Light scattering in earthlike atmospheres?

[Evil Dr Ganymede]

Say you have a planet with an earthlike atmosphere. What kind of apparent visual magnitude would an object in the sky need in order to (a) cast noticeable shadows or (b) turn the sky vaguely blue (like what you see during a nearly total eclipse of the sun) or (c) turn the sky really blue (like normal daylight on Earth)

I know the full moon is bright enough to cast shadows, and I've heard it said that on a really really dark night (say, in the middle of a desert with no lights for miles and miles), a bright Venus can cast shadows - is that true?

And is the angular size of the object in the sky important in this regard? If the Sun was about the size of Venus in the sky, but had the same apparent visual magnitude as it does now (-26-ish), would it still turn the sky blue?

And would an M dwarf turn an earthlike planet's sky blue (assuming one was in a habitable orbit)? Or is there not enough blue light to scatter?

[Spaceman Spiff]

Ah, interesting set of questions. I was commenting (rambling may be a better word) about how it would be wonderful if better physics modelling went into Celestia, so that we could put ourselves in alien situations and See What It Might Really Look Like (Something Different-Celestia As A Way Of Rendering Space Art http://www.shatters.net/forum/viewtopic.php?t=4563, but there was little response (memo to self: write shorter posts..., then people might read them). Appearance of sky does seem one of the items necessary to what Don Edwards brought up.

Say you have a planet with an earthlike atmosphere. What kind of apparent visual magnitude would an object in the sky need in order to (a) cast noticeable shadows or (b) turn the sky vaguely blue (like what you see during a nearly
total eclipse of the sun) or (c) turn the sky really blue (like normal daylight on Earth)

... it depends on so many factors. But...

I know the full moon is bright enough to cast shadows, and I've heard it said that on a really really dark night (say, in the middle of a desert with no lights for miles and miles), a bright Venus can cast shadows - is that true?

It is true. At least, I read that some ancient Greek philosopher wrote that he saw this shadow. Of course, that was well before light pollution.

And is the angular size of the object in the sky important in this regard? If the Sun was about the size of Venus in the sky, but had the same apparent visual magnitude as it does now (-26-ish), would it still turn the sky blue?

Yes, very. The reason Venus's shadow can be seen is because the edges are so sharp. If Venus had been half a degree wide in the sky, I think you wouldn't find its shadows at all. Shadow umbra and penumbra diverge at an angle equal to the extent of the light source.

If the sun was pinpoint, the sky would be just as blue - there's no less light to be scattered in the sky. Shadows would be very stark with ultrasharp edges. There is the other effect that the surface brightness density would be even higher. There was some talk of 'retinal burnout' recently in the discussion about the relative effects of Alpha Cen A and B in a planet's sky there. I've sometimes wondered if any of our historical supernovae ('bright enough to read a book by at night') ever caused people to develop permanent spots before the eyes - high surface brightness density, all that UV radiation...

In summary, some observations:

1. Venus as a point source of magnitude -4.4 casts shadows.
2. A diffuse Venus would not, but how diffuse we don't know?
3. The full moon at half a degree wide and magnitude -18 casts shadows and just about allows colour vision. The sky is noticeably blue.
4. The half moon or less does not cause the sky to be blue, but it remains quite black (Note the half moon is much less than half as bright as a full moon, due to a lunar soil backscatter effect around full moon).
5. During a deep partial solar eclipse, the sky remains bright blue, but the scene appears 'washed out'. Very roughly (no figures to hand), for a partially eclipsed sun to be reduced to the brightness of the full moon, 99.95% of it must be covered.
6. The sun appears about 60 times brighter than our full moon at Jupiter, about twice as bright at Neptune.

We might interpolate expected effects from the above.

And would an M dwarf turn an earthlike planet's sky blue (assuming one was in a habitable orbit)? Or is there not enough blue light to scatter?

I think it would, if bright enough.

There was a discussion on this forum a couple of years ago about the 'colour' of the sun. The conclusion was that really it's white, not yellow - but this is almost tautological. Apart from our eyes perhaps broadly evolving to match the sun's spectrum in sensitivity, our eyes also 'colour-balance'. Don't believe me? On a bright sunny day, close one eye for a couple of minutes, then open it and close the other eye, and alternate. Watch the world change colour - blue - red - blue - red.

We'll only get the right answers if we could shift discussions and Celestia into being more quantitative, but that's not a simple task. A lot of users would become lost as well. However, we could then calculate fluxes of light per wavelength at particular wavelengths following black body emission from stars, add scattering models for atmospheres, convolute with eye response per RGB channel, etc. We could specify atmospheric ground pressure/temperature and using local planet surface gravity, compute scale height of atmospheres for isothermal conditions, blah blah.

Skipping numbers, I think of the colour of K stars being similar to candle flame, and M stars like the orange flame of fires. Even so, because the blue colour of the sky is caused by Raleigh scattering and the colour of K and M starts isn't so red after all, I think the colour of the sky might shift to a bit turquoise or cyan. For A, B and O stars, maybe more indigo (we don't see violet so well)...

We haven't even mentioned the effect of dust or haze: The expectation of Mars' deep, deep blue sky was eventually disproven.

Spiff.

[Evil Dr Ganymede]

It is true. At least, I read that some ancient Greek philosopher wrote that he saw this shadow. Of course, that was well before light pollution.

I knew I wasn't imagining that

If the sun was pinpoint, the sky would be just as blue - there's no less light to be scattered in the sky. Shadows would be very stark with ultrasharp edges. There is the other effect that the surface brightness density would be even higher. There was some talk of 'retinal burnout' recently in the discussion about the relative effects of Alpha Cen A and B in a planet's sky there. I've sometimes wondered if any of our historical supernovae ('bright enough to read a book by at night') ever caused people to develop permanent spots before the eyes - high surface brightness density, all that UV radiation...

Interesting point...

2. A diffuse Venus would not, but how diffuse we don't know?

By "diffuse" you mean "larger angular diameter", right?

3. The full moon at half a degree wide and magnitude -18 casts shadows and just about allows colour vision. The sky is noticeably blue.

Is it? I've never noticed that (and I'll have to wait 28 days to see again now, since it was new moon last night!). It's more a dark navy, I guess. But it's nothing like daylight.

5. During a deep partial solar eclipse, the sky remains bright blue, but the scene appears 'washed out'. Very roughly (no figures to hand), for a partially eclipsed sun to be reduced to the brightness of the full moon, 99.95% of it must be covered.

During the total eclipse in the UK a few years ago, I could only see about 80%-90% of the sun covered up (I think. all that was left was a crescent), and the sky turned a very weird colour about 180 degrees away - it looked like it was a dark blue/purple.

On a bright sunny day, close one eye for a couple of minutes, then open it and close the other eye, and alternate. Watch the world change colour - blue - red - blue - red.

I've notice that when I just rub my eyes for a while, actually...

We'll only get the right answers if we could shift discussions and Celestia into being more quantitative, but that's not a simple task.

well, I figure on this board at least we can get quantitative. I'm not sure if it's really necessary for Celestia to do it too though!

[Spaceman Spiff]

By "diffuse" you mean "larger angular diameter", right?

Yes, I do...

Is it? I've never noticed that (and I'll have to wait 28 days to see again now, since it was new moon last night!). It's more a dark navy, I guess. But it's nothing like daylight.

Only 14 days - lucky you! OK, not bright blue liek daylight, but dark navy is blue. For some reason, I recall it being 'brighter' than navy blue, but maybe that depends on how far away from the full moon you look, 20° or 90°. Even so, at near-full moon, the moon is so dazzlingly bright, it can hurt my eyes, and the sky does appear to me (psychologically?) lighter than navy blue. Most stars are really drowned out, too - so there's the concept of limiting magnitude to deal with too.

During the total eclipse in the UK a few years ago, I could only see about 80%-90% of the sun covered up (I think. all that was left was a crescent), and the sky turned a very weird colour about 180 degrees away - it looked like it was a dark blue/purple.

I saw an eclipse at 40%, the sky didn't appear much different in terms of blue, but the whole scene seemed faint, washed out. Another time, I went to see a total eclipse, and the sky seemed silvery-blue though darker a few minutes before. Maybe it depend on many factors like water content, cirrus cloud, or haze.

well, I figure on this board at least we can get quantitative. I'm not sure if it's really necessary for Celestia to do it too though!

Oh, I think it is. Celestia will hit limits because it won't model certain effects for lack of quantification in SI units. I mean, distances and sizes are quantified in Celestia, but light levels are not. For multiple light sources due to planets in binary star systems, how will we work out the lighting effects on atmosphere and ground if we don't have the spectral flux densities of starlight? How then can the relative strengths of Earthshine and Moonshine be modelled when there is currently no quantification of Earth and Moon luminosity? And how does one compute the limiting magnitude for stars in a sky given two faint suns and a big moon? My experience is that you have to lay foundations with physical quantities in SI units. But, I ramble... That stuff's for the future. Plenty else to do with Celestia now.

Spiff.

[Evil Dr Ganymede]

Only 14 days - lucky you!

Ack. Me no am think straight.
I plead "brain fart" - I meant 14 days. 28 days is how long til the next NEW moon.

OK, not bright blue liek daylight, but dark navy is blue. For some reason, I recall it being 'brighter' than navy blue, but maybe that depends on how far away from the full moon you look, 20° or 90°. Even so, at near-full moon, the moon is so dazzlingly bright, it can hurt my eyes, and the sky does appear to me (psychologically?) lighter than navy blue. Most stars are really drowned out, too - so there's the concept of limiting magnitude to deal with too.

True. Is there any way to actually figure out what the limiting magnitude is given a light source in the sky?

Oh, I think it is. Celestia will hit limits because it won't model certain effects for lack of quantification in SI units. I mean, distances and sizes are quantified in Celestia, but light levels are not. For multiple light sources due to planets in binary star systems, how will we work out the lighting effects on atmosphere and ground if we don't have the spectral flux densities of starlight? How then can the relative strengths of Earthshine and Moonshine be modelled when there is currently no quantification of Earth and Moon luminosity? And how does one compute the limiting magnitude for stars in a sky given two faint suns and a big moon? My experience is that you have to lay foundations with physical quantities in SI units. But, I ramble... That stuff's for the future. Plenty else to do with Celestia now.

Well, it'd be cool to add for those reasons. I'd just kill to have multiple light sources in Celestia though .

[granthutchison]

I've heard it said that on a really really dark night (say, in the middle of a desert with no lights for miles and miles), a bright Venus can cast shadows - is that true?

For sure - I've seen it myself on a nocturnal ski traverse on the Cairngorm plateau. Venus at max magnitude is about a tenth as bright as the whole of the rest of the sky, including airglow, which is more than enough to make a detectable luminacy difference for a dark-adapted eye, provided the edge is sharp, as Spiff points out. It's also possible to see shadows cast by Jupiter and Mars at opposition (mag -2.9), but you have to get yourself into a shady place to minimize the illumination by airglow - people have seen leaf-shadows cast by Mars through a forest canopy on to snowy ground, for instance.

And would an M dwarf turn an earthlike planet's sky blue (assuming one was in a habitable orbit)? Or is there not enough blue light to scatter?

There's enough blue light. If you integrate out the luminous sensation associated with the black-body spectrum, you find that only 6.8% of the luminous sensation we get from the Sun's 5800K white light is coming from the blue+violet (400-500nm) end of the luminous range. At 3000K, that drops to 3.6% and at 2500K to 2.7%, so by no means dramatic reductions.
If you're close enough to such stars to get an Earth-like mean black-body temperature, you of course get less illumination from them than you would from the Sun, because they're putting out more of their radiation in IR. But factoring that in, I find blue skies ~12% and ~4% as bright as Earth's, assuming Earth-like scattering. Very much ball-park figures, of course, but illustrative.

3. The full moon at half a degree wide and magnitude -18 casts shadows and just about allows colour vision. The sky is noticeably blue.
4. The half moon or less does not cause the sky to be blue, but it remains quite black (Note the half moon is much less than half as bright as a full moon, due to a lunar soil backscatter effect around full moon).

Neat tie-in with the theoretical threshold for photopic (colour) vision, there.
The daytime blue sky has a luminance of around 1000cd/m?. The threshold luminance for colour vision is about 0.001cd/m?. Full moonlight is about a half-millionth as bright as sunlight, and the half moon sheds about a five-millionth as much light as the Sun. So the luminance of the sky due to blue light scattered from a full moon should be 0.002cd/m? (just bright enough to detect a hint of blue), but from a half moon 0.0002cd/m? (too dim for colour).

Grant

[granthutchison]

Is there any way to actually figure out what the limiting magnitude is given a light source in the sky?

Two things go on, unfortunately.
First is just a pure contrast effect - a "point source" of light has to add about 50% to the sky luminance before it's detectable at all. ("Detectable" isn't by any means synonymous with "obvious", though, as you'll know if you've seen Venus in daylight.) This effect is straightforward to calculate.
A second factor comes in to play as the sky gets darker - your primary light source starts to interfer with dark adaptation. That's the problem with a full Moon, for instance - the sky isn't nearly bright enough to drown out the stars, but the illumination of the Moon and the moonlight reflected from your surroundings is usually enough to stop you adapting below a limiting magnitude of 4. This effect is hugely variable, though ... you can imagine that standing in the middle of a snowfield and looking towards the Moon would give you a rather different limiting magnitude from a situation in which you looked away from the Moon across dark lava.

So, interestingly, the old story about seeing stars in daylight from the bottom of a deep well is complete twaddle (because the luminance of a spot of sky isn't changed simply because you block out the rest of the sky); but it certainly improves your limiting magnitude by moonlight (because blocking out the Moon and the landscape improves your dark adaptation).

Grant

[Spaceman Spiff]

On a bright sunny day, close one eye for a couple of minutes, then open it and close the other eye, and alternate. Watch the world change colour - blue - red - blue - red.

I've notice that when I just rub my eyes for a while, actually...

Ooh, goody, someone else noticed this!

3. The full moon at half a degree wide and magnitude -18 casts shadows and just about allows colour vision. The sky is noticeably blue.
4. The half moon or less does not cause the sky to be blue, but it remains quite black (Note the half moon is much less than half as bright as a full moon, due to a lunar soil backscatter effect around full moon).

Neat tie-in with the theoretical threshold for photopic (colour) vision, there.

Thank you! Actually, I meant that things on the ground appear in colour to me as well at brightest full moon. Good that you had those blue light black body figures to hand to back me up .

Is there any way to actually figure out what the limiting magnitude is given a light source in the sky?

Two things go on, unfortunately.
First is just a pure contrast effect - a "point source" of light has to add about 50% to the sky luminance ---8<--- snip ---8<---

I agree, and there's a zero-eth reason too: that the point source is simply too dim to trigger eye receptors, even in a totally dark night sky. But, here's what I'm saying: if Celestia can be given the correct equations for calculating sky or star brightnesses (whether single or multiple light sources), limiting magnitude would automatically be taken care of in the process. You can see it already working to some extent with the new near-surface atmospheric modelling: any planet's daytime sky shows no stars in it. But Celestia does allow planets to be easily visible, which is strictly wrong. Also, the moon in the Earth's daytime sky has a blue tint, and that's because Celestia renders the moon less bright than in real life, and so its colour doesn't shine through the sky so much. There's also partly the 8-bit RGB dynamic range problem.

Well, it'd be cool to add for those reasons. I'd just kill to have multiple light sources in Celestia though .

Oh yes, indeedy. I think the next great step for Celestia will be getting binary (multiple) star systems down to pat. Trouble is, I think Celestia needs to change its approach - even revising the current STC and SCC file layouts - before it could move forward. I think there's no time or point starting listing everything to be done right now - there's plenty of other things to be done with Celestia. But, I'll give the first step I see as necessary to illustrate.

We currently have too little control over defining stars in Celestia to make sensible multiple star systems. Initially, we had to pick up whatever Hipparcos gave us in stars.dat, but this usually gave single star systems. Then we had the Tycho catalogue extend stars.dat, to include wide systems but it has two problems: a) wide binaries/multiples consist of 'fixed' stars the cannot move in orbits; b) entire systems that are close binaries are usually missing - why? - because the stars' fast orbital motions caused Hipparcos to read their positions with larger errors and the catalogue bad-parallax filter rejected them for it. Alula Australis was a perfect example - a naked eye star that 'disappeared' with the Tycho-based stars.dat for being a naughty pair of close binaries. Then we got STC files, but addition of companion stars using STC files still leaves them fixed in space, and addition of stars as 'emissive' planets in SCC files is, well, ugh. Even then, adjacent planets still have a single light source appearance.

So, my proposal on the first step:

We reduce each star system to a single 'invisible' class reference marker to be some median position for that system (e.g., the 4 or 5? stars of the Alula Australis system). To do this, we need to process all stars in the catalogue to derive a median point for each star system - that's the hard bit: Alpha Cen A and B obviously belong together, but do we for example tie Alcor to Mizar or not? Maybe distant companions are better left to drift under proper motion instead.

In the absence of any STC files to define that system's stars, Celestia just uses the Hipparcos/Tycho catalogue 'default' star(s) to render in the sky. Otherwise, if there's a STC file bearing the star system name or HIP name, it takes over. Note that there's no need to consider this reference marker until we 'enter' the system (at whatever 1000 A.U.'s that is), so for distant systems in the sky, we just render the star according to the good old-fashioned catalogue.

The reference marker won't end up being the true barycentre, so we need to be able to specify its offset from that - this can be worked out by knowledge of masses and positions of stars as observed for visual binaries, or totally made up for spectroscopic, hypothetical, fantasy or simply unknowable systems. It may be some tricky 3D geometry, but I'm sure enthusiats will start building up these STCs like people make Add-Ons for anything else. From this barycentre, we can reference the usual Celestia orbits - the kinematic (Keplerian) kinds - and reference further barycentres of further binaries as being in orbit about prior barycentres (like what you did with the Nearby Stars STC/SCC files, Grant). All barycentre, star, and star orbit stuff goes into this STC file.

Then, when we've got the stars in the STC file in the right orbits, we add the planets in SCC files. Planets either orbit a star or a pair of stars' barycentre at a distance, maybe even the main barycentre, maybe even double planets have their barycentre orbit another barycentre. The possibilities are endless! Reference plane for orbit inclination may need a bit of thought.

That, I hope, would at least lay the foundation for multiple star systems in Celestia, even before we start on working out the resultant multiple-source lighting problem. There's also the Roche-lobe star shape problem for close/contact binaries - Beta Lyrae, here we come! Or, maybe I've made myself totally unclear... let's see if it goes quiet again .

Spiff.

[granthutchison]

Oh, something I meant to mention the last time we had an outing on this topic - the effects of atmosphere density on the colour of the sky.
The brightest part of Earth's sky is the horizon, because in that direction you're looking though the longest column of scattering molecules. In fact, the horizon sky looks white, because there's enough air out there to scatter all wavelengths.
So if the atmosphere were more dense, the horizon whiteness would spread upwards, and the zenith blueness would fade - eventually you'd have an entirely white sky. If the atmosphere were less dense, the zenith would become darker and the horizon would become bluer - eventually you'd have a black sky and a blue horizon, which would look intriguing.
Astro and SF artists generally get this wrong when depicting a thin atmosphere - they put a patch of blue around the sun in an otherwise dark sky, instead of a blue band around the horizon.

Grant

[Toti]

Spiff:
Regarding realistic computer simulation of light phenomena I think you will find this paper most fascinating. It is not directly suited for real-time graphics (it uses raytracing and MonteCarlo integration among other very CPU-expensive devices) but the proposed solutions -and the stunning results- are formidable (the text includes some screenshots).
To reproduce a night scene, the above mentioned model takes into account light emitted from:

-Moon
-Planets
-Stars (as function of magnitude, temperature and position)
-Milky Way
-Nebulae
-Zodiacal light
-Atmospheric airglow

The extension to include cometary light is fairly straightforward. There is also room for adding aurorae (the paper mentions Baranosky et al. work on this subject), urban glow and light pollution.

I was commenting (rambling may be a better word) about how it would be wonderful if better physics modelling went into Celestia, so that we could put ourselves in alien situations and See What It Might Really Look Like (Something Different-Celestia As A Way Of Rendering Space Art http://www.celestiaproject.net/forum/viewtopic.php?t=4563, but there was little response (memo to self: write shorter posts..., then people might read them).

Personally I read your posts with great interest.

Bye

[chris]

In the version of Celestia after 1.3.2, I'm plan to focus my efforts on multiple star support and reworking the renderer to support multiple light sources and better atmosphere rendering. The implementation of multiple star systems that I've been playing around with is a lot like what Spiff described.

--Chris

[Evil Dr Ganymede]

That's excellent news, Chris! I can't wait!!

[Spaceman Spiff]

Personally I read your posts with great interest.

Hurrah!

In the version of Celestia after 1.3.2, I'm plan to focus my efforts on multiple star support and reworking the renderer to support multiple light sources and better atmosphere rendering. The implementation of multiple star systems that I've been playing around with is a lot like what Spiff described.

Another Hurrah!

Oh, something I meant to mention the last time we had an outing on this topic - the effects of atmosphere density on the colour of the sky. ---8<--- snip ---8<---

I think you must be right. In the Alps, or on flights, you can gauge the visual appearance of lower density atmospheres. Looking to the horizon, you still have 1 atmosphere density below you, but you can imagine there is a cut-off at a less pale level a degree or so above the horizon (limb?). The sky is darker blue above, and the sun doesn't have such a great effect about it compared to the paleness trend to the horizon.

Regarding realistic computer simulation of light phenomena I think you will find this paper most fascinating.

I read through the paper, and it is well worth a read for clues on how to go about the matter of this topic, and also should allow generalisation to other more alien worlds. However, I do think we need to get the mechanics of multiple star systems done first, so it's good what Chris has mentioned. It alone will greatly increase people's fun in tinkering with systems.

Actually, I've been to the Kleine Matterhorn itself (pictured in that paper, it's a few km from the more famous Matterhorn!). If anyone's goes, don't forget to visit the glacier tunnels.

By the way, some ideas for what to put in new STC's (if that's how it'll work for specifying the stars):
1. Can we have a 'corona on/off'? - I think the stark edge of the photosphere was more reaslistic, as in the earlier Celestias (1.0.x)
2. Can we specify star mass? It might help people if they can just specify the size of each orbiting body's orbit, and Celestia will work out a default period ('correct' as per Kelpler's 2nd law) from the orbited mass (or sum of masses for an orbited barycentre)... Maybe it'll save people some guesswork?
3. Can we specify individual textures for the stars like for planets in SCC files, should we want to provide them?
4. Also, an option to specify effective surface temperature of the photosphere (to determine colour, intrinsic surface brightness), Radius, Rotation period - all to override the stars.dat bits.
5. Also, maybe to supply a shape file for tidally (Beta Lyrae A,B) or spin distorted stars (Pleione, Achernar).

Must go, bloatoids at 08:00...

Spiff.