Read NASA’s plain-language Earth facts page and it lands like a spec sheet for the only planet we have to build on: equatorial diameter 12,756 km, one rotation every 23.9 hours, 365.25 days to the Sun and back, exactly one astronomical unit — 150 million km — from the star that heats it, eight light-minutes away. The line that should stop an architect, though, is buried mid-page: Earth’s axis of rotation is tilted 23.4 degrees to the plane of its orbit. That single angle is why you draw overhangs at all.

Start from the frontier, not the site. That 23.4° is not fixed and not the whole story. The axis itself traces a slow cone — the precession the ancients called the Great Year. Aristotle and his contemporaries guessed at its length; the modern figure for one complete loop of the axis is about 25,772 years (a drift of roughly 50 arcseconds a year), not the 2,351 that sometimes gets quoted. And the sphere itself is a fiction. NASA’s newest gravitational model, as WIRED put it, shows “the Earth is a lumpy mess” — a geoid whose equipotential surface bulges and dimples by tens of metres because mass is not evenly packed under your feet. The planet you survey is a slightly pear-shaped, wobbling top.

Why this reaches the drawing board: every façade is a local answer to a planetary geometry, and the local part is your latitude. Zurich sits at 47.37°N. Plug that into the solar-noon relation and the summer Sun tops out near 66° while the December Sun barely clears 19° — the entire brise-soleil problem in two numbers. Move the site to Palermo (38°N) or Tromsø (69°N) and the correct overhang depth, the correct PV tilt, the correct daylight factor all change, because the Sun–Earth angle at that Lat/Long changed. NASA’s own Earth-observation stack — the same programme that just certified Tomorrow.io’s Ka-band precipitation radars for science use — exists precisely to measure this planet as a coupled system rather than a smooth ball.

←TODAY: Zurich at 47.37°N sees solar-noon near 66° in June and ~19° in December — fix those two numbers before you sketch the shading. →3012: Envelopes that read their own latitude and re-tune to a sky whose axis has wobbled a measurable fraction of a degree since the drawings were signed. Fulcrum: You cannot detail the overhang without first pinning the tilt, the latitude, and the projection — the local façade is downstream of the whole planet’s geometry.

There is a second flattening no one escapes: the move from the 3D planet to the 2D sheet. Gauss proved it with his Theorema Egregium — a curved surface cannot be laid flat without distorting distance, angle, or area; you must choose which to sacrifice. Every site plan, every GIS layer, every set of survey coordinates is that choice made concrete. In Switzerland it is made for you by the LV95 / CH1903+ frame — an oblique Mercator on the Bessel ellipsoid, centred on the old observatory in Bern. Import a model in the wrong reference and your building lands metres off its neighbours, rotated by the projection’s convergence angle. PAZ has walked the tessellation lineage before — the same Voronoi-and-projection mathematics that panelises a curved façade also governs which flat map is telling you the truth.

Atelier: The Büro that treats “north” and “the site” as givens inherits two silent errors — an unset project geodetic frame and a sun study run at a default latitude. Both compound once an AI massing tool starts iterating façades against a wrong sky. Monday move: open your BIM template, set the project coordinate system explicitly to CH1903+ / LV95 (EPSG:2056) and the true site latitude, then re-run the solar study before a single shading fin is drawn.

Hack: Compute the noon-Sun altitude for your actual site latitude before you trust any default. The one relation that carries the whole shading argument is altitude = 90 − latitude + declination, where the Sun’s declination swings ±23.44° across the year — the tilt, doing its work. Run it for both solstices and you have the envelope your brise-soleil must bracket. This is Physics, four lines of it.

import math
decl = lambda d: -23.44 * math.cos(math.radians(360/365 * (d + 10)))
for day, label in [(172, "summer solstice"), (355, "winter solstice")]:
    print(label, round(90 - 47.37 + decl(day), 1), "deg")  # Zurich 47.37 N

Swap 47.37 for your latitude and you get the two altitude limits in degrees — the numbers that set overhang depth, panel tilt and glare risk long before the parametric model runs.

Keep the desk habit: one number in your pocket per claim. The tilt is 23.4°, the precession loop is ~25,772 years, the geoid deviates by tens of metres, your latitude is a fixed input you can look up in ten seconds. Before the next site meeting, pull those four for the actual plot — and let the façade be the local, honest answer to a planet that is neither smooth nor still.

Source: science.nasa.gov