Equations in the live experiment
Solar altitude: sin α = sin φ sin δ + cos φ cos δ cos H, where φ = 41.90°, δ is approximate seasonal declination, and H = 15° × (solar time − 12).
Oculus area: A = π(d/2)². Beam power: P = G × A × max(0, sin α), for the stated direct-normal irradiance G. This is incident power through a horizontal opening, not illuminance inside the building.
Ray location: a centre ray is intersected analytically with the dome, cylindrical wall, or floor. The glowing marker depicts the centre ray, not the complete illuminated surface. The 128-sided polygon area is calculated independently as (128/2)r²sin(2π/128).
Historical confidence
Documented: 43.30 m interior diameter and comparable interior height, approximately 9 m oculus, 16 portico columns, five rings of 28 dome coffers, Hadrianic building, and large supporting drum.
Reconstructed: simplified annular dome thickness, segmented wall construction, selective interior finishes, and approximate architectural details. Artistic: marble colours, surface wear, surrounding paving, and model lighting. No claim is made about lost decoration.
Limitations
The declination is a standard seasonal approximation, local clock effects and atmospheric refraction are ignored, sunlight is a single parallel-ray direction, beam reflections and scattering are not simulated, and irradiance is an adjustable scenario. The section view and assembly sequence are teaching diagrams.
Sources
- Direzione Musei nazionali della città di Roma — Historical background (direzionemuseiroma.cultura.gov.it/en/pantheon/historical-background/)
- Janet DeLaine, “Pantheon,” Oxford Classical Dictionary (2015) (doi.org/10.1093/acrefore/9780199381135.013.4706)
- Turismo Roma — The Pantheon (www.turismoroma.it/en/places/pantheon)
- Museo Tattile Statale Omero — The Pantheon (museoomero.it/en/opere/the-pantheon/)
Educational reconstruction; details marked as reconstruction are interpretive.