun is +0,5 - conspicuous but comparable to Betelgeuse, Procyon or Beta Centauri. In the sky of Proxima b, Alpha Centauri AB are by far the brightest objects after Proxima and Proxima d
In terms of separation from each other... From Sun, AB true maximum separation is 26 seconds, but due to inclination and argument of apsides, the apparent maximum is just about 22 seconds and apparent minimum 1,7 seconds. What precisely is AB-s apparent orbit as viewed from Proxima - inclination, maximum and minimum separation, epochs? A separation in the region of 7...8 minutes would be easy for naked eye! It is quarter the width of full Moon.

I think you just read way too much into the ”not distinguishable from background stars” part.

 

[russ_watters]

I sometimes get surprised by things that do not seem to exist in this world. For example, as far as I know, nobody has ever, during the entire history of photography, made a photographic time-lapse of lunar libration.

You didn't google it, did you?
https://www.google.com/search?q=lun...AAQCIAQCSAQCYAQDIAQjAAQE&sclient=gws-wiz-serp

 

[Vanadium 50]

The libration stuff is a continuation of his previous thread here. https://www.physicsforums.com/threads/lunar-libration-time-lapse-with-real-photographs.1010877/

That thread was a drive-by: after the initial post, the OP lost interest. I suspect it will be similar with this thread.

You didn't google it, did you?

Easier to toss a stink bomb and run. But it might be better to separate the stink bombs.

And since this thread is now completely off the rails...

The computer game Elite: Dangerous

Can you go from Earth to Alpgha Centauri? Should take about a day at the pace you describe.

 

[Orodruin]

Can you go from Earth to Alpgha Centauri? Should take about a day at the pace you describe.

No. Each star system is a separate instance. The game has two main forms of superluminal travel through made up physics: Hyperjumps and supercruise. Hyperjumps is essentially making small wormholes between gravity wells (i.e., to system "main" stars) and supercruise is essentially warp drive. Due to game limitations, if you just start travelling in supercruise towards the next system it will just not load. You will get to the correct position but the star won't be there, you need to make the hyperjump for the system to actually load.

 

[russ_watters]

Easier to toss a stink bomb and run.

Is it? I mean, it only took me like four words and three clicks. But then again, I am exceptionally talented.

 

[Vanadium 50]

You will get to the correct position but the star won't be there

So you'd need to drive to the right spot, and then make a zero distance jump? Sounds complicated.

 

[Vanadium 50]

Oh, and for fun. Proxima is actually visible in Alpha Centauri's sky (which is one more red dwarf than visible in Earth's sky). It would be about a 4th magnitude styar. (About because it's variable)

 

[snorkack]

Indeed. I think Proxima from Alpha is somewhere in Orion. But where could Alpha Centauri sky map with AB orbit be found? With epochs.
Especially relevant because of another instalment of Avatar...

 

[Drakkith]

Note some nasty errors here. No proper error bars for the Proxima-AB distance. And I doubt that the Sun-Proxima-AB angle is known to minutes, let alone seconds!

What do you mean? I can find both positions with a home telescope down to arcseconds. It seems to me to be a trivial problem to professional astronomers to come up with the Sun-Proxima-AB angle.

 

[snorkack]

What do you mean? I can find both positions with a home telescope down to arcseconds. It seems to me to be a trivial problem to professional astronomers to come up with the Sun-Proxima-AB angle.

No. What you can measure with a home telescope to arcseconds, and Hipparcos to milliarcseconds, is one angle of the triangle - the one at the Sun.
The two long sides of the triangle are both known only to the error of parallax - and Alpha is too bright for Gaia, so you´re stuck to Hipparcos data for that.
Which means that what you have is a small difference of a large distance, both with large relative errors to begin with. And these amplified errors make up the two remaining angles of triangle - the ones at Proxima and AB.

 

[Orodruin]

So you'd need to drive to the right spot, and then make a zero distance jump? Sounds complicated.

No, you just make the hyper jump - assuming your hyperdrive range is sufficient. Travelling in supercruise is what won’t change your instance. People have of course tried this with systems closer than Earth-Alpha Centauri.

If you are in a particular star sysem’s instance, the background sky will be generated based on the location of the center of the system - meaning that stars outside of the instance will not show any parallax regardless of how far you go in supercruise.

 

[Drakkith]

No. What you can measure with a home telescope to arcseconds, and Hipparcos to milliarcseconds, is one angle of the triangle - the one at the Sun.
The two long sides of the triangle are both known only to the error of parallax - and Alpha is too bright for Gaia, so you´re stuck to Hipparcos data for that.
Which means that what you have is a small difference of a large distance, both with large relative errors to begin with. And these amplified errors make up the two remaining angles of triangle - the ones at Proxima and AB.

Ah, I see now. I forgot that we need the distances as well as the angular positions to get the angles.

 

[Tom.G]

You didn't google it, did you?
https://www.google.com/search?q=lun...AAQCIAQCSAQCYAQDIAQjAAQE&sclient=gws-wiz-serp

And you didn't read the text below that video, did you?

Second paragraph, first line:

This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation.

 

[russ_watters]

And you didn't read the text below that video, did you?

Second paragraph, first line:

Whoops. Try this one instead:

https://www.space.com/full-moon-dance-one-year-video-animation

 

[Vanadium 50]

University of Colorado's Fiske Planetarium has a scale model of the solar system. The sun is about the size of a grapefruit, terrestrial planets are tiny specks, and gas giants are the size of small marbles. The model takes up the entire campus.

On this scale, placing Alpha Centauri where the sun us places Proxima Centauri in Colorado Springs. If you want both star systems on the same "map" one is in Boulder and the other is in Panama.

 

[Orodruin]

University of Colorado's Fiske Planetarium has a scale model of the solar system. The sun is about the size of a grapefruit, terrestrial planets are tiny specs, and gas giants are the size of small marbles. The model takes up the entire campus.

In Sweden there is a scale model of the solar system. Avicii arena (formerly Stockholm Globe Arena) is the Sun. The scale is 1:20000000. Venus is located outside my job and has the size of a big beach ball (62 cm diameter). Unfortunately, the Saturn model is not yet created so there is arguably something important missing.

Edit: Link: http://www.swedensolarsystem.se/en/

 

[Vanadium 50]

1:20000000

On that scale, if Alpha Centauri A were in Stockholm, there is nowhere on Earth you could place Proxima Centauri.

 

[Orodruin]

On that scale, if Alpha Centauri A were in Stockholm, there is nowhere on Earth you could place Proxima Centauri.

With the Sun where it is in the model, Alpha Centauri A would be 5.4 times further away than the Moon.

 

[Drakkith]

On that scale, if Alpha Centauri A were in Stockholm, there is nowhere on Earth you could place Proxima Centauri.

With the Sun where it is in the model, Alpha Centauri A would be 5.4 times further away than the Moon.

So will my model made out of paper mache and balsa wood survive in space??

 

[Orodruin]

So will my model made out of paper mache and balsa wood survive in space??

Is it 72 m in diameter. That would be the size of Alpha Centauri A at this scale?

 

[Drakkith]

Is it 72 m in diameter. That would be the size of Alpha Centauri A at this scale?

Oof. A paper mache sphere 72 meters in diameter is very roughly 1.37x10^8 kg in mass, or 137,000 metric tons. This is probably larger than the sum of every payload ever brought into Earth orbit by mankind.
For comparison (much rounding and many assumptions were made to simplify the calculations):
ISS: 445 tons
Apollo 10-17: roughly 971 tons combined (8x S-IVb with LOI fuel + attached CSM and LM).
Space Shuttle: Very roughly 16,000 tons (135 launches x 120 tons of orbiter + payload that reached orbit).

A user over at stack exchange wrote a program to calculate the sum of all payloads ever launched (link to post), but the website they got their data from doesn't appear to track things like the S-IVb and the fuel it contained to get the CSM and LM to the Moon, so it severely underestimates the total mass ever brought to Earth orbit in my opinion.
Their estimate as of 15 Feb 2022: 14,933,443 kg, or about 15,000 tons. Without even counting commercial companies like Space X or non-U.S. launches I'm already over 17,000 tons.

Either way, we'd have to add over 100,000 tons to either number to get close to the paper mache ball.

 

[Tom.G]

So will my model made out of paper mache and balsa wood survive in space??

"Survive", is a rather open-ended requirement.
But it would have a chance if all the trapped air and other gasses have a way out.Oh, don't forget the G-force of the launch.

Ahh, enough negativism, GO FOR IT!

And please notify us of the launch date.

 

[Vanadium 50]

137,000 metric tons

Hmmm...at that scale, might as well go 1:1. Then we can use pre-exising and pre-positioned objects.

 

[ezfzx]

I sometimes get surprised by things that do not seem to exist in this world. For example, as far as I know, nobody has ever, during the entire history of photography, made a photographic time-lapse of lunar libration. There are plenty of computer renderings, but no photographic time-lapse showing the real thing. One would think that it's a topic interesting enough for at least someone to attempt, but apparently not. (If such a time-lapse exists, I have not found it.)

Ok, maybe getting good-quality photographs of the Moon every night for an entire month is too difficult. However, sometimes things don't seem to exist that should be much, much simpler.

Alpha Centauri is a rather interesting star system in that it's a triple star system, with two of the stars orbiting each other relatively close, and the third one orbiting them really, really far away. In order to get an idea of how far away, I would like to see a to-scale orbit diagram of the Alpha Centauri triple star system.

If such a picture exists, I have been unable to find it. It baffles my mind a bit why not. Is our closest stellar neighbor being a triple star system such a boring subject that nobody has bothered even just drawing a diagram (at least one that's to-scale)?

Well, considering how hard it is to find a diagram of the solar system orbits to-scale (they exist, but they seem to be quite a rarity) I suppose I shouldn't be that surprised.

You mean like this?
I found this online 7 years ago.

 

[Devin-M]

I was able to approximate the Proxima Centauri system with 5 pictures...

First we have Alpha Centauri A to scale:

Next we have an imaginary planet Earth at 1 AU from Alpha Centauri A:

Next we have the orbits of Alpha Centauri A and Alpha Centauri B with an elliptic orbital distance varying between 35.6 AU and 11.2 AU:

Next we have Proxima Centauri's orbit around Alpha Centauri A & Alpha Centauri B, which has an eccentric orbit between 4300 AU and 13000 AU from the barycenter:

Finally we have the Sun, relative to Proxima Centauri at a distance of 4.2 light years:

Video Version:

 

[snorkack]

A simple problem of stellarium:
Suppose that you are in a stellarium whose dome is 40 m diametre. Size of Pantheon of Rome. Pretty big.
This is 20 m radius.
α Centauri is 260 000 AU away. Which means that at the ceiling, the scale is 13 AU for one mm.
That one mm represents 2 000 000 000 km. Which means 1 μm on your stellarium ceiling must represent 2 million km, and the image of α Centauri A (1 700 000 km diametre) on your stellarium ceiling must be a disc 850 nm across.
How about other conspicuous heavenly bodies, not as bright and of higher surface luminosities? Like, oh, the stars of Orion´s Belt - how big are their images on stellarium ceiling?

 

[Devin-M]

I numerically simulated an Earth sized planet in the Habitable Zone of Alpha Centauri A for a span of a million years to see whether the presence of Alpha Centauri B would significantly change the orbit or presence of liquid water within that time span... It didn't. Orbital period remained 1.49 years for 1 million years and the planet retained liquid water.

 

[snorkack]

Compare Moon.
Moon is strongly perturbed by Sun. For Sun is close to Moon, with only 13 months in a year.
The result is that the dragon moves rapidly - the eclipses do not only happen in two fixed seasons. And the apsides of the Moon move even more rapidly. Also the nominal eccentricity of the Moon changes rapidly.
And yet all these perturbations are periodic and stable. In a long term, the perturbations by Sun change neither the length of month, eccentricity of moon nor inclination of moon outside the range of their periodic variability.
A habitable zone planet of either α Centauri component, if on a low inclination orbit, would be similarly stable with purely periodic perturbations.

 

[Devin-M]

Strangely, one thing I was not able to successfully simulate was Proxima Centauri in a stable orbit around Alpha Centauri A & B...

First I set Alpha Centauri B to have an orbit around Alpha Centauri A with a Pericenter distance of 11.2 AU and an Apocenter distance of 35.6...

Next I set Proxima Centauri with a Pericenter distance of 4300 AU and an Apocenter distance of 13000 AU... I note the orbital speed near Apogee is on the order of the speed of an airplane... about 733 kilometers per hour.

The orbit immediately becomes unstable:



Even after I cheat by re-circularizing the orbit it still immediately becomes unstable.

 

[Vanadium 50]

Why do you think Proxima's orbit is stable? It probably isn't.

The period must be close to a million years. That's comparable to the motion of the "external" stars - for example, Gliese 710 will become the closest star to the sun in about a million years. The present orbit has almost certainly been perturbed by other stars, and it will continue to be perturbed in the future.

 

[Vanadium 50]

see whether the presence of Alpha Centauri B

I think your stability problem is with gas giants farther away - B perturbs the gas giant and the gas giant perturbs the terrestrials. If Jupiter's orbit where chaotic, well, there goes the neighborhood.

 

[snorkack]

I think your stability problem is with gas giants farther away - B perturbs the gas giant and the gas giant perturbs the terrestrials. If Jupiter's orbit where chaotic, well, there goes the neighborhood.

If gas giants are farther away.
If the gas giant is in the habitable zone, B perturbs or does not perturb it just as much as it perturbs a terrestrial planet or an asteroid.
What precisely is Pandora´s orbital period around Polyphemus?

 

[Ibix]

The orbit immediately becomes unstable:

Rounding error? To what precision are distances, velocities and accelerations stored? What's the time step and how is the integration performed?

 

[Devin-M]

There weren't any planets in the system, just 3 stars - Alpha Centauri A, Alpha Centauri B and Proxima Centauri, all with the appropriate masses.

This page describes the N-Body integrator: https://universesandbox.fandom.com/wiki/N-Body_Simulation

I did 2 more tests to try to make the system more stable, one of which was successful.

In the first (successful) test, Alpha Centauri A & B were simplified into a single star with their combined mass of 2 solar masses and 0 momentum. Then I placed Proxima Centauri in orbit with an apogee of 13000AU and a perigee of 4300 AU. This test remained completely stable and completed multiple orbits:



The next test, both Alpha Centauri A & B were used with the appropriate masses, but their orbits were simplified to have 0 eccentricity and 0 net momentum with a separation distance of 35.6 AU. Next Proxima Centauri was added with the appropriate mass, and placed in an orbit with an apogee of 13000AU and a perigee of 4300 AU. This test resulted in Proxima Centauri being flung from the system before completing a single full orbit:

 

[Devin-M]

I was able to get Proxima Centauri to complete multiple orbits at close to 400 AU from the barycenter... I also think I identified the problem with getting a semi-stable orbit solution. When you have 2 bodies you can just type in the orbital parameters and the resulting orbit comes out correctly, but when you have 3 bodies, typing in the desired orbital parameters doesn't give the correct results, probably because it can't compute the future time steps in advance. But by starting with an approximate orbit, then continually modifying the parameters I was able to bring the orbit into a state of metastability (skip to 8:00).

 

[Devin-M]

In this one by continually adjusting the paramaters in the beginning, I was able to get the orbit somewhat stable, somewhat close to the actual orbital parameters (but not exact - skip to 16:25 for final orbit)...

 

[Vanadium 50]

The issue of inner planet stability is separate from the issue of Proxima's stability.

Gas giants make inner planet stability more complicated. I would not be surprised if there are no terrestrial planets orbiting A if there are (maybe even were) any gas giants in the system.

Proxima's orbital stability is highly questionable. It's barely bound, and in its history lots of stars are likely to have made close approaches. I would not be in the least surprised if throughout its history it has been both bound and unbound. The age of Proxima is usually given assuming co-evolution with A and B, but there is not a lot of observational evidence there: models range between 4 and 7 Gy or so. If I had to bet, I'd bet that it co-formed rather than captured, but I don't think it's 100% settled.

 

[Devin-M]

You could have a gas giant in the habitable zone with an exomoon.

 

[snorkack]

You could have a gas giant in the habitable zone with an exomoon.

Just why I inquired about the orbital period of Pandora around Polyphemus.

 

[Devin-M]

There’s an unconfirmed observation of a potential Neptune sized gas giant in the habitable zone about 1.1 AU from Alpha Centauri A discovered in Feb 2021 but it has yet to be fully confirmed:

https://en.m.wikipedia.org/wiki/Candidate_1

The discovery image of Candidate 1, taken by the NEAR instrument at ESO's Very Large Telescope in 2021.

https://www.universetoday.com/150088/possible-super-earth-in-the-habitable-zone-at-alpha-centauri/