Wikipedia:Reference desk/Archives/Science/2021 February 24

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February 24

Is it night 50% of the time on average everywhere?

The lengths of the day and night depend on the season, so days are longer in the summer and nights are longer in the winter. But if you average it over a long period, does it always come to 50% day, 50% night, regardless of your latitude and longitude? I just mean on Earth (not in space obvs) and to the nearest 1% (not worried about weird edge effects that might make 0.1% difference one way or the other). Thinking about solar power. Thanks. 2601:648:8200:970:0:0:0:C942 (talk) 21:01, 24 February 2021 (UTC)

Let's put it this way: the effects that create an asymmetry are pretty small, but I'm not sure if they're in the 0.1% range where you say you don't care, or the 1% range where you say you do. One example is the fact that the Earth's orbit isn't circular: the Earth's distance varies by about 3%, being closest to the Sun during the southern hemisphere summer. This means that the period from the equinox in March to the one in September is longer than the other part of the year, so the North Pole gets more hours of sunlight than the South Pole. It gets complicated. --142.112.149.107 (talk) 21:43, 24 February 2021 (UTC)

If you ignore effects like the the ones mentioned above, ignoring asymmetry with respect to the equator, then the answer is yes, the average time between sunrise and sunset is exactly 50% of the day, regardless of one's position on Earth. Consider that wherever you are on Earth, there is always a point on the opposite side of the Earth that is the same distance from the equator, and where it is night during your day, and day during your night. If your daytime lasted e.g. 55% of 24 hours on average, it would follow that on the opposite side, people had only 45% daytime, even though they are the same distance from the equator as you are. So while there are a few caveats, it is generally true the average length of the day is indeed quite close to 50% wherever you are on Earth. With regards to solar power, however, that does not mean that solar panels are equally effective everywhere on Earth, because the amount of energy that can be harvested from the sunlight depends also on the Sun's angle to the horizon. - Lindert (talk) 22:05, 24 February 2021 (UTC)

So it does matter a little bit how you define "night". If you mean the time between civil dusk and civil dawn, that's certainly going to be less than 50% on average (and certainly the error is a lot more than 0.1%, though I don't know exactly how much). This is because the disk of the Sun takes up some space, and even when it's below the horizon, you still get a significant amount of light because of dispersion and refraction.

The fact that you say you're interested in solar power throws another wrinkle into the mix, because solar power doesn't work very well when the Sun is low in the sky, whether because it's close to twilight or because you're at a high latitude. --Trovatore (talk) 22:17, 24 February 2021 (UTC)

The length of a year is not synchronized with the length of a day, so Earth's orbit not being circular should have no effect on the average, and we can take it to be circular. The flattening of the shape of the Earth compared to the idealized spherical Earth is very small. Imagining a perfectly spherical Earth with no atmosphere and a pinpoint Sun, day and night should be sharply defined. The incoming light rays are nor perfectly parallel, but at that distance this is close enough of an approximation, so let's put the Sun at infinity. In this idealized mathematical model, day and night have, on the average, a perfect fifty-fifty split.  --Lambiam 10:38, 25 February 2021 (UTC)

But again, seeing as the sun has a diameter, even if you define night as "as soon as the last part of the disc of the sun sinks below the horizon", you're still going to get a slightly longer day, by the amount of time it takes for 1/2 sun's diameter to cross the horizon. It would be exactly 50/50 if we measured from the midpoint of the disc, but measuring from the top edge of the disc at both ends causes us to have a slightly longer daytime. --Jayron32 18:02, 25 February 2021 (UTC)

That is why a wrote: "Imagining ... a pinpoint Sun".  --Lambiam 18:56, 25 February 2021 (UTC)

Well, yeah, OK. At some point, though, your cow is too spherical to be useful. Of all of your approximations, the assumption that the sun is a pinpoint introduces the greatest error, by several orders of magnitude than the others. --Jayron32 19:16, 25 February 2021 (UTC)

To get an idea of the relative effect, take a look at these sunrise/set charts. The 'error' is roughly equal to the duration of the sunrise (or half that of the sunrise + sunset combined). At the equator, this amounts to about 2.5 minutes, or 0.17% of a full day; at 60 degrees north/south, it averages about 6.5 minutes, or 0.45%. Near the poles, the error increases dramatically, as sunrise can literally take hours on some days. - Lindert (talk) 20:21, 25 February 2021 (UTC)

Consider a cone into which both the Sun, as bulky as it is, and Earth fit snugly. Its aperture is practically the same as the angular diameter of the Sun viewed from Earth, slightly less than 0.01 radians. That means that the ratio of directly illuminated area to the rest is slightly closer to fifty-fifty than 1.005 : 0.995. So on the average, taken over the whole Earth, the effect is less than 1%. If it is locally more, then it is less elsewhere.  --Lambiam 22:22, 25 February 2021 (UTC)

While my model may be a spherical cow, its Earth need not be spherical. For the result to go through, it is sufficient that it be convex and enjoys antipodal symmetry, so any Earth ellipsoid will do.  --Lambiam 22:37, 25 February 2021 (UTC)

The effect from the Earth's orbit's eccentricity, as mentioned by 142.112..., is big enough. On the poles the day and night last from equinox to equinox. From the March equinox to the September equinox is 186 days, from the September equinox to the March equinox is 179 days. The length of the day is a bit longer due to the sun not being a point and refraction. That's more or less symmetric between hemispheres, but a stronger effect at higher lattitudes. So the North Pole has one week more of sunlight per year than the South Pole. The deviation from the mean is about 1%, so that's enough for OP to care about. At lower latitudes the effect is less.

But if you think about solar energy, the thing you should really care about is cloud cover. Clouds have some vertical extend, so the lower the sun is in the sky, the more likely it is that it's behind a cloud. Further, Western Europe, for example, is almost continuously overcast from mid-November to mid-February, cutting power from PV panels by over 90%. The Sahara is quite sunny year-round. PiusImpavidus (talk) 09:25, 26 February 2021 (UTC)

Harrumph. Whether it's true that "on the poles the day and night last from equinox to equinox" depends on how you define day and night, as discussed above. --142.112.149.107 (talk) 08:48, 28 February 2021 (UTC)

If you have a distant source of light and you suspend a sphere (put your pedantry to one side) wherever that sphere is within the light source half of it will be lit. If you want to count crepuscular light it's up to you. But the answer is simple. Richard Avery (talk) 17:11, 26 February 2021 (UTC)

This is an answer, but not to the original question. The question is not whether there is illumination half the time when averaging over the whole sphere, but whether this is also the case for any location on the sphere. Obviously, it is not if the axis of rotation points to the light source. However, the direction the light is coming from also rotates.  --Lambiam 10:32, 27 February 2021 (UTC)