How are Stars Visible if they are so far away?

DavidB66

Senior Member
I recently came across a flat earth argument about stars that was new to me, so it may be worth recording here.

I will try to present the argument as convincingly as I can.

According to standard scientific doctrine, the following points are true:

1. The sun is a star, and a fairly ordinary one at that.
2. The sun is about 93 million miles from earth.
3. The nearest stars (other than the sun) are over a light year from earth
4. A light year is about 6 million million miles, which is about 60,000 times the distance of the sun.
5. The nearest stars are therefore over 60,000 times as distant as the sun.
6. As viewed from earth, with the naked eye, the sun has a visual angle of about half a degree (30 minutes of arc.)
7. The visual angle of an object is inversely proportional to its distance from the observer.
8. At the distance of more than a light year, a star the size of the sun would have a visual angle of about 1/120,000 degrees of arc, or 1/2000 minutes.
9. But the smallest visual angle the human eye can resolve is about 1 minute of arc, which is about 2000 times larger than the angle derived at (8).
10. Therefore stars the size of the sun, or even much bigger, would not be visible to the naked eye from earth.

Since we evidently can see stars, the inference is that something must be wrong with the standard doctrine. Either the sun is not an ordinary star, or the sun is not 93 million miles away, or the stars are not light years away. ( I suppose in principle one might argue that the stars we can see are just those that happen to be much larger than the sun, but I wouldn't want to go down that road!)

I presume the correct response to the argument is that it confuses visibility with having a definite visual arc. Points 1-9 in the argument are correct, but the conclusion at point 10 is invalid. In astronomy texts the stars are usually described as point sources of light, having no definite angular size, even when seen through a powerful telescope. Even at a distance of light years, they may still emit enough light to register on the retina (or other sensor) as a point of light. Some stars appear brighter than others, but this depends on the amount of light emitted, not their size. The same principle presumably applies to other light sources; for example, at a distance of 2 miles, a bright street light would have less than 1 minute of visual arc, but still be clearly visible. (I think.)

A more sophisticated answer would probably go into the number of photons emitted by a star; how many photons are needed to form a point image; and so on, but I hope I have got a valid answer in principle.
 

Mick West

Administrator
Staff member
Here's a photo of a star:
Metabunk 2018-06-04 13-59-50.jpg

That's Antares, it has a radius 630x that of the sun, and it's 620 light years away. There's more here.

That probably not helpful though. You are correct that all the stars in the sky are just points of light. If you zoom in on them with a telescope they do not get any bigger. In fact all the stars in the sky look like the same size - but some are brighter than others so they look larger. This is confused more by atmospheric effects.
 

Z.W. Wolf

Senior Member.
I presume the correct response to the argument is that it confuses visibility with having a definite visual arc.

Yes, that's exactly it. Thanks for starting this thread, as I've been "meaning to do" for a long time. Procrastination.

A standard argument (chestnut) you see about the ISS goes something like this: They say the ISS is about the size of a 747. How small is a 747 at 30,000 feet? But they say we can see the ISS at 200 miles. LOL !!!


A bright and distant object, in a dark background, can be visible as a dimensionless point of light, even when it couldn't be seen in a bright background, as something with a visible shape.

Example: Stand on a hill at night. You can see a streetlight 20 miles away with the naked eye as a dimensionless point of light. Wait until dawn. Do you have any hope of seeing that same streetlight with the naked eye in daylight? It has no visible shape. It's beyond the distance the human eye can resolve shapes. It's a tiny thing lost in all the other bright daylit objects around it. Come the night and it's visible again... as a dimensionless point of light.

It needs to be bright.
It can't be overwhelmed by all the other photons entering your eye. Contrast!
The photons it is emitting don't fall over or poop out along the way. They are still entering your eye. You can still see it... as a dimensionless point of light.


More technical:

Let's talk about resolution:

It's not how far we can see. It's how small we can see. Something far away looks small, yes? But can you see a single bacterium with your naked eye if it's on a table top? (The answer in one case is "yes." There's one species of bacteria that's just big enough to see: Thiomargarita namibiensis.)

There are problems with the human lens and pupil size that are too technical to get into, but another problem is: The rods and cones in the human retina have a physical size. Any image on the retina that's small enough is only going to stimulate a critically small number of them. There will be no detail. No visible size. You can't resolve it. You can't see it. Unless... it's bright enough and contrasty enough to see as a dimensionless point of light.

Let's talk about dimness:

There's a bit of confused folk belief about a match (or candle flame) at 30 miles being the smallest thing we can see with the naked eye. But this actually comes from an old standard example in textbooks about how dim something can be and still be visible, as a dimensionless point of light.

Obviously we can see things farther away than 30 miles... if they are big enough. Do the sun and moon disappear at 30 miles? So things "disappear" simply because the image size gets too small. There's no set mileage of course. It depends on how big it is versus how far away it is.

But how far away can something be and still be visible as a dimensionless point of light? It doesn't depend on size or distance. It depends on brightness, at our eye, and contrast. How many of its photons are hitting our retina, versus how many other photons are hitting our retina? If the latter is zero the former can be one. One photon is enough to see!


Further reading: http://www.bbc.com/future/story/20150727-what-are-the-limits-of-human-vision


What's the smallest number of photons we need to see?

To yield colour vision, cone cells typically need a lot more light to work with than their cousins, the rods. That's why in low-light situations, colour diminishes as the monochromatic rods take over visual duties.

In ideal lab conditions and in places on the retina where rod cells are largely absent, cone cells can be activated when struck by only a handful of photons. Rod cells, though, do even better at picking up whatever ambient light is available. As experiments first conducted in the 1940s show, just one quanta of light can be enough to trigger our awareness. "People can respond to a single photon," says Brian Wandell, professor of psychology and electrical engineering at Stanford. "There is no point in being any more sensitive."

In 1941, Columbia University researchers led subjects into a darkened room and gave their eyes some time to adjust. Rod cells take several minutes to achieve full sensitivity – which is why we have trouble seeing when the lights first go out.

The researchers then flashed a blue-green light in front of the subjects’ face. At a rate better than chance, participants could detect the flash when as few as 54 photons reached their eyes.

After compensating for the loss of photons through absorption by other components in the eye, researchers found that as few as five photons activating five separate rods triggered an awareness of light by the participants.

What is the smallest and farthest we can see?

Now here’s a fact that may surprise you: There is no intrinsic limit to the smallest or farthest thing we can see. So long as an object of whatever size, distance or brevity transfers a photon to a retinal cell, we can spy it.

"All the eye cares about for vision is the amount of light that lands on the eye," says Landy. "It's just the total number of photons. So you can make [a light source] ridiculously tiny and ridiculously brief, but if it's really strong in photons, you can still see it." [As a dimensionless point of light.]

Psychology textbooks, for instance, routinely state that on a clear, dark night, a candle flame can be spotted from as far away as 48 kilometres. In practice, of course, our eyes are routinely inundated by photons, so stray quanta of light from great distances get lost in the wash. "When you increase the background intensity, the amount of extra light you need to see something increases," says Landy.

The night sky, with its dark background pricked by stars, offers some startling examples of long-distance vision. Stars are huge; many we see in the night sky are millions of kilometres in diameter. Even the nearest stars, however, are more than 24 trillion miles away, and are therefore so diminished in size our eye cannot resolve them. Lo and behold, we can still see stars as intense, gleaming "point sources" of light because their photons cross the cosmic expanse and hit our retinas.
Content from External Source
 
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StarGazer

Member
In astronomy there are many methods for obtaining stellar radii such as stellar interferometry, lunar occultations or eclipsing binaries, however, even after obtaining the true sizes of distant stars can we assume that the apparent sizes can be much, much larger, if we take for account that a solar glare extends much further giving the impression of larger angular diameter of any star?

As an example, we have our own Sun, where if we apply a solar filter we can see that it's true angular size is much smaller than observed with a naked eye, as discussed in this thread here.


As reference to my question here is one of the largest know stars named UY Scuti:



UY Scuti is a red supergiant and pulsating variable star in the constellation Scutum. It is currently among the largest known stars by radius and is also one of the most luminous of its kind. It has an estimated radius of 1,708 solar radii (1.188×109 kilometres; 7.94 astronomical units); thus a volume nearly 5 billion times that of the Sun. It is approximately 2.9 kiloparsecs (9,500 light-years) from Earth. If placed at the center of the Solar System, its photosphere would at least engulf the orbit of Jupiter.



Relative sizes of the planets in the Solar System and several stars, including UY Scuti:


Content from External Source
Since UY Scuti has 1 708 solar radii, if we consider that it's glare extends much further, then it's apparent size could be dozens or even more times larger than it's true size, so it would be normal for us to be able to see it from 9 500 light-years away.
 
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StarGazer

Member
10. Therefore stars the size of the sun, or even much bigger, would not be visible to the naked eye from earth.

Since we evidently can see stars, the inference is that something must be wrong with the standard doctrine. Either the sun is not an ordinary star, or the sun is not 93 million miles away, or the stars are not light years away. ( I suppose in principle one might argue that the stars we can see are just those that happen to be much larger than the sun, but I wouldn't want to go down that road!)

@DavidB66
There are stars in the Milky Way Galaxy which can be as large as 1 700 times the radius of our Sun (see my post above) and you are forgetting that many of the points of light on the night sky are actually binary, triple and even quadruple star systems, not to mention that a single point of light can be an entire galaxy or cluster of galaxies, but we see their combined points of light as just one because they are too far away in order to distinguish their individual light sources without the use of powerful telescopes such as Hubble. This combination (merging) of multiple light sources greatly increases the visible magnitude of what we perceive as just a single point of light in space.

The Milky Way has a diameter of 100 000 light-years, so imagine a galaxy that has thousands of light years in diameter but since it's so far away we see it as just one star on the night sky.


Another good example of stellar merging is Polaris North, which we think that it's only a single star close to the North Geographical Pole, when in reality Polaris North is a Triple Star System.



Source https://www.spacetelescope.org/images/opo0602a/
 
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sharpnfuzzy

Active Member
9. But the smallest visual angle the human eye can resolve is about 1 minute of arc, which is about 2000 times larger than the angle derived at (8)

Easily busted by aircraft. At night, you can see their nav-lights when they are flying at cruising altitudes. But at say 30,000 feet the nav-lights would need to be over 8 feet in diameter to fill 1 arc minute. Nav-lights vary in size by aircraft type but none are 8 feet in diameter.
 

Tedsson

Member
This image was taken by Hubble Ultra Deep Field camera when it was pointed at a "dark" area of space:

B6C0BFB9-9AD7-41B9-AFBB-9D5CAF62A2F9.jpeg

Even more room for thought when you realise the dashes are side on spiral or elliptical galaxies and many of the dots are globular clusters.

So that picture probably contains many trillions of times more stars than you can actually see.

So much for a “dark” region of space.

(Given that the universe is finite I can’t help but think what it must look like from the outermost planets stuck on the extreme periphery. One side everything. The other side nothing and ultimate darkness. Excuse the whimsy.)

Source of picture: https://en.m.wikipedia.org/wiki/Hubble_Ultra-Deep_Field

Explanatory content from site (My bold):

The Hubble eXtreme Deep Field (HXDF), released on September 25, 2012, is an image of a portion of space in the center of the Hubble Ultra Deep Field image. Representing a total of two million seconds (approximately 23 days) of exposure time collected over 10 years, the image covers an area of 2.3 arcminutes by 2 arcminutes, or approximately 80% of the area of the HUDF. This represents approximately one thirty-two millionth of the sky.

The HXDF contains approximately 5,500 galaxies, the oldest of which are seen as they were 13.2 billion years ago. The faintest galaxies are one ten-billionth the brightness of what the human eye can see. The red galaxies in the image are the remnants of galaxies after major collisions during their elderly years. Many of the smaller galaxies in the image are very young galaxies that eventually developed into major galaxies, similar to the Milky Way and other galaxies in our galactic neighborhood.​

I think we are getting plenty of photons from out there and it is easily possible to see stars without any FE sophistry.
 

Mick West

Administrator
Staff member
Easily busted by aircraft. At night, you can see their nav-lights when they are flying at cruising altitudes. But at say 30,000 feet the nav-lights would need to be over 8 feet in diameter to fill 1 arc minute. Nav-lights vary in size by aircraft type but none are 8 feet in diameter.

I suspect you could also use the red beacon lights that are on things like radio masts as a good example. They are about 2 feet high, yet visible from tens of miles away. A true zetetic could verify this by climbing up to measure the bulb.
Metabunk 2018-06-05 07-06-41.jpg

With aircraft nav lights they are rarely perfectly overhead, so probably 10+ miles away with the horizontal distances.

Then there's these guys with two spotlights, visible from the ISS. >250 miles away.
Source: https://youtu.be/2UoY15WDuHQ
 
9. But the smallest visual angle the human eye can resolve is about 1 minute of arc, which is about 2000 times larger than the angle derived at (8).
There is no limit to how small a speck of light you can see, but there is a limit to how small shapes we can resolve. If something is smaller than that limit it will appear as a dot. So it doesn't matter if the star is small (it does matter how bright it is though.)

Besides the quality of lenses and such there are two basic factors that limit the resolution of an optical system.

The first is the number of 'pixels' of the sensor. The lens of the eye projects an image onto the retina the same way a camera projects an image onto the photographic plate/film/CCD-sensor. The retina consists of light sensitive cells of finite size (pixels). Lets say we look at a bright T-shaped object. If it is big (and close) it's image will cover the area of many cells on the retina and you can tell it is indeed shaped like a T. However, if it is small (far away) its image might be smaller than a single cell so only one of the cells will register it and it will look like a singel point (pixel) being lit up. You can see a bright dot, but you won't be able to make out any shape. (If it is very dim there might not be enough light for the cell to register it though).

The second is the aperture size. There is a phenomena called diffraction that limits how small shapes an optical system can resolve. It causes small shapes to be blurred out (i.e you can still see it, but it will be blurry). This means there is a physical limit to how high resolution a camera system can have that depends on the diameter of the camera lens (aperture size). The diffraction limit of the human eye is larger than 10 arcsec (about 0.16 arcmin or 0.003 degrees), under typical lighting conditions it will be about 30 arcsec (0.5 arcmin). However, the human eye is not diffraction limited, we can normally only resolve about 100 arcsec (1,7 arcmin). 20/20 vision is the ability to resolve a spatial pattern separated by a visual angle of one arcmin.
 
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