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wd40
2011-Feb-17, 07:32 PM
Even though at 4.3 light years it's the closest star visible to the naked eye to us, even the largest optical device can barely determine directly the angular diameter of the Sun-size Alpha Centauri.

My question is: at what sort of closer distances would Alpha Centauri have to be for its actual stellar disc, as opposed to being a pin-point source of light, to be easily resolvable to a 1) a x600 home telescope, 2) x12 binoculars, and 3) the naked eye?

Is 1 light year enough? Or much closer?

Grey
2011-Feb-17, 08:45 PM
Here (http://en.wikipedia.org/wiki/Angular_diameter) is a discussion of angular size, including a list with various objects. The resolution of the human eye is about a minute of arc, but that's to separate two points. So to see disc, you'd probably need it to be a little larger than that. You can see that at their closest approaches, Venus and Jupiter are right around that value, so you've probably noticed that at times it seems like you can just barely make out that they aren't point sources. Alpha Centauri's angular size is about 8,500 times smaller than that, so to appear as large as Venus or Jupiter at their biggest*, it would have to be to be about 8,500 times closer. So that means about 0.0005 light years, or 32 astronomical units, which is just a little farther away than Neptune. Yes, that means that if we look at it the other way, from Neptune our Sun just barely has a visible disc. Which makes sense because here at 1 AU, 32 times closer, the size of the Sun is about 32 arc minutes.

* Which is big enough to make it clear that it's not a point source to the naked eye, show a small disc in even modest binoculars, and show a very clear disc with some detail visible in a small telescope.

Amber Robot
2011-Feb-17, 09:08 PM
Well, the naked eye has a resolution of 1 arcminute. If you assume that Alpha Centauri is the same size of the sun, then the stellar diameter is 1.39e6 km. So, to subtend 1 arcminute, it would have to be no farther than 4.78e9 km, better known as 5e-4 light year. That's only 32 AU!!

Did I do the math right?

Grey
2011-Feb-17, 09:12 PM
Did I do the math right?Well, you got the same result as me, so either we both got it right, or we both coincidentally made exactly the same mistake. :)

astromark
2011-Feb-17, 09:21 PM
Good answers... and a warning. As you get to a distance from where the disk is resolvable. So to does the magnitude become dangerous to your eye. Filters... please use filters.:razz:

chornedsnorkack
2011-Feb-17, 09:29 PM
Note that Jupiter and Venus are not dazzling. Toliman A would be - certainly at a distance where it might be resolved into a disc.

The disc of Sun can burn human eyes. Not accidentally, though. People can get around in sunshine, and when they accidentally look at the Sun, the eyes will react to blink and avert the gaze - and the eyes receive no permanent harm. And an accidental or quick glimpse on the Sun will promptly show that it is a disc.

But eyes can be damaged by intently staring at Sun against blink reflex. And crescent Sun at eclipse is said to be particularly perilous, perhaps because the smaller total luminosity of the narrow crescent fails to trigger blink reflex, yet the surface luminosity is still quite enough to burn eyes.

Would a star seen from afar, like Sun-like G star from 10...30 AU cause accidental eye damage by frequent unintentional dazzling? And would a disc, say, 3 minutes across be resolvable despite dazzle if it is as bright as Toliman A?

How would Toliman A look like from 10,7 AU (periapse distance of B minus appropriate distance from B to a habitable planet)?

Toliman A at periapse is about 80 times dimmer than Sun and thus 5000 times brighter than full moon. At apoapse it is 800 times dimmer than sun and 500 times brighter than Moon. Could any fixed stars (such as Sirius or Sun) ever be visible through a breathable atmosphere when Toliman A is above horizon?

x12 binoculars would point at about 120 AU. x600 home telescope would point at 6000+ AU. Proxima is about 15 000 AU. Precisely where is Proxima relative to the orbital plane and apside line of Toliman? What are the maximum and minimum distances of Toliman AB seen from Proxima? Would the orbit be easily observed from Proxima, and could the disc be resolved by a small home telescope?

For the matter, could any planets of Toliman A or B be seen from Proxima?

korjik
2011-Feb-17, 09:48 PM
Note that Jupiter and Venus are not dazzling. Toliman A would be - certainly at a distance where it might be resolved into a disc.

The disc of Sun can burn human eyes. Not accidentally, though. People can get around in sunshine, and when they accidentally look at the Sun, the eyes will react to blink and avert the gaze - and the eyes receive no permanent harm. And an accidental or quick glimpse on the Sun will promptly show that it is a disc.

But eyes can be damaged by intently staring at Sun against blink reflex. And crescent Sun at eclipse is said to be particularly perilous, perhaps because the smaller total luminosity of the narrow crescent fails to trigger blink reflex, yet the surface luminosity is still quite enough to burn eyes.

Would a star seen from afar, like Sun-like G star from 10...30 AU cause accidental eye damage by frequent unintentional dazzling? And would a disc, say, 3 minutes across be resolvable despite dazzle if it is as bright as Toliman A?

How would Toliman A look like from 10,7 AU (periapse distance of B minus appropriate distance from B to a habitable planet)?

Toliman A at periapse is about 80 times dimmer than Sun and thus 5000 times brighter than full moon. At apoapse it is 800 times dimmer than sun and 500 times brighter than Moon. Could any fixed stars (such as Sirius or Sun) ever be visible through a breathable atmosphere when Toliman A is above horizon?

x12 binoculars would point at about 120 AU. x600 home telescope would point at 6000+ AU. Proxima is about 15 000 AU. Precisely where is Proxima relative to the orbital plane and apside line of Toliman? What are the maximum and minimum distances of Toliman AB seen from Proxima? Would the orbit be easily observed from Proxima, and could the disc be resolved by a small home telescope?

For the matter, could any planets of Toliman A or B be seen from Proxima?

At the same luminosity of the Sun, Alpha Centauri at 32 AU should be about 1/1000 as bright, so about 8 magnitudes dimmer, or about magnitude -19. Quite a bit brighter than the moon.

antoniseb
2011-Feb-17, 10:22 PM
Just as a side note, I doubt that your eye would tell you it was seeing a disk any smaller than 3 minutes of arc.
So, I get the same distances as chornedsnorkack.

6000 AU is about six times the Aphelion distance of Sedna, but it is well inside the Oort Cloud, and it is about 1/46th the distance to Alpha Centauri right now.

wd40
2011-Feb-17, 10:38 PM
According to this http://en.wikipedia.org/wiki/VY_Canis_Majoris the largest known star is 2000 Solar radii, so presumably it would be visible as a disc to the naked eye at 1 light-year.

WayneFrancis
2011-Feb-17, 10:39 PM
Here (http://en.wikipedia.org/wiki/Angular_diameter) is a discussion of angular size, including a list with various objects. The resolution of the human eye is about a minute of arc, but that's to separate two points. So to see disc, you'd probably need it to be a little larger than that. You can see that at their closest approaches, Venus and Jupiter are right around that value, so you've probably noticed that at times it seems like you can just barely make out that they aren't point sources. Alpha Centauri's angular size is about 8,500 times smaller than that, so to appear as large as Venus or Jupiter at their biggest*, it would have to be to be about 8,500 times closer. So that means about 0.0005 light years, or 32 astronomical units, which is just a little farther away than Neptune. Yes, that means that if we look at it the other way, from Neptune our Sun just barely has a visible disc. Which makes sense because here at 1 AU, 32 times closer, the size of the Sun is about 32 arc minutes.

* Which is big enough to make it clear that it's not a point source to the naked eye, show a small disc in even modest binoculars, and show a very clear disc with some detail visible in a small telescope.

Well, the naked eye has a resolution of 1 arcminute. If you assume that Alpha Centauri is the same size of the sun, then the stellar diameter is 1.39e6 km. So, to subtend 1 arcminute, it would have to be no farther than 4.78e9 km, better known as 5e-4 light year. That's only 32 AU!!

Did I do the math right?

You both did it right I believe. This is something that many people don't get. At the distance of Neptune the sun is very small. At Pluto it isn't much better then any other star.

Githyanki
2011-Feb-17, 10:43 PM
Just need to make more-powerful telescopes.

Hornblower
2011-Feb-17, 11:14 PM
According to this http://en.wikipedia.org/wiki/VY_Canis_Majoris the largest known star is 2000 Solar radii, so presumably it would be visible as a disc to the naked eye at 1 light-year.

Its diameter would be roughly one arcminute. For something as dazzling as even an M star, not clearly distinguishable as a disk without some optical aid.

chornedsnorkack
2011-Feb-18, 10:20 AM
What 3 arc minutes looks like when not dazzling - it is about 350 km on Moon, like Mare Nectaris.

Exactly how bright would a body have to be to dazzle an onlooker and prevent resolution of a 3 arc minute disc?

Venus gets 2 times the illumination of Moon and has 10 times the albedo. So 20 times the surface brightness.

Mercury gets 4...10 times the illumination of Moon and has about the same albedo, so 4...10 times the surface brightness.

When Venus or Mercury are viewed with small telescopes or binoculars, how much magnification (resulting angular size) is needed to resolve disc, and does their dazzling brightness hamper it?

Hornblower
2011-Feb-18, 12:56 PM
What 3 arc minutes looks like when not dazzling - it is about 350 km on Moon, like Mare Nectaris.

Exactly how bright would a body have to be to dazzle an onlooker and prevent resolution of a 3 arc minute disc?

Venus gets 2 times the illumination of Moon and has 10 times the albedo. So 20 times the surface brightness.

Mercury gets 4...10 times the illumination of Moon and has about the same albedo, so 4...10 times the surface brightness.

When Venus or Mercury are viewed with small telescopes or binoculars, how much magnification (resulting angular size) is needed to resolve disc, and does their dazzling brightness hamper it?

There are no exact answers because of variations in visual acuity from one observer to another. My educated guess is that with good sharp 20/20 vision a 2' (arcminutes) spot will look distinctly larger than a 1' spot of the same total luminosity. The 1' spot may or may not be distinguishable from something smaller. This is based on my own observations of Jupiter, Saturn and Uranus with various amounts of magnification.

I am going to make some test patterns in my computer artwork. I will make spots of various sizes and adjust each one's surface brightness to equalize their luminosity. Then I will look at them from across the room.

Grey
2011-Feb-18, 02:20 PM
You both did it right I believe. This is something that many people don't get. At the distance of Neptune the sun is very small. At Pluto it isn't much better then any other star.In the sense of just being a point source, yes. But it's still much brighter than any star.

I am going to make some test patterns in my computer artwork. I will make spots of various sizes and adjust each one's surface brightness to equalize their luminosity. Then I will look at them from across the room.Very cool plan; please report your results. Of course, if the reason you can't make out a disc is just because the brightness is dazzling, it's easy to wear sunglasses, or mount a filter on your telescope or binoculars.

chornedsnorkack
2011-Feb-18, 04:10 PM
How far are Venus, Jupiter and Mercury from each other at the night of 10...11 May 2011, and what are their respective angular diametres, phases and magnitudes?

Hornblower
2011-Feb-19, 12:09 AM
For my test pattern I started with ten spots at 1/4 mm increments from 0.25 to 2.5mm. When viewed from 3.5 meters it was one arcminute/mm. These were bright spots on a dark background to simulate stars at night.

The 1mm spot looked slightly larger than the smaller ones in side by side comparisons, but it was not obvious when standing alone. The 2mm and up were obviously larger than any point source.

Next I made pairs at separations of 1, 2 and 3mm. At the viewing distance the first one looked slightly elongated while the wider ones were clearly split. They looked like zero magnitude or brighter stars. The 3mm was about the separation of Epsilon Lyrae. When I dimmed them down to about 4th magnitude I could no longer split even the wide one with any certainty.

My visual acuity with a new pair of glasses is a solid 20/20.

antoniseb
2011-Feb-19, 12:49 AM
For my test pattern I started with ten spots at 1/4 mm increments from 0.25 to 2.5mm. ...
Nice test! Can you repeat it using light shining through holes in opaque material (e.g. Aluminum foil)? and varying intensity illumination? I suspect that situation might reveal more doubts. When I look at Venus when it is bright, my eye-brain combination tells me I'm seeing a disk, but I can't be because it is a crescent, and too small to resolve.

Hornblower
2011-Feb-19, 12:58 AM
Nice test! Can you repeat it using light shining through holes in opaque material (e.g. Aluminum foil)? and varying intensity illumination? I suspect that situation might reveal more doubts. When I look at Venus when it is bright, my eye-brain combination tells me I'm seeing a disk, but I can't be because it is a crescent, and too small to resolve.Yes, holes in foil with a suitable diffuse light source behind it would work great. You could adjust the brightness of the individual holes with pieces of paper behind them, with as many thicknesses as needed for the desired dimming.

Venus at its largest crescent phase is on the threshold of being resolvable, and some observers have reported being able to just see it. Bright twilight or full daylight might help. In a dark sky something that bright tends to look larger.

astromark
2011-Feb-19, 02:05 AM
I would back out of that discussion and come back to this resolution of Alpha Centari's disk...
As we can calculate the emitted light and luminosity of the stars A and B of Alpha Centari...
Its entirely well reasoned that we already know from what distance they would be perceived as larger than a point source... or even two point sources... and how that might change with resolution and magnifications... It is just maths...
I understand that from this solar system you only need to get just beyond Saturn to no longer be able to define the sun as a disk. So the question of how close to those Alpha Centari stars do I need to get in order to be able to see without magnification that they are two and they are disks... I am throwing knives in the dark, but would guess it at about ten AU's Which is near to their distance apart. Could one of you more capable mathematicians ( magicians ) contribute to correct my guesswork please... ?

chornedsnorkack
2011-Feb-19, 08:01 AM
Of course, if the reason you can't make out a disc is just because the brightness is dazzling, it's easy to wear sunglasses, or mount a filter on your telescope or binoculars.

Is the disc/crescent of Venus bright enough that sunglasses/filter would improve resolution of its shape?

Venus passed greatest western elongation on 8th of January, so gibbous Morning Star is slowly approaching inferior conjunction with Sun on 16th of August, getting smaller and fuller.

And in April-May, planets pile up to align in morning sky - all of them except Saturn. And outer planets are gibbous all the time.

In end of April, it seems that Venus comes within 9 minutes of Neptune. It seems that they could be caught in a single field of view for magnifications as big as 200?

1st of May - 25 minutes between Mars and Jupiter (does that mean their satellite systems get mixed up?).

10th of May - Mercury (then IIRC gibbous and near aphelion) 1,5 degrees from Venus - would 20x magnification resolve Mercury disc and allow comparing with Venus?

11th of May - Venus 0,6 degrees from Jupiter.

Given that some of you have long observational histories, have there been previous conjunctions where a small binocular or telescope could get two planets simultaneously in field of view and resolved?

astromark
2011-Feb-19, 09:01 AM
I have travelled to the mountain tops to see Saturn And Jupiter together, but that was a few years ago and I am embarrassed to remember how many... It was what got me.. and they were not in the same field of view... just a couple of fingers apart...
Now I have the Keys to that observatory.

Maybe we are leaving this subject a... seeing Venus as anything other than a point of light is beyond the human eye... just a pair of bino's or a small telescope will reveal shape... but this question of how close to Centari., and I need a mathematicians input...

chornedsnorkack
2011-Feb-19, 09:59 AM
Apart from the most inclined planets (Mercury, Mars, Pluto, asteroids) all conjunctions seem to happen within 4 degrees.

What are the typical eyepiece fields of view (heaven field of view times magnification)? 40 degrees?

Then a binocular with x8 or x10 magnification should get 4...5 degree field of view, and any conjunction should have the planets simultaneously visible.

If 2 arc minutes are consistently resolved then a x8 binocular should show planetary discs over 15 arc minutes across. Jupiter at all times, Saturn too, Mars at opposition.

Resolving Neptune should take x50 magnification, or telescope apertures over 25 cm. But 40...45 cm Dobsonians are said to be quite common. Then again, 50x magnification (which also increases brightness by 8,5 magnitudes, or Neptune to about -0,5 and Triton to +5) restricts field of view to perhaps 45 minutes.

Tomorrow, Mercury, Mars and Neptune shall meet... but less than 4 degrees from Sun.

The next conjunction over 15 degrees from Sun seems to be 16th of March, Mercury and Jupiter 2 degrees 21 minutes...

glappkaeft
2011-Feb-19, 11:41 AM
What are the typical eyepiece fields of view (heaven field of view times magnification)? 40 degrees?

A really expensive wide-field eyepiece like an Tele Vue Ethos has an apparent field of 100 degrees. I don't think there is anything that's significantly better than that.

chornedsnorkack
2011-Feb-19, 12:34 PM
A really expensive wide-field eyepiece like an Tele Vue Ethos has an apparent field of 100 degrees. I don't think there is anything that's significantly better than that.

Then a binocular might have 10x magnification and yet 10 degree field of view, with two Tele Vue Ethos eyepieces? Nice... And at 50x magnification, still 2 degree field.

Hornblower
2011-Feb-19, 02:26 PM
I would back out of that discussion and come back to this resolution of Alpha Centari's disk...
As we can calculate the emitted light and luminosity of the stars A and B of Alpha Centari...
Its entirely well reasoned that we already know from what distance they would be perceived as larger than a point source... or even two point sources... and how that might change with resolution and magnifications... It is just maths...
I understand that from this solar system you only need to get just beyond Saturn to no longer be able to define the sun as a disk. So the question of how close to those Alpha Centari stars do I need to get in order to be able to see without magnification that they are two and they are disks... I am throwing knives in the dark, but would guess it at about ten AU's Which is near to their distance apart. Could one of you more capable mathematicians ( magicians ) contribute to correct my guesswork please... ?

Your guess is a well educated one. The two stars are roughly the Sun's diameter, with A being a bit larger and B a bit smaller. Thus at 10 AU they will be about 3' in angular diameter, a sure thing to see as disks with the aid of a welder's glass, provided your vision is good and sharp.

For splitting the pair visually, we can do it from much farther away. Their maximum separation as seen from 4 lightyears is about 20". If we get 10 times closer, 0.4 lightyear, they will be over 3', and my test pattern indicates easy naked eye separation. A more modest filter or viewing in bright twilight may help by reducing glare. Their brightness at that range would be similar to that of Venus.

chornedsnorkack
2011-Feb-19, 05:16 PM
For splitting the pair visually, we can do it from much farther away. Their maximum separation as seen from 4 lightyears is about 20". If we get 10 times closer, 0.4 lightyear, they will be over 3', and my test pattern indicates easy naked eye separation. A more modest filter or viewing in bright twilight may help by reducing glare. Their brightness at that range would be similar to that of Venus.

A more interesting distance would be about 0,25 AU, the distance of Proxima. The brightnesses would be about -6 and -5. But what are the angular separations if Alpha Centauri components seen from Proxima - where is Proxima relative to orbital plane and apside line?

ngc3314
2011-Feb-21, 03:27 AM
Given that some of you have long observational histories, have there been previous conjunctions where a small binocular or telescope could get two planets simultaneously in field of view and resolved?

From 23 February 1999, here are Venus and Jupiter from a 25-cm refractor. Venus in particular is dramatically overexposed here so as to catch the Galilean moons, but visually detail on Jupiter and the gibbous phase of Venus were clear. The minimum apparent separation some hours later was about 9 arcminutes.

http://www.astr.ua.edu/keel/telescopes/jupvenusxs.jpg

CJSF
2011-Feb-21, 08:26 PM
So, what was the actual answer to the OP? If it's in that nest of posts up above, I lost it. Even a ballpark figure would be neat to know.

CJSF

Grey
2011-Feb-21, 09:04 PM
So, what was the actual answer to the OP? If it's in that nest of posts up above, I lost it. Even a ballpark figure would be neat to know.For the naked eye, the answer is "much, much closer" than one light year. Bare minimum would be inside the orbit of Neptune, and you'd really want it closer than that if you want to see a clear disk, rather than just barely making out that it's an extended object. Something like 10 AU (orbit of Saturn) would definitely present a disk (about 3 minutes of arc) to the naked eye. You'd probably need to look through a filter to see it well, though, because it would be really bright. Angular size scales linearly with distance, so for any given magnification, you can just multiply the distance. For example, if you move it from 10 AU to 1,000 AU, but then use a magnification of 100x to view it, the apparent size is the same.

CJSF
2011-Feb-21, 09:25 PM
Thank you, Grey!

CJSF

chornedsnorkack
2011-Feb-21, 09:25 PM
From 23 February 1999, here are Venus and Jupiter from a 25-cm refractor. Venus in particular is dramatically overexposed here so as to catch the Galilean moons, but visually detail on Jupiter and the gibbous phase of Venus were clear.

Here on Earth, snow does dazzle eyes in sunlight. Do clouds of Venus in twice the sunlight overexpose the eyes?

wd40
2011-Jun-16, 01:49 AM
Could a Hubble circling Alpha Centauri resolve our own Sun's disc? Could it pick up the planets of the Solar System? The Earth even?

StupendousMan
2011-Jun-16, 12:20 PM
No, possibly Jupiter, definitely no.