[zarmin]

slightly off-topic thought experiment that's been on my mind lately:

to us, the sun appears to be the size of, let's say, a quarter held at arm's length. this is at 93M miles (1AU, or ~8 light minutes) distance. if we moved the sun 100 miles away from earth, it would take up the entire sky. now in the other direction, if we doubled the distance, to 2AU, it would appear to us as half its normal size and 1/4 as bright (irradiance follows inverse square law). at 3AU the sun would be 1/9 as bright and 3x smaller than a quarter. at 100AU, we're talking about brightness of 1/100^2 (one ten-thousandth) the sun's apparent brightness. with me so far?

Sirius A: the brightest star we can see; 25x more luminous than the sun; 2x the size of the sun; 8.6 light YEARS distance (544,000AU) from earth.

if we moved the sun to the same distance as Sirius A, it would appear 296 BILLION times dimmer and 544,000 times smaller. yet Sirius A is easily visible - the brightest star in our sky - despite being only 25x more luminous and 2x larger.

do you see the discrepancy? 25x more luminous doesn't compensate for a 296-billion-fold brightness loss. The numbers we are given don't make sense, not even close. (and this is without considering diffusion, which would make the discrepancy even worse.) i'm not proposing an explanation or a modification to the model, i just think the data don't make sense.

[hmorgan]

I've found that when I have a thought that seems to contradict the "established" model of the world, I tend to just be missing some critical factor. A recent example is when I thought: "why don't we just use physical objects to communicate information? Wouldn't that be instantaneous?" Turns out, no, pushing on one end of an object only communicates information to the other end at the speed of sound. Not intuitive when you only think about observable experience (it sure seems like if I push a steel bar, the other end moves instantly), but that's how the world works.

In the case of your thought experiment, the critical factor is that our eyes are able to observe and adjust to a very wide range of brightness in different conditions. Sirius A really is billions of times dimmer than the sun to our eyes (hard to find a good reference for that, but this mentions it: https://ecampus.matc.edu/mihalj/astronomy/test5/stellar_magn...).

[zarmin]

Your steel bar example isn't analogous. You had an intuition, discovered a physical constraint (speed of sound), and the math checked out. The constraint explained the phenomenon. What would it look like if the "established" model of the world were actually wrong?

Here, the math doesn't check out. That's my point.

I'm not saying "it seems like stars should be invisible but they're not", Im showing that inverse square law - which we can verify at human scales - predicts invisibility at stellar distances, and the proposed compensation (25x more luminosity) is insufficient by orders of magnitude.

Sirius is "billions of times dimmer" than the sun to our eyes IF you mean the Sun as seen from Earth versus Sirius as seen from Earth. But that's not the comparison. The comparison is:

Sun moved to 544,000 AU (Sirius's distance): 296 billion times dimmer than Sun at 1 AU Sirius at 544,000 AU: 25x brighter than that

25x doesn't bridge a 296-billion-fold gap, plus the eye's dynamic range is irrelevant; we're comparing what brightness should reach the eye versus what compensation the model claims.

If your claim is "the eye can see across many orders of magnitude, so even though the Sun would be invisible at stellar distances, Sirius being slightly brighter makes it visible," then do the actual calculation. Show that 25x more luminosity produces enough photons to cross the detection threshold. Because the math I'm showing says it doesn't.

You're assuming the model works and looking for why my intuition is wrong. I'm showing the model's numbers are internally inconsistent. Those aren't the same thing.

>I've found that when I have a thought that seems to contradict the "established" model of the world, I tend to just be missing some critical factor.

Does it bother you that to make relativity work, they had to invent dark matter and dark energy - 96% of the universe's mass-energy - as fudge factors? At what point does "missing a critical factor" become "the model requires constant patching to match observations"?

[ceejayoz]

> Does it bother you that to make relativity work, they had to invent dark matter and dark energy - 96% of the universe's mass-energy - as fudge factors? At what point does "missing a critical factor" become "the model requires constant patching to match observations"?

This would be a lot more compelling from someone who doesn't believe in astrology.

https://news.ycombinator.com/item?id=45631792

(It's interesting that you forget the inverse square law in that case.)

[hmorgan]

I think I see what you mean now, but what makes you think that the sun would be invisible at 544,000 AU?

Here are the numbers as far as I understand them.

Apparent magnitude of the sun: -26.74 Apparent magnitude of Sirius A: -1.46

Excepted magnitude of the sun after moving to 544,000 AU: 296 billion times weaker, leading to +1.96 magnitude, according to a calculator (https://www.1728.org/magntude.htm).

I don't trust that calculator a lot, so to check that math, I used a formula to calculate the difference between those magnitudes (https://lco.global/spacebook/distance/comparing-magnitudes-d...) and got a result of 23.34. Not far off from the expected 25x difference.

So the sun at 544,000 AU wouldn't make the top 25 brightest stars in the night sky, but it wouldn't be far from that (https://www.britannica.com/science/list-of-brightest-stars-2...) and definitely well within what would be visible (https://en.wikipedia.org/wiki/Limiting_magnitude).

[GolfPopper]

>The numbers we are given don't make sense

These are all numbers you just provided, with no source for them.

But even using your numbers, 300 billion is 3x10^11. The Sun provides about 10^5 lux, while starlight overall provides about 10^-4 lux[1], which is a difference of 10^9, meaning the difference between "all the starlight on a dark night" and "just the starlight from Sirius" would be around 10^2, which... seems about right?

1. https://en.wikipedia.org/wiki/Orders_of_magnitude_%28illumin...

[zarmin]

Look up the provided numbers if you disagree.

You're comparing the Sun's illuminance at Earth (10^5 lux at 1 AU) to all starlight combined (10^-4 lux), then trying to work backward to what a single star should provide. That's not how this works.

The question isn't "what's the ratio between sunlight and all starlight." The question is: what happens when you move the Sun to stellar distances using inverse square law?

At 1 AU: ~10^5 lux

At 544,000 AU: 10^5 / (544,000)^2 = 10^5 / 3×10^11 ≈ 3×10^-7 lux

That's the Sun at Sirius's distance. Multiply by 25 for Sirius's actual luminosity: ~7.5×10^-6 lux.

Your own Wikipedia source says the faintest stars visible to naked eye are around 10^-5 to 10^-4 lux. So we're borderline at best, and that's with the 25× boost.

But moreover, you said "the difference between all starlight and just Sirius would be around 10^2." There are ~5,000-9,000 stars visible to the naked eye. If Sirius provides 1/100th of all visible starlight, and there are thousands of other stars, the math doesn't work. You can't have one star be 1% of the total while thousands of others make up the rest - unless most stars are providing almost nothing, which contradicts the "slightly brighter" compensation model.

Address the core issue: inverse square law predicts invisibility. The 25× luminosity factor is insufficient compensation. Citing aggregate starlight illuminance doesn't resolve this.

[GolfPopper]

It's been a long time since my astrophysics, but I think the seeming contradiction you're running into might be from treating lux (illuminance) as a measure of emitted energy, when its actually a measure of received energy.

The Sun's (or any star's) emitted energy is measured in terms of solar luminosity.[1] The nominal value of solar luminosity is 3.83×10^26 watts. At twenty five times as luminous, Sirus' luminosity is 9.5710^27 watts. We can divide that by your 296 billon times, which gives.. 3.2x10^16 watts as what actually makes it to Earth. If the we convert that back into solar luminosity (to figure out the apparent brightness at Earth), its 8.3595 10^-11.

Now, if we look up at the sky, and check how bright the Sun and Sirius are from Earth on the magnitude scale, which each step is ~2.5 times brighter than the one below it (and vice versa), the Sun has an apparent magnitude of -27, while Sirus' is -1.46. I.e. the Sun in the sky is about 8 billion times brighter that Sirus is. That's within an order of magnitude of what its calculated solar luminosity should be. Again, it seems about right.

1. https://en.wikipedia.org/wiki/Solar_luminosity

[ceejayoz]

Yeah, people get really messed up by just how good our eyes are. (For a close-to-home example, people think indoor plants get a lot closer to sunlight-level amounts than they really do.)

We can spot a single photon in the right conditions. https://www.nature.com/articles/ncomms12172

[zarmin]

Eye sensitivity isn't the issue. Sirius isn't barely visible at the detection threshold, it's the brightest star in our sky. If a 25x luminosity boost over the Sun only gets you to the edge of naked-eye visibility at that distance, where do the additional orders of magnitude come from to make it one of the most prominent objects in the night sky? Show me the math.

[ceejayoz]

> Sirius isn't barely visible at the detection threshold, it's the brightest star in our sky.

And it's entirely washed out during the day. The full Moon is very bright, but it's still 400,000 times dimmer than the Sun when seen from Earth, and that's only ten different. The brightest star in our sky is simply not very bright; our eyes are just pretty awesome.

That star you are seeing is 25 orders of magnitude dimmer.

https://astro.wku.edu/labs/m100/mags.html

"While you may perceive one star to be only a few times brighter than another, the intensity of the two stars may differ by orders of magnitude. (Light intensity is defined as the amount of light energy striking each square cm of surface per second.) The eye is a logarithmic detector. While the eye is perceiving linear steps in brightness, the light intensity is changing by multiplicative factors. This is fortunate; if the eye responded linearly instead of logarithmically to light intensity, you would be able to distinguish objects in bright sunlight, but would be nearly blind in the shade! If logarithms are a faint memory, you should peruse a refresher on logs and logarithmic scales before continuing."

https://physics.stackexchange.com/questions/329971/how-many-... says looking up at a sunny sky lets you take in 3×10^14 photons per second per eye. Yet you can see a single photon! https://www.nature.com/articles/ncomms12172

Or, we can conclude the entire field in dozens of countries simply can't do math. Your choice.