EARTH, SUN & THE EQUATION OF TIME
The Sun keeps
its own time.
A sundial and a clock can both be working perfectly—and still disagree.
Move through a year. Watch Earth’s orbit and tilt shift solar noon. See the same story unfold in the sky, on a dial, and in the numbers.
Based on “Earth’s Tilt Makes Time Slippery” ↓One orbit. Two sources of drift.
Earth spins on its axis while revolving around the Sun. Scrub the year or the UTC time of day to turn the globe at the shared instant. Playback starts at 6 hours/sec; choose 1 hour/sec for a closer look or 12 days/sec to follow the orbit. At that fastest speed, daily rotation is too fast to follow. Sizes are enlarged; the axis stays fixed in space.
Drop a pin. Follow the Sun.
Click or drag to place the pin. Arrow keys move it 1°; Shift moves it 10°. Coordinates drive the model; coastlines are schematic. Dark shading shows the night side.
Higher settings exaggerate the effect. “Neither” gives a circular orbit, no tilt, and no seasonal clock drift.
Not every shift goes east.
Earth-centred sky view: gold is the ecliptic, mint is the equator. The dashed line projects the Sun onto the equator. The inset magnifies one day’s angular change; east is measured around the spin axis.
A full turn isn’t quite a day.
Earth spins and orbits counterclockwise when viewed from the north. After one turn relative to distant stars, it has moved along its orbit. Your meridian must turn a little further to face the Sun again.
This replay advances the shared instant from one local solar noon to the next at your observer pin. Every view follows the same time. Orbital movement and the extra turn are enlarged 20× in this drawing; readouts use the unscaled model and rotation remains uniform.
A few seconds each day. Minutes over a season.
Click or drag across the curve to choose a date. Positive = sundial ahead. Negative = sundial behind.
The sundial’s correction table
Read the date, then add or subtract the correction—just like the plaque in the video.
| Date | Equation of time | To get mean time | Solar day vs 24h |
|---|
Table rows sample each date at 00:00 UTC; the live correction above uses your selected time and can differ by a few seconds. Corrections recover local mean solar time. Your civil clock also needs longitude, zone and daylight-saving adjustments. Video · 24:03 ↗
The figure eight has a reason.
Plot the Sun at the same mean time each day. Tilt moves it north and south; its east–west timing offset changes too. On Earth, those motions trace an unequal figure eight.
Coordinate plot: horizontal = solar time offset; vertical = solar declination. A photograph’s orientation and height also depend on location and time of day.
A curve built into a sundial
The Schmoyer Sunquest dial uses a shaped gnomon and a narrow band of light to incorporate this seasonal correction. The user turns the gnomon to sharpen the beam; correct latitude, longitude and seasonal setup still matter.
This switch demonstrates the arithmetic, not a mechanical replica. Video · 25:38–31:03 ↗
Noon isn’t always overhead.
Longitude, time zone & clock corrections
Longitude changes local solar time by four minutes per degree. Places farther east reach noon earlier. Rail timetables helped make shared civil times useful.
Offsets and daylight saving are educational settings, not a live legal time-zone database. Changing them preserves UTC; changing the time-of-day slider advances or rewinds the shared instant.
Geometric horizon; no atmospheric refraction. Daylight hours vary, while an ordinary civil day is 24 hours. A vertical stick illustrates shadows, not a calibrated latitude-aligned sundial.
FROM THE FULL TRANSCRIPT
The rest of the time story.
Small details matter. These notes retain the video’s related points without confusing them with the annual equation of time.
01 A day can mean three different things 03:22 ↗
Daylight is sunrise to sunset, and changes with latitude and season. An apparent solar day is one meridian crossing of the Sun to the next. A mean solar day averages out the seasonal variation. Sand, water, mechanical and atomic clocks count regular intervals; they do not automatically follow changing daylight. Civil calendars usually label days from midnight to midnight.
02 Is Earth’s spin really constant? 10:10 ↗
The episode explicitly sets aside small rotational changes and orbital perturbations to isolate the annual effect. Over geological time Earth’s spin has slowed; daily and seasonal growth bands in fossil coral provide evidence of more, shorter days per year. Atomic clocks are a stable comparison, but this model is not a simulation of atomic standards or leap seconds. The fish-bone example at 12:29 concerns seasonal dating of past events, rather than keeping a clock.
03 Stars, navigation and sidereal time 17:34 ↗
A sidereal day measures rotation against distant stars, about 23 hours 56 minutes. Their great distance makes the annual parallax tiny compared with the Sun’s apparent orbital motion. The video relates this stable reference to navigation. The etymology of “consider” is presented as a possibility, not an established explanation of timekeeping.
04 The subsolar point and Lāhainā noon 32:43 ↗
The subsolar point is where the Sun is directly overhead. It moves around Earth during the day and north or south over the year. With Earth’s tilt, an overhead Sun is possible only between the tropics. At tropical latitudes it usually occurs twice per year; at the tropics, once. Hawaii’s Lāhainā noon makes vertical objects’ shadows fall beneath their bases. Ordinary solar noon only means the Sun is crossing the local meridian—it need not be overhead.
The Skygate sculpture at 37:00 illustrates a shaped object making a special shadow under overhead light. The shadow view uses a simple stick to make the same geometry clear.
05 Moon shadows don’t mark midnight 37:55 ↗
An overhead Moon is not a definition of midnight. Its position follows its own orbit, and its range in declination changes over an approximately 18.6-year cycle. A high Moon in London still does not reach the zenith. The episode’s named “Lāhainā midnight” is playful and immediately questioned by the speakers. This solar model does not predict lunar events.
06 What happens at night—or under clouds? 47:35 ↗
A Sun-based dial needs direct sunlight. Clouds, tree cover and night prevent useful readings. Near an overhead Sun, a vertical stick’s shadow becomes very short; that does not mean every sundial design becomes useless. Moon dials need a sufficiently bright Moon above the horizon and a clear sky; moonrise does not simply coincide with sunset. Neither the Sun nor the Moon guarantees an always-available clock.
07 Other time-related asides 42:33 ↗
The Uranus closest-approach calculator illustrates that an event’s exact timing can depend on the observer’s location and altitude. It is not a mechanism behind the equation of time. Geological seasonal dating, discussed at 12:29, is also retained above. Advertising, linguistic jokes, manufacturing claims, unrelated art discussion and ocean geography are outside this timekeeping simulation.
Sources, assumptions & how the model works
This guide was mapped to the supplied English auto-caption transcript of Earth’s Tilt Makes Time Slippery (00:00–49:41). Captions can contain transcription mistakes; time links let you check the original explanation.
Kepler’s equation gives position on a fixed elliptical orbit. Solar longitude is projected onto a tilted equatorial plane to obtain right ascension and declination. The equation of time is mean longitude minus right ascension, converted at four minutes per degree. Tilt and orbit contributions sum exactly in this model; the tilt contribution depends on the current orbital position.
A representative 365-day calendar labels a 365.2422-day model orbit, with perihelion near 4 January. No claim of year-specific ephemeris precision: precession, nutation, aberration, atmospheric refraction, solar disk size and changes in rotation are omitted. Solstice/equinox buttons are approximate calendar markers and move slightly in the model when eccentricity changes. Noon-to-noon readouts solve for successive transits starting on the selected model day. Values are educational, not navigation or precision timing predictions.
Supporting references: US Naval Observatory: equation of time; North American Sundial Society: Schmoyer Sunquest.