Solargraphy: Long-Exposure Sun Paths on Paper

Solargraphy: Long-Exposure Sun Paths on Paper

"Leave a pinhole alone for weeks, and the Sun writes its own diary."

Solargraphy is ultra-long-exposure photography of the Sun's path using a simple pinhole camera and photographic paper (often scanned without traditional darkroom development). From Guyana (~6°N), solar arcs stay high and dense, ideal for dramatic multi-week canvases if you seal against humidity.

Why it works

A tiny aperture projects a dim solar image onto paper. Over days and weeks, each clear period adds density where the Sun tracked. Clouds leave gaps; rainy weeks leave blank bands. The result is a semi-abstract climate record as much as an image.

Harmonic and sinusoidal motion

The physics you meet in class as simple harmonic motion (SHM) is the same pattern that shapes a solargraph.

Circular motion → sine wave

If a point moves at constant speed around a circle, its shadow on a diameter slides back and forth. That one-dimensional motion is SHM. Position vs time is a sinusoid:

y(t) = A · sin(ωt + φ)

Play with the piece below: the point turning on the circle, its gold projection, and the gold curve of the Sun's height are the same idea drawn three ways.

What the gold means: it is the height of the SHM projection, a classroom stand-in for the Sun’s height above the horizon plane over one day (the sine of its altitude: low at sunrise, high near noon, low at sunset). It is not a photograph of the sky; it is the math of y = A sin(ωt).

A point turning 15° an hour on a circle, and the Sun's real height through one day from Georgetown or Lethem.

Why the Sun looks sinusoidal

Earth turns at a nearly constant angular speed, and relative to the Sun one turn takes one solar day (24 h). From a fixed site, the Sun rises, peaks near local noon, and sets. Plot its height above the horizon plane (the sine of its altitude) against time and you get part of a sine curve, because that height is exactly the projection of a point turning on a circle.

The altitude angle itself is not a sine curve, and near the equator it is furthest from one. At Georgetown around the zenith dates (about 6 April and 4 September) the Sun climbs almost in a straight line, about 15° every hour (2° at 6 a.m., 17° at 7, 32° at 8, 47° at 9, 62° at 10, 76° at 11), to a sharp peak near 89° at noon: a steep triangle, not a rounded arch.

Around 6 April at Georgetown, how does the Sun's altitude change from 6 a.m. to noon?

Near the equator on the zenith days the Sun climbs almost straight up: about 2°, 17°, 32°, 47°, 62° and 76° on the hours from 6 to 11, then a sharp peak near 89°.

Near the equator (Georgetown ≈ 6°N):

The figure-8 (analemma): not the same as a day’s sine

If you photograph the Sun at the same clock time every day for a year, the spots form a tilted ∞ / figure-8 called the analemma. That shape comes from two yearly effects together:

  1. Declination: the Sun’s noon height drifts between the tropics as Earth orbits (≈ ±23.4°). That stretches the figure vertically.
  2. Equation of time: Earth’s elliptical orbit and axial tilt make “sundial noon” run fast or slow vs clock noon (by up to ~16 minutes). That wobbles the figure sideways and closes the 8.

The piece below plots it flat, EoT × declination: declination alone draws a vertical path, the equation of time alone draws a sideways wiggle, and both together stamp each noon as (x, y) = (equation of time, declination), that vector sum is why the year paints a figure-8.

The Sun at clock noon every fifth day of the year: declination, the equation of time, and both together.

So:

| Motion | What you hold fixed | Shape | |--------|---------------------|--------| | Daily height (sine of altitude) | One calendar day, all hours | Part of a sine curve (the gold curve in the first piece); the altitude angle itself is a steep triangle near the equator | | Analemma | One clock time, all year | Figure-8 (second piece) | | Solargraph | Long open shutter, many days | Stacked daily arcs on paper, not an analemma |

A multi-week solargraph does not draw the ∞ by itself, because the box sees the Sun all day, every day. The figure-8 only appears when you sample one instant per day. The slow seasonal drift of arcs on a solargraph is still the same physics that builds the analemma’s vertical span.

Does a three-month solargraph draw the figure-8 analemma?

A solargraph stacks whole daily arcs. The figure-8 appears only when you record the Sun at the same clock time each day.

See also Why Seasons Happen.

So a solargraph is not random streaks: it is periodic sun motion sampled every clear minute, burned into paper.

From sinusoid to pinhole trail

  1. The Sun moves on the sky (a daily arch + slow seasonal drift).
  2. Rays through the pinhole paint an inverted spot on the cylindrical paper.
  3. Unwrap that cylinder to a flat rectangle, the 2D paper image (what you scan).
  4. As the Sun climbs and falls, spots merge into daily arcs; next days shift slightly → stacked trails.

The interactive 3D → 2D projection panels show this mapping: gold burn on the can, purple dashed unwrap to the floating paper plane, and the matching 2D image on the right.

The burn on the curled paper, unwrapped to the flat sheet: Georgetown facing east against 45° N facing south, tilted up.

Compare two sites in June:

Tune your own geometry in the Solar Pinhole Camera simulator.

Building for the tropics

  1. Light-tight box: cardboard or tin; paint matte black inside.
  2. Pinhole: thin foil, clean round hole (~0.3-0.5 mm to start). Preview with the Solar Pinhole Camera and Optics Calculator.
  3. Paper: black-and-white photo paper loaded in darkness; seal in a bag until mounting.
  4. Weather seal: tape seams; shield from direct rain; expect high humidity to fog or stick paper if moisture enters.
  5. Aim: face a clear solar path and avoid deep shade all day. In Guyana the noon Sun is north of overhead from about 7 April to 4 September and south of it from mid-September to March, so a south-facing can misses or flattens the arcs for five months. For installs that span April to September, aim east or west, or tilt the can up, as in the field examples below.

Exposure strategy

A solargraph from Georgetown built up day by day, solstice to solstice: the Solar Pinhole Camera's own trails for its default can aimed east, one arc a day, 21 December 2026 to 21 June 2027.

Scanning and finishing

Open the can in dim light and scan the paper straight away (colour mode picks up subtle tones): it is not fixed, so it keeps darkening in light, and each extra scan fades it. Invert/curves carefully, solargraphs are soft by nature. Document location and dates for STEM / climate storytelling. Ask students to mark approximate noon on a day’s arc and relate it to the arc's highest point.

Field examples (AstroPhotosGY)

These three scans are from sealed pinhole cans on photographic paper (scanned, not developed). Photos: Samir Mohammed / AstroPhotosGY. Compare the arcs with the simulated paper below, east vs west vs tilted north.

The Solar Pinhole Camera's Sun track: aim and tilt the can, pick a start date and a number of days, and compare with the scans.

Safety and ethics

Never look at the Sun directly, or through binoculars, a telescope or a camera, without a certified solar filter fitted over the front of the optics. Aim the can by its shadow, and never look through the pinhole at the Sun. Get permission for rooftop or school mounts.

Practice with AstroPhotosGY

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