# Under what conditions would a planet's night sky look like this to the human eye?

The angular speed of the stars relative to the planet would need to be high enough for the stars to blur into themselves. Is there a (realistic) way for such a planet to exist?

I'm not sure how the incredibly fast rotation of said planet (compared to earth) would affect the objects on its surface.

# EDIT

Thanks to LSerni and all others for the in-depth answers to my question.

What if, instead of the planet rotating faster on its own axis, the speed at which the planet orbited its star would be increased by a massive amount? Could mass of said star, the planet's distance to it and the speed at which it orbits the star be set in a way that allows for stars appearing as lines? The planets rotation around itself could in the reverse direction to allow for relatively longer day/night cycles.

Or: Could an internally stable system rotate this fast in relation to the other stars?

I believe that this addition does not alter the original question's content. In case this edit violates any guidelines, please let me know, as I'm new to both WB and SE.

• I suspect that the planet would have to be spinning so fast that the viewer might be thrown into space, along with the atmosphere. Unless the planet had significant gravity, Or the viewer was able to stay stationary for a long time. Nov 7, 2017 at 23:49
• Given sufficient alcohol...
– A C
Nov 8, 2017 at 2:59
• But the idea itself is pretty cool. Humans would envision stars totally different, as long, curved arcs basically instead of points, and the focus of the “whirlpool” is where many religions are going to place their creator etc. I mean, if Marvel superheroes are feasible, then just go with 1 rotation per 15 seconds of your planet, and don’t care about the disintegration Nov 8, 2017 at 6:34
• A cylindrical space station might spin fast enough for this if you look out one of the ends. Nov 8, 2017 at 18:08
• I currently don't have the time to write a full answer, but is it acceptable if the stars don't rotate as fast but do create those streaks? E.g. what if the atmosphere works similar to how phosphorus glows; and therefore artifically creates the effect of prolonged exposure because light "lingers" in the atmosphere? Nov 9, 2017 at 17:08

Is there a (realistic) way for such a planet to exist?

# No.

The minimum exposure time for such a photo is about 10 minutes (360 degrees in 24 hours means that to have 15-degree arcs you need one hour of exposure; five minutes will yield blurred arcs of less than three degrees).

The scotopic retinal persistence (bright lights seen at night) has a relaxation time of about 1/10", slower than the normal which is around 1/25" but still too much.

You would need to compress those 10 minutes (600 seconds) in one tenth of a second, which means a rotation six thousand times faster than Earth's - one revolution every 15 seconds approximately, or 4 rpm.

At that speed, even if the planet is much smaller and denser than Earth, on the equator (let's say 3000 km radius) you get a centrifugal acceleration in excess of fifty thousand G (centripetal acceleration is proportional to the square of the rotation frequency. Six thousand times the speed gives you thirty-six million times the force; even dividing the radius by two leaves you with an eighteen million times increase). The planet would disintegrate almost instantly.

You cannot simply increase persistence of vision by positing a really long scotopic decay alone, because we're dealing with a factor of six thousand; at that point, just moving your head would completely compromise your vision. You would need to move thousands of time slower. But this means that days will flash by, and you'd see the sky blazing on and off. So, you need also a perpetual night (at least in the inhabitable zone of the planet).

You could get something like that, therefore, on a very small planet where humans lived in slowed down time (e.g. Charles Sheffield's Sight of Proteus, and Between the Strokes of Night again by Charles Sheffield). If their "day" actually lasted sixteen years, they would see a 24-hour day's night sky like that. Of course you would need to have no day at all, so either make it very small and tidally locked to a very near, very dim star (or a black hole - e.g. in Greg Egan's Incandescence), or have it be a rogue planetoid far away from any star.

The scenario would be halfway between Between the Strokes of Night and, perhaps, the backstory of Blish's Surface Tension: humans found themselves on a very low gravity, perpetually dark planet. There are some biological reactions available but energy gathering times are too long to sustain human life (the energy in a field of wheat requires one year's solar output and can feed X humans for one year. Lower the energy due to darkness, and X drops so low that you no longer have a population).

So their solution is to cheat. By slowing perceived time using Sheffield's S-Space by a factor of six thousand, the bioengineered humans will receive six thousand times more light, and be able to see. And the sluggish semiorganic crops of the land will grow six thousand times faster, supplying the raw materials to produce everything else for a population that requires six thousand times less food and oxygen. Also, the negligible gravity of this asteroid is apparently multiplied (9.81 meters per second squared, but a second is now almost two hours) and - handwaves quickly - is now almost exactly Earth normal.

# Edit: fast planet.

What if, instead of the planet rotating faster on its own axis, the speed at which the planet orbited its star would be increased by a massive amount? Could mass of said star, the planet's distance to it and the speed at which it orbits the star be set in a way that allows for stars appearing as lines?

The rotation has still more or less the same speed - we need five degrees' worth of rotation to take place in less time than it takes the perceptual image to fade. The planet has to rotate very fast around its primary. This is along the lines of pulsar planets (one example is PSR_J1719-1438 b, aka the "Diamond Planet" - it's thought to be the compressed diamond core of a shattered star - now how cool is that?). In truth, any planet orbiting near enough a sufficiently massive object will do.

The problem is that the planet needs to be even nearer and/or the star heavier than the pulsar case, which places the planet inside the accretion disk of a probable neutron star or black hole; indeed, this latter one is the exact scenario of Greg Egan's Incandescence. It is very doubtful that the overall conditions, primarily the radiation flux density, would allow people to stay in the open and look at the stars.

But if they could and did, yes, they might see something like the image you seek. I strongly suspect that whatever they saw, it would manage to be even more mind-blowing. Parallel to the "axis of the heavens", they might see the Blue Ghost of Larry Niven's Smoke Ring. And all around, the Highway of the Gods.

• The surface of a neutron star might be rotating fast enough for this... however standing on a neutron star is another problem... Nov 8, 2017 at 11:38
• You could be on a planet in orbit around a neutron star. Then, the neutron star's gravity would be neutralized by the orbital acceleration (you would have impressive tidal stresses, which is why the planetoid would have to be very, very small to avoid disintegration, and dense enough to have a decent surface gravity in spite of the small size). Nov 8, 2017 at 12:16
• What if the stars were rotating around some central body themselves, rather than the planet spinning quickly beneath them? Nov 8, 2017 at 18:08
• Thank you for your answers. I updated the question to include alternate versions alike to what TheEnvironmentalist suggested. Nov 8, 2017 at 18:15
• Pulsar planets aren't guaranteed to spin at any significantly fast speed. They're simply planets that happen to orbit pulsars. I think you're misusing the term. Nov 8, 2017 at 22:47

Don't change the planet, change the biology.

Allow your planet dwellers to select long exposure mode for their eyes (perhaps an improved night vision thing). It would be useless most of the time, but if selectable by the person, they could see such an image.

• It's called Persistence of Vision. The commonest example is in movies. Or still frame animation. If the mind of humans were able to have a long enough persistence of Vision, we would be able to see this on earth. The problem is, the person would have to stay perfectly still for the entire 'exposure'. However, if you spun someone fast enough, while looking at the north pole, they might simulate such an image. But keep the Gravol handy. Nov 7, 2017 at 23:42
• As noted by @JustinThyme, this would only work if the planet dwellers didn't move very much. But to be fair, I think that would be implied by them having this kind of vision. I'd think of a very long lived, very slow moving creature (or even a plant, rooted to the spot, but with vision). Totally alien to us. Maybe something to get your imagination going. Nov 8, 2017 at 11:26
• I@Spudley - I would assume that with a persistent mode, the combination of eye movement and brain processing would enable the effect of a stable camera platform. We have all seen video of chickens that have a fixed head position when the body is moved and the human brain already compensates for some types of eye movement (by ignoring data) Nov 8, 2017 at 13:51
• Oooh! From now on that's how I'm going to picture Low Light/Dark vision on D&D! Nov 8, 2017 at 15:44

In his Orthogonal Trilogy author/mathematician Greg Egan reimagines physics and a side effect is a night sky comparable to what you've asked. In his novels stars produce motion trails as they cross the sky because the speed of light is not constant: different wavelengths travel at different speeds, producing a red-blue streak that reveals the path of the star as the wavelengths reach the viewer at different times.

Reinventing physics might be a bit more than you're asking for or prepared to implement.

To answer the question as asked: no, it is not possible for the sky to present to the human eye an image exactly like in the picture, simply because the human eye does not have a "shutter" to set sharp start and end times for the exposure. If the planet rotated very very quickly (see L.Serni's answer for the calculation of the rotation speed), and the planet's rotation axis was tilted with respect to the orbital plane, and the observer was near a pole (so that they would experience continuous dark skies), then they may observe something similar, that is, they would observe the stars as arcs; however, the arcs would not have the uniform luminance shown in the picture, but rather they would have a bright head and diminishing luminance towards the tail.

The fatal problem is that the planet would need to rotate so fast that it would immediately break apart; not to mention that away from the poles any inhabitants would be thrown into outer space, together with any liquid water... Of course, you can imagine that the eyes of the inhabitants have incredibly long image decay times; but in this case their usefulness would be greatly diminished.

If there were some reason that meteors were coming into the atmosphere of the planet in a spiral, they might look like that, but very briefly for each streak:

The stars behind them would still be stationary points of light, however.

• Did you take this photo? If so, congrats, very nice! If not, could you add a source attribution? Nov 9, 2017 at 18:08

Well, pushing the limits of a fictional story, there could be a lot of phosphorous pollution in the upper atmosphere causing the effect. It would be a visual effect and the stars wouldn't actually be moving that fast.

If you could twist and/or rotate space-time in a fashion then you could have the rotational effects without tearing the planet apart itself. How you achieve that rotation is beyond known science and discovery, but non-flat spacetime is a very real aspect of physics, so it's not a huge leap to other manipulations, whether natural or artificial.

If it helps, visualise a plastic ball floating on a drain in a large bathtub as it empties. The ball will spin with the water and rotate. Relative to the draining water the rotation is quite slow as the ball is spinning with the water but relative to the rest of the standing water in the tub the rotation may be much faster.

Sort of but it might require a huge kludge to get it working:

Use time dilation by putting your planet very close to huge black hole and put it on a fast orbit, but not too close that it's torn apart

The minimum exposure time for such a photo is about 10 minutes (360 degrees in 24 hours means that to have 15-degree arcs you need one hour of exposure; five minutes will yield blurred arcs of less than three degrees). Now those

Now those 10 minutes of exposure can happen in the blink of an eye! Or rather your eye took 10 minutes to blink from an external reference point due to time dilation. Note that this isn't really a long exposure, and has more in common with fast motion blur

Granted, for every blink of an eye 10 minutes outside the time dilation field have occurred, those stars aren't moving very fast they just look like they are. Conversely you appear to be moving very slowly to any remote observers

## Obstacles

You're going to have to be very particular, for one, you don't want too large a planet, or to get too close, or your planet will suffer from tidal forces. This means volcanics, heat, and in the extreme case, ltierally being torn apart.

Stars will also consequently appear blue shifted due to the time dilation effects.

You may also have additional time dilation effects as the planet rotates, bringing you closer to the black hole. These effects must be small else the planet will tear itself apart.

So we're probably looking at a small moon. The smaller the better, definately has volcanic and seismic activity of some kind, even if it's cryo volcanoes ( see Jovian moons in our own system )

You're also going to face issues with space travel, and it will be easier to fudge if you get rid of the day night cycle, any star that could provide daylight is either sucked into the blackhole, or orbiting, meaning days would last a long time and have inconsistent lengths.

This planet will likely require a moon or be in some sort of binary formation to prevent it becoming tidally locked. You'll also need to be sure the blackhole has cleared its surroundings, a large accretion disc will obscur your view, and probably kill all life on the planet, if it doesn't destroy or pull the planet in

Suffice to say life on this planet would be very uncomfortable

## Other Consequences

From outside the system, your planet will appear to be in slow motion. Remember, there's no long exposure effect here, only fast moving stars. The appearance desired is granted via motion blur instead.

This also means that the desired appearance of the stars will disappear in high frame rate footage, don't point any slow motion cameras at the sky

• No, the 10 minutes have to happen in the reference frame of the planet. The whole point of relativity being called "relativity" is that the rules are the same, locally. Someone on a planet near a black hole will observe the same laws of physics as everyone else. If it takes 10 minutes in the reference frame of the planet for stars to move that far, then it takes 10 minutes in the reference frame of anyone on the planet. For someone in an external reference frame, the planet would appear to be rotating very slowly. Nov 9, 2017 at 4:20
• Exactly, for someone in an external reference frame the planet would be rotating slowly. For people on the planet, the stars would seem to be moving very fast as every moment they experience locally is a lifetime of moments elsewhere. So no it doesn't take 10 minutes for the stars to move that far, not on the planet anyway, time dilation makes the local passage of time slower, in the same way clocks in orbit run slightly faster than on earths surface Nov 9, 2017 at 12:44
• Also keep in mind with this solution, a high speed camera would reveal that the stars are really just moving very quickly, removing the effect the OP desires in film, no long exposure effect actually takes place, just the appearance of it via motion blur. Try replicating this in a starfield by turning quickly to get similar results, only spin the starfield, and slow down passage of time for you but not the stars. As your local time slows down, the stars appear to move faster, just as from the stars perspective you appear to have slown down Nov 9, 2017 at 12:46
• No, you're not listening. In an external reference frame, the planet would be rotating slowly. For people on the planet, the stars would be moving at normal speed. The time dilation is between planet and outside, not planet and people on the planet. The idea that a planet and people on the planet would be in different reference frames is absurd. If it takes 10 m for the planet to rotate far enough, the people would experience 10 m. In an external reference frame, it would much longer than 10 m. The people experience less time than that external time, not less than the 10m of the planet's RF. Nov 9, 2017 at 15:01
• I never said the planet and the people on it would be in different time frames, I agree its absurd, and reject it as silly. The only difference this makes is that the pattern the stars move in would be different and more in tune with the black holes rotation than the planets rotation. Which mostly means added motion sickness and nausea. Don't forget the fast orbit! The planet is moving fast for the people on the planet, even if by comparison the stars are moving orders of magnitude faster from that frame of reference Nov 9, 2017 at 15:28

# Yes, But!

Well, I'm going to stretch the question along the lines of Gary's answer and say: "If the humans evolved to live on a very low-light planet." Humans have a short visual persistence because our planet is very bright during the day. As you probably know, the ability to form images is directly proportional to the number of photons impinging your retinas. So under a bright sky, you get more than enough photons to see what is going on with only a very brief exposure. But on a moonless night, it may take you a while staring at something to gather enough photons to guess at what you are looking at.

Optical telescopes and cameras can see much better than human eyes not only because they have gigantic light collectors, but also because they can collect photons over a very long time and form a single picture from them. If humans ended up on a planet with a dim star (or far from their star, so daytime was still dark), and little danger (few to no carnivores, not many natural hazards), then you could say they are pressured to adapt to the low light levels.

# Backstory

Maybe the humans crash-landed on the planet with minimal supplies and learned to live in harmony but without advanced technology. Or the humans could be ultra-ecological explorers that have a societal directive to colonize planets in the least disruptive way possible (i.e.: massive light pollution is strictly forbidden). Or, they could be protecting the planet as an astronomical preserve, with ideal conditions for building large telescopes without industrial light pollution.

Perhaps all the flora on the planet subsist on geothermal energy, and there is too little energy for any fast-moving animals. As the humans slow down to the pace of the planet, the need for fast optics would decline. Visual persistence would increase, to gather more photons, and light would get smeared out as they moved, or sat still but the planet rotated.

# Math

Just kidding. I'm not going to do the math. I'll just point out that the stars in your picture are only smeared out over a dozen degrees or so, which is maybe 1 hour of exposure. If your planet is smaller/faster, you could plausibly reduce this to maybe 10 minutes of persistence. That's pretty huge compared to to the milliseconds of persistence of earth vision, but if your daytime is orders of magnitude darker, and there is no need for urgent action, this is one way to adapt.

What if everyone on the planet just won the "This is where our planet is located" lottery? Completely scientifically feasible (though hilariously unlikely), it might just be the case that they're viewing tightly packed strings of stars that just, by chance, happen to look like that when viewed from their night sky. Might be a few non-line stars, even, just most of them are that way, maybe as a particular result of how the universe was formed around it.

I wonder if you might be able to cheat.

To get this kind of streaking from stars, you would need the planet to be spinning very fast - as others mention - since stars are so far away, and they won't really move in relation to the planet.

But, you might be able to get some of the same effects from celestial objects that are much closer, since they wouldn't need to move nearly as much to give a larger apparent movement arc. You could probably get streaks that way, though they might not be quite so circular.

I'd thought, if you had an asteroid belt in the next orbit over, you could have lots of little objects (visible through proximity). They could even be moving relatively fast in relation to the planet, in the opposite direction, which would help lower the speed needed to form streaks. Especially if whatever had caused the asteroid belt was relatively (on a planetary scale) recent, so the chunks were still moving at a (relatively) high speed.

Alternately, if you had clouds of space debris from some planetary-timescale-recent event that were relatively close to the system, they would get pulled towards the star and might appear to elongate as the nearer parts get drawn in faster than the outermost, so that they would for a time appear as streaks against the night sky.

In either case, you would still see star-specks in the night sky, they might be fainter or harder to see due to the brighter streaks (essentially light pollution), but they would be visible in places. And the streaks would almost certainly be across the sky parallel to its rotation, rather than rotating in a circular pattern as your original picture has it.

If... we can ignore the unimportant fact that everybody will be dead and torn to bits, then yes (at least I believe so, it will be hard to verify).

All we need is the planet being sufficiently close to a black hole so gravitational time dilation becomes noticeable.

If time passes slower from your point of view, then time in the remaining universe passes faster.

While you will not see streaks due to your planet's rotation (it actually rotates slower!) you will see streaks because stars are not stationary themselves. And if you are slow, then oh heck, they move fast!

The funny thing is that time passes slower for the emitted light as well, so light moves more slowly the closer it gets to you (or rather, the black hole), too. So, some of that slow light will yet have to arrive at your eyes while the star has already noticeably moved sideways, and you should have a nice streak effect.

So basically, you need Miller's planet where one minute is what... 7 years on Earth?