The Sun appears to revolve around a spherical Earth (or vice versa) and is eclipsed below a geometric horizon at sunset.
H₀
Null hypothesis · flat
The Sun appears to recede and fade above a flat Earth into an apparent horizon.
ONLY ONE CAN BE TRUE.
Each hypothesis carries a mutually exclusive geometric outcome for the behavior of shadows at sunset. These real-world geometric consequences can be tested.
The setup
Two Sun models, one window
H₁ Globe
93,000,000 mi away · near-parallel rays · drops straight down.
H₀ Flat
Local Sun · diverging rays · recedes & fades.
Method · experimental design
Control, independent & dependent
Each model forces an opposing, observable shadow behavior. H₁ (globe): the Sun drops below the geometric horizon, so the projected shadow must climb above the object casting it and a terminator shadow must overtake the wall. H₀ (flat Earth): the Sun recedes, so the projection slows, stops short, and fades. The next two slides show both outcomes in the Shadow Reveal simulation; below are what varies, what we measure, and what stays fixed.
Control
The vertex
the window's bottom edge, the fixed limit by which all light rays pass
the vertex altitude is carried across the room to the 30 mm magnet
Independent variable
Distance to the projecting surface
window vertex → wall: 6,735 mm
distance to the ridge obstruction: 1,396 m
Dependent variable
The inversion, or lack thereof, created by the sunset
inverts: the shadow climbs above the vertex line (H₁)
never inverts: the climb slows, stops 117 mm short, and fades (H₀)
H₁ · the globe predicts
Projected shadow rises above the object casting it, terminator overtakes it
Astart
Bclimbing the wall
Cabove the window
Dterminator shadow overtakes · crisp
H₀ · the flat Earth predicts
Projection rises, slows, stops short, fades
Astart
Bclimbing
Cslows · below the window
Dstops short · fades out
The method · an absolute reference
A magnet fixes the vertex
Vertex = the sill
the fixed pivot the shadow turns about
30 mm magnet
stuck on the opposite wall at the same altitude, carried straight across the room
Absolute
it sets the reference and the scale. The sill's height off the floor never enters the math — run it on any floor of a skyscraper.
The decisive test
Only H₁ causes a shadow above the vertex
Page 5 · the real geometry
This is the room
6,735 mm
door (vertex) → opposite wall
910 × 2060
the door (mm) — the sunset window
2000 × 1500
north window (mm) — ambient light only
Page 5 · handed to the globe
A ridge 16 m higher than the window
1,396 m
to the ridge · heading 252°
16 m
ridge above the window (212 m → 228 m)
170 m
valley low point — land plays no part
Recording one
November 2024
The lit window-shape climbs the wall over ~20 minutes, then levels off as the disc fades.
Recording two · the clear-cut measurement
February 2025 — the departure
Inverted to match the Sun's actual downward motion: the measured rate departs from the constant-rate line in the final minutes; it slows, stops, and the disc fades. In geometric terms, on a globe, the downward component of the Sun's apparent movement rate increases toward its maximum at one's zenith minus 90 degrees.
Page 8 · 117 mm · 0.34° · 70%
The measurement
117 mm
shortfall below the sill / magnet
0.995° & 0.655°
red = top-of-Sun ray → 24.3 m above the sill line at the ridge · green = ridge crest → 16 m
0.34° ≈ 70%
the 8.3 m gap at 1,396 m — 70% of the Sun's 0.53° disc still above the ridge
Page 9 · the geometric truth
70% of the Sun, still above the ridge
"We can still see 70% of the Sun as it fades out above the horizon. That is the geometric truth."
Setting while on a globe, the Sun cannot still be 70% above the alleged geometric horizon. It descends at 15°/hour and is eclipsed in production of a terminator shadow (the Earth-curve).
But we do not experience that shadow.
Refraction only slightly delays when it appears to set; it does not cause the rate of climb to slow, stop and then fade.
Both observations · Nov + Feb
The verdict
Negated
H₁ — the globe
The Sun appears to revolve around a spherical Earth and eclipse below a geometric horizon. Not supported by the data.
Affirmed
H₀ — flat
The Sun recedes and fades above a flat Earth into an apparent horizon. Supported by the data.
The wall is the instrument: the shadow died 117 mm below the magnet, marking the top of the Sun at 0.995° above the vertex. That same angle passes the ridge 24.3 m above the Sill line, clearing the 16 m peak (which should obstruct it) by 8.3 m. That is 0.34° above the ridge: ~70% of the solar disc still visible above the local point of occlusion as the Sun fades out. The globe model requires the shadow to rise above the vertex. It never does because the Sun doesn't go down; it goes away.
Game over, gang. The Earth measures flat with respect to sunsets; affirmed through shadow geometry.
Amendment · show the work
The trigonometry
Every number in this deck comes from two right triangles sharing one vertex. Here is the full work: the equations, the inputs, the results.
01
The wall angle · measured in the room
θwall = arctan( 117 mm / 6,735 mm )
= arctan( 0.01737 ) = 0.995°
inputs: 117 mm shadow shortfall below the magnet · 6,735 mm room depth, window vertex → wall
02
The ridge angle · from the topography
θridge = arctan( 16 m / 1,396 m )
= arctan( 0.01143 ) = 0.655°
inputs: ridge 228 m − house 212 m = 16 m · 1,396 m @ 252° (Google Earth)
03
The ray at the ridge plane · one straight line
Hray = 1,396 m × tan( 0.995° ) = 24.3 m
ΔH = 24.3 m − 16 m = 8.3 m
the top-of-Sun ray, carried out the door to the ridge's distance
Aether Cosmology · Man of Stone
Bclimbing the wall
Cabove the window
Dterminator shadow overtakes · crisp
Bclimbing
Cslows · below the window
Dstops short · fades out
