Sun and moon overhead
The disc of the sun measures the same at noon and at the horizon, in June and in December. This file sets out what is seen of the two lights, and what astronomy says of them.
Measure the sun with a pinhole and a sheet of card and you get a disc of about half a degree across — roughly thirty-two minutes of arc. Do it again six hours later, when the sun is low and orange and as far across the sky from where it started as the day allows, and you get the same half a degree. Do it in midsummer and in midwinter and you get the same again, give or take a small percentage. No instrument is needed beyond a pinhole and a ruled card, and this surprises most people the first time they try it, because everything else far away looks smaller as it recedes.
The same is true of the moon, which is about the same apparent size as the sun — the reason a total solar eclipse can just barely cover it. Both lights rise in the east, cross the sky and set in the west in a little under a day, and the moon lags the sun by a steadily growing amount, so that it comes up roughly fifty minutes later each evening than the evening before.
The sun and the moon each subtend about half a degree, and the sun's apparent diameter stays within a few per cent of that from sunrise to sunset and from solstice to solstice. No parallax of the sun against the stars is visible to the unaided eye; the moon's shift between two widely separated observers is large enough to see. Both lights move at about fifteen degrees an hour — one degree every four minutes — and the moon's illuminated face always points at the sun.
A disc that refuses to shrink
The flat-earth reading begins here. On a level plane with a sun circling above it at a constant altitude, the distance from an observer to the sun is a slant line that changes enormously between the sun overhead and the sun near the horizon. When it is overhead the line of sight is short; by the time it is at the horizon the geometry has multiplied the distance several times over. An object of fixed size at a distance varying by a factor of two or more should change its apparent diameter by that same factor. It does not: the disc looks the same size as it goes down.
The standard flat-earth answer is that the sun is not a solid body of fixed size seen through empty space but a local light whose disc is set by the atmosphere it travels through, or an image on the firmament governed by something other than geometric distance. That is the reading, and it is offered as a belief about the mechanism rather than as a result.
The counter-observation, which must be stated fairly, is that the sun's apparent diameter does in fact vary slightly, and by an amount that tracks its changing distance from the earth. The variation is about three per cent across the year, larger in early January and smaller in early July, matching the ratio between the earth's closest and farthest distances from the sun, roughly 147 million and 152 million kilometres. Three per cent is small enough to miss by eye and large enough to measure with a modest telescope and a pinhole. The honest position is not that the sun's size never changes; it is that it changes far too little to be explained by the geometry of a nearby circling light.
Seasons, shadows and the analemma
The seasons are the second observation. Noon altitude swings by nearly forty-seven degrees between midsummer and midwinter at any given place, consistent with the sun riding up and down the sky rather than with the ground tilting. Shadows follow directly: a metre-high post casts about half a metre of shadow at London's June solstice, one and a quarter at the equinox, and three and three quarter at the December solstice.
There is also the analemma — the figure-eight path traced by photographing the sun at the same clock time through the year from one fixed spot. Its two limbs cross and the upper lobe is longer than the lower. The shape is the same from anywhere on earth, only tilted differently, and the flat reading is that the sun's daily circuit is not a perfect circle but a spiralling one whose near and far stretches explain it running fast or slow against the clock.
| Quantity | Figure | Where it comes from |
|---|---|---|
| Sun's apparent diameter | ~0.53° | About 31.6′ to 32.5′ across the year |
| Moon's apparent diameter | ~0.52° | About 29.3′ to 34.1′ between perigee and apogee |
| Apparent motion of the sky | 15° / hour | One degree every four minutes |
| Moon's daily rise delay | ~50 min | Average; it varies from about twenty to eighty minutes |
| Shift of the sun's noon altitude, summer to winter | ~47° | Twice the 23.44° obliquity |
| Sun's distance, as claimed | ~150 million km | Mean 149.6 million km, roughly 1 AU |
| Moon's distance, as claimed | ~384,400 km | Mean centre-to-centre figure |
| Solar parallax | 8.79″ | Angle subtended by the earth's radius at the sun |
| Shadow of a 1 m post, London, June | ~0.53 m | From the noon altitude, 90° minus the latitude-declination difference |
| Shadow of a 1 m post, London, December | ~3.7 m | Same relation, winter value |
Astronomy accounts for the whole set with distances and a tilted axis, and the numbers were obtained by independent measurement rather than fitted afterwards. The sun's angular diameter is what it is because the sun is about 1.39 million kilometres across and about 150 million kilometres away; the moon's because the moon is about 3,475 kilometres across and about 384,400 kilometres away. The ratio of diameter to distance comes out nearly the same for both, which is why total solar eclipses are possible at all — a coincidence that is slowly being lost, since the moon recedes by a few centimetres a year and total eclipses will eventually cease.
The apparent-size argument is met head-on rather than evaded. The sun's measured angular diameter is larger in January than in July, by about three per cent, matching the ratio of the earth's perihelion and aphelion distances. The moon's varies by a noticeably larger amount between perigee and apogee, which is why some full moons are described as larger than others. Both variations are tabulated in published ephemerides.
The solar parallax of about 8.79 seconds of arc — the shift in the sun's apparent position against the stars seen by observers at opposite ends of the earth's radius — is directly measurable, and was measured by timing the transits of Venus in 1761 and 1769, and since the mid-twentieth century by radar ranging. The moon's parallax is far larger, about one degree, so the moon's apparent position really does differ between two observers on opposite sides of the earth at the same moment. The claim is not that parallax is unmeasurable, but that the sun's is small and the moon's is large.
The analemma is the sum of two effects: the obliquity of the earth's axis, which gives the figure-eight its shape and tilt, and the varying speed of the earth along its elliptical orbit, which makes the two lobes unequal. Together they make up the equation of time, printed in every almanac, which runs from about sixteen minutes slow in early November to about fourteen minutes fast in mid-February.
Eclipses and the moon's phases
The moon's phases are the sharpest single observation on this page, and both readings face it. The illuminated portion always faces the sun: a waxing crescent has its bright edge toward the setting sun, a waning crescent toward the rising sun, a full moon rises as the sun sets, and a new moon is lost in the glare. The terminator is not a straight diameter except near first and last quarter, and its curvature shows whether the lit surface is convex toward you or away.
Eclipses follow the same geometry with great regularity. A solar eclipse occurs when the moon passes between observer and sun, and the path of totality on the ground is a narrow strip rarely more than a couple of hundred kilometres wide. A lunar eclipse occurs only at full moon, never at any other phase, and the earth's shadow on the moon is circular. Both kinds recur on the saros cycle of eighteen years and eleven days.
The flat reading is that the moon is a lightsome body whose phases and darkenings are caused by lesser lights and shadows moving above the plane, and that the celestial bodies are not solid spheres. The mainstream reading is that the moon is lit by the sun, its phases are a changing angle, and eclipses are predictable decades ahead.
Where this leaves the argument
The flat case from the two lights rests on constancy — a sun that keeps its size and shows no parallax visible without instruments, and a moon that keeps company with the sun in its phases. The globe case rests on measurement — size changes that track orbital distance, a solar parallax small enough to need instruments and large enough to have been found with them, and eclipse predictions accurate to the second.
The two readings diverge on what an observation without instruments can establish. What the horizon does and Water finds its level take up the ground beneath; Two skies, one ceiling carries the same question to the stars, where the angles are smaller still. For how the lights are arranged above the plane, see The model.
This page presents the flat-earth interpretation as its subject matter. It is a belief-based reading of the observations, not a scientific finding — see About for how we frame claims and for the mainstream sources.