Tap anywhere on the globe to stand there. Then watch the year run and the daylight pile up — with the solar disc, refraction and orbital eccentricity switchable in real time.
Drag to spin the globe · tap to plant the marker · the shaded half is night right now in the simulation.
The ticking counter is the raw accumulation over this one exact window. The full-year figure above averages the window start across a whole day, which removes the ±2.8 h artefact of where the year boundary happens to fall in the diurnal cycle — so at the end of the year the two can differ by up to about three hours. The report explains why.
Draw the Sun as a point. Take away the air. Now sunrise is a clean little bit of geometry — a dot crosses a line — and on the equinox every latitude on Earth gets exactly twelve hours of day and twelve of night. No exceptions. No rounding.
It's a beautiful result. It's also wrong.
Two things ruin it, and here is the part that got me curious in the first place: they both ruin it in the same direction. Neither one has ever shortened anybody's day.
It's a disc, about 32′ across — half a degree, roughly your little fingernail held out at arm's length. And we don't start the clock when the centre arrives, we start it when the first sliver shows. So the day opens with the Sun's centre still 16′ below the horizon, and closes with it 16′ below on the other side. No atmosphere required. This one is pure geometry and it would happen on a dead airless rock.
Air thickens as it goes down, and light grazing the horizon bends downward through that gradient, lifting the Sun's apparent position by about 34′ when it's sitting on the horizon. Sit with that number a second. It is bigger than the Sun is wide. The Sun you watch touching the sea at sunset has already set. You're looking at a picture of it.
Stack the two and you get 50′ of grace at each end of the day. The Sun's centre can sit fifty arcminutes under the true horizon and the day still counts as running.
Fifty arcminutes is nothing. So why does it add up to anything?
Because you aren't banking angle. You're banking time — and the exchange rate between the two is not the same everywhere you stand.
That's the whole answer, and it turned out simpler than I expected it to be. On the equinox the Sun runs along the celestial equator, and the celestial equator meets your horizon at an angle of exactly 90° minus your latitude. At the equator the Sun comes straight up, dead vertical, and clears those fifty arcminutes in about three and a half minutes. At 60° it arrives at a 30° slant and has to walk twice as far to climb the same height. At the pole the path is parallel to the horizon — the Sun doesn't rise in any daily sense at all. It gets lifted by the slow seasonal drift of its declination, and crossing 50′ takes it about two days.
Same fifty arcminutes in every panel, measured at the equinox. The gold stretch is how far the Sun has to walk to cross it — that length is the time.
So the hunch was right, and it's worth being precise about how big it is. The equinox day at the equator isn't 12 h 00 m, it's about 12 h 07 m. Seven free minutes, twice a day, three hundred and sixty-five days a year — call it 42 extra hours. Move up to 60°, where that same 50′ costs the Sun two and a half times as long to cross, and it swells to about 103 hours. Every latitude on the planet finishes the year with more day than night, and the further you get from the equator the fatter the margin.
Then, somewhere around 60°, it stops growing. Past there you stop trading fast sunrises for slow ones and start trading many sunrises for few, and the two very nearly cancel.
Which leaves the other half of the question. Earth's orbit is an ellipse, so it doesn't travel at a constant rate, and the two halves of the year that the equinoxes cut are not the same length. That certainly sounds like it ought to hand somebody extra daylight too.
It doesn't. It only moves it around. The third switch below lets you watch it do exactly that.
Each switch takes one piece of physics away. Whatever the number does when you flip it is what that piece was worth. That's the entire method, and it's the reason there are three switches here instead of one.
What it changes. On, the day runs from first sliver to last sliver. Off, the Sun collapses to a point and its centre has to do the crossing itself. Watch the rise threshold in the readout move by 16′.
Why you'd flip it. This is the half of the bonus that owes the atmosphere nothing at all. It's here because the Sun is an object and not a coordinate. Turn it off and you're asking a clean question: how much of this would survive on an airless planet?
What to watch. The year loses about 13.5 h at the equator and about 33 h at 60°. Now notice that the ratio between those two is the same ratio refraction gives you. Both effects buy time at the identical exchange rate, because they're buying the same thing.
What it changes. On, the horizon threshold carries 34′ of refraction — the standard IAU number for an ordinary atmosphere. Off, light travels in straight lines like a textbook diagram.
Why you'd flip it. Refraction is the bigger of the two, worth about 2.13× the disc. It's also the only part of this that isn't a fixed fact about the solar system. Real horizontal refraction runs from something like 28′ in warm thin air to well past 42′ over polar ice — so if you want to know where the uncertainty in all of this lives, it lives right here.
What to watch. Go stand at the South Pole and switch it off. The year goes negative — more dark than light. The South Pole's entire surplus is on loan from the atmosphere.
What it changes. Off — the default — Earth runs its real ellipse, e = 0.0167, moving fastest at perihelion in early January. On, the orbit gets circularised: constant speed, constant distance, same year length, same tilt. Nothing else touched.
Why you'd flip it. Aphelion lands in early July, so Earth dawdles through the northern summer and hurries through the southern one. 186.4 days from the March equinox to the September one; 178.8 days to come back. That lopsidedness is worth ±90 hours at the poles, which is bigger than everything else on this page put together.
What to watch. Flip it on and the planet goes symmetric. The North Pole hands over 90.6 h and the South Pole picks up 90.6 h — the same number, to the minute. Nobody gains. The hemispheres are splitting one fixed pot, and the ellipse only decides who gets the bigger half.
Surplus over the day = night line, in hours per year. The outlined bar is where the switches are set right now.
The bottom bar is the control — point Sun, no air, circular orbit. It lands on zero at every latitude on Earth, and that is the only reason to trust anything above it. If the machinery were lying to me, that bar is where it would show.
Each one jumps to the end of the year so you can read the total straight off, then hit ⟲ Restart and Play to watch it accumulate.
Lit hours in local solar time, equinox to equinox. Scrubbing never re-runs the simulation — the year is solved once into a list of sunrise/sunset instants and a running total, so any moment is a lookup. The sim only re-solves when you move the marker or flip a switch (about 45 ms).