I’ve tried to figure this one out in my head, by imagining a rotating globe orbiting the sun, and it seems that over the course of a year, the average spot on the planet’s surface should see about 12 hours of daylight per 24 hours.
(For our purposes, daylight is defined as the sun being above the horizon, ignoring unusual geographic features such as high mountains, deep valleys, etc.)
For example, at the equator, day and night length don’t change much, about 12 hours each and every day. Average: 12 hours of daylight/24 hours over the year.
Meanwhile, at the poles, it’s mostly 6 months of daylight, followed by 6 months of night, averaging to 12 hours of daylight/24 hours over the year.
But is that really true? I turn to my fellow dopers to affirm/shred this hypothesis of mine…
Yes. Or it would if the Sun was a point, since its like a half degree in diameter you get another minute (someone check my math) of daylight then you do darkness.
So theres that to cheer you up when your feeling blue, averaged out you’ll spend a couple more hours of your life under the sun then you will in darkness.
I believe this would be true if the Earth’s orbit were exactly circular. But the Earth is a bit closer to the Sun in the (northern hemisphere) winter so with a constant rotation rate, I suspect it’s not exactly true, but I can’t tell what part gets more. It should be very correct to a high approximation.
Of course the quality of the sunlight is not the same. The North Pole, for example, gets its fair share of sunlight, but the sun is never higher in the sky than 23 1/2 degrees.
The Earth and the Moon rotate around a common center of gravity and there are Peaks of Eternal Light on the Moon, so I’d use that as evidence to say that all spots on Earth do not have the same amount of daylight per year.
I would think a larger issue than the elliptical orbit would be the fact that the period of orbit is not an exact multiple of the # of Earth axis rotations. Something like ~365.25 days per year.
Therefore, without doing any complicated math at all, there’s already approximately 3/4ths of the Earth’s surface that didn’t get daylight equal to the other 365 days of the year.
If Earth’s year was something closer to 365.0001 days per year it seems like we could ignore the discrepancy but 0.25 is quite a bit I think.
ETA: After rereading OP, I believe he is asking a different question to validate the intuition of daylight visible to the Earth’s surface as a **geometry **question. For that purpose, I guess we should assume 365.00 exactly to avoid over-complicating it.
Elliptical orbit causes the apparent diameter of the sun to be about 3% smaller in early July than it is in early January: Sun at Perihelion and Aphelion
That’ll mess with perfect symmetry of daylength in the northern vs southern hemispheres.
There has to be an accounting for total solar eclipses in some years when the moon is blocking the sun over some part of the earth. So there wouldn’t be an equal amount of daylight in every spot, in every year.
The Earth’s varying speed of revolution does, just as you say, skew the share of daylight time betwixt the hemispheres. Aphelion occurs around the Fourth of July (and isn’t that handy as a reminder) and the Earth is moving more slowly at this point in its orbit. (And how about a big shout-out to Kepler for figuring that out with little more than pure genius!) July 4 is not too far from the summer solstice so the Northern Hemisphere gets more than its fair share of daylight as the Earth lolly-gags along with its top end showing itself to the Sun.
Pure genius and extensive tables of the best observational astronomical data ever collected at the time, thanks to his mentor Tycho Brahe. Both deserve credit for that one.
There’s another effect that’s bigger than that: atmospheric refraction. Because of this, the Sun appears to rise several minutes earlier than it would on an airless planet and set several minutes later.
To see this, here’s a page with the sunrise/sunset/time of daylight for Portland in the month of Sept. The equinox is the 22nd when you’d expect daylight to be exactly 12 hours long. Instead it’s 10 minutes longer than that. It doesn’t get down to 12 hours until the 25th.
Also, the Earth is flatter closer to poles. That should give some extra minutes for those who live far from the equator, and particularly in midsummer. Around my latitude the sunrise is then in NNE and sunset in NNW.
Thanks for all the help, gang. Especially the NOAA tables, they’re fun to play with!
Yes, this was essentially a geometry question, in which I had reduced orbits and globes to perfect circles and spheres, and wondered if said globe got uniform “sun over the horizon” time over the course of a year.
Also a big shout-out to Kepler and his silver-nosed teacher, too, for having done the background work.
