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 the interactive demo below the article: the cyan point on the circle, the gold projection, and the teal sine curve 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 apparent altitude over one day (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).

Why the Sun looks sinusoidal

Earth rotates once per sidereal day at nearly constant angular speed. From a fixed site, the Sun’s altitude over a clear day rises after sunrise, peaks near local noon, and falls to sunset, a smooth arch. Plot altitude against time and you get a curve that is approximately sinusoidal for much of the day (especially away from the horizon, where refraction and the flat-horizon cutoff warp the edges).

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 interactive demos show this two ways: a flat EoT × declination plot, and a 3D projection board where tilt alone draws a vertical path, orbit timing 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.

So:

| Motion | What you hold fixed | Shape | |--------|---------------------|--------| | Daily altitude | One calendar day, all hours | Near-sinusoid (gold height in the first demo) | | Analemma | One clock time, all year | Figure-8 (second demo) | | 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.

See also Earth’s Motion and Seasons.

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 (daily sinusoid + 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.

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 (southward arcs still matter near the equator; avoid deep shade all day).

Exposure strategy

Scanning and finishing

Scan paper (often colour mode picks up subtle tones). 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 sine peak.

Field examples (AstroPhotosGY)

These three scans are from sealed pinhole cans on photographic paper (processed). Compare the arcs to the interactive projection demos below, east vs west vs tilted north.

Safety and ethics

Never look at the Sun through improvised optics. Solargraphy uses a closed box, still treat solar viewing tools with respect. Get permission for rooftop or school mounts.

Practice with AstroPhotosGY

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