The Sun, the seasons and the clock: one time for every measurement

On 21 June 2026, the day lasts 16 h 11 in Paris and 9 h 54 in Sydney. At the same instant, 12:00 UTC, it is 14:00 in Paris and 22:00 in Sydney. Solar irradiance follows two cycles at once, the day and the year, and these cycles do not fall at the same hour from one place to another: to compare and align measurements, one clock is needed, Coordinated Universal Time (UTC).

Go to:

1. The Earth around the Sun

2. Why the tilt makes the seasons: longer days, higher Sun

3. Day and night on Earth

4. One clock (UTC), two local times

The starting case: this morning, 25 October 2026

The animation opens at 06:00 UTC. In Paris it is 07:00 and still night: the Sun rises at 07:24 (06:24 UTC). In Sydney it is 17:00 and the Sun will set at 19:15. Last night at 03:00, Paris went back to winter time (UTC+1); Sydney has been on summer time (UTC+11) since 4 October. The two clocks are therefore 10 hours apart today, 8 hours in June. Move the date and the instant, or play a year or a day.

1. Around the Sun: the seasons

The Earth's rotation axis is tilted by 23.44° and keeps the same direction in space all year. In June the North Pole leans towards the Sun: the northern hemisphere gets higher and longer sunshine, it is summer; in December it is the reverse, and summer is in Sydney. The latitude where the Sun is overhead at noon is the declination δ; it goes from +23.44° (June solstice) to −23.44° (December solstice). Distance plays no part: the Earth is closest to the Sun in early January, in the middle of the northern winter.

The tilt acts in two ways that add up. Longer days (view 2): when the axis leans towards the Sun, the circle of latitude of Paris spends more than half its turn in the light, that of Sydney less; at the equinoxes every circle is half lit, 12 h. A higher Sun (sketch under view 1): the same 1 m² beam of rays covers 1.11 m² of ground in Paris on 21 June (Sun at 65°) but 1.85 m² in Sydney (Sun at 33°): each square meter receives less. More time and more energy per square meter: that is summer.

2. Rotation: day and night

The Earth turns by 15° per hour. Solar noon, when the Sun crosses the local meridian, therefore comes 4 minutes earlier per degree of longitude to the east. In Paris (2.35° E) it falls around 11:51 UTC on 21 June, 13:51 on the clock; in Sydney (151.2° E) around 01:56 UTC, 11:56 on the clock. Up to a few minutes (the equation of time, from −14 to +16 minutes over the year), noon is the same nowhere: the map shows the lit area and the point where the Sun is overhead.

3. Day length

The higher the latitude and the more the declination has the same sign, the larger the lit part of the parallel. On 21 June the day lasts 16 h 11 in Paris (sunrise 05:46, sunset 21:57, summer time) and 9 h 54 in Sydney; on 21 December, 8 h 15 in Paris and 14 h 25 in Sydney. In UTC, Sydney's day straddles two dates: on 21 June the Sun rises there on 20 June at 20:59 UTC. Below, the top scale is one single clock, UTC, shared by both cities: a UTC instant is the same everywhere (red line). Each band shows day (yellow), twilight (gray) and night (blue); under each band, the scale of the local clock shows that the same instant does not carry the same number in Paris and in Sydney.

4. The double seasonality of irradiance

Outside the atmosphere, on a horizontal plane, irradiance is G₀ = G_sc·E₀·cos θ_z, with G_sc = 1361 W/m², E₀ = 1 + 0.033·cos(2π n/365) and θ_z the zenith angle. It carries two cycles: the daily cycle (rotation) and the yearly cycle (tilt), which modulates the height and length of the first. On the heat maps each column is a day and each row a UTC hour: the bright band of Paris is centred near 12 h UTC, that of Sydney near 2 h UTC, cut in two by UTC midnight; one widens in June, the other in December. Forecasting methods use this structure, for instance through the clear-sky index or cyclic persistences such as BLEND.

Outside the atmosphere, by date and UTC hour

The chosen day: G0 against UTC hour

The year: extraterrestrial energy per day

5. Timestamping measurements: one clock

Legal time is UTC plus an offset that changes twice a year, on dates that differ between countries: Paris is UTC+1 in winter and UTC+2 in summer, Sydney UTC+10 in the austral winter and UTC+11 in the austral summer. A series stamped in legal time therefore loses one hour in spring and sees one twice in autumn, and two stations in different countries are not aligned. The tables below show it, half-hour by half-hour, around the three changes of 2026.

Timestamp in UTC (ISO 8601, for instance 2026-10-25T06:00Z) and keep the site longitude to move to solar time.
State whether the stamp marks the start, the middle or the end of the averaging period: a half-period shift moves the whole daily curve and biases the comparison with a model.
Check the alignment on a clear-sky day: the measured maximum must fall near the computed solar noon.

The same instant on three clocks

Words of the page

Declination δ: latitude where the Sun is overhead at noon; from −23.44° to +23.44° over the year.
Equation of time: difference, from −14 to +16 minutes, between true solar noon and the noon of a mean Sun; due to the elliptical orbit and the tilt.
True solar time, hour angle: true solar time is UTC + equation of time + 4 min per degree of east longitude; the hour angle is zero at solar noon and grows by 15° per hour.
Zenith angle θz: angle between the vertical and the direction of the Sun; cos θz = sin φ sin δ + cos φ cos δ cos h.
UTC: Coordinated Universal Time: one clock for the whole Earth, without summer time.
Legal time: UTC plus an offset set by each country, which may change in summer.
G0: extraterrestrial solar irradiance on a horizontal plane: the upper bound of any ground measurement.

Method and checks

Declination and equation of time: Fourier series of Spencer (1971), as used in the NOAA solar position calculations; sunrise and sunset at a zenith angle of 90.833° (refraction and solar disc radius). Checked against pvlib 0.15.2 (NREL SPA algorithm) for Paris and Sydney on the 2026 equinoxes and solstices: sunrise, noon and sunset within 3 minutes. G_sc = 1361 W/m² (Kopp and Lean, 2011). Legal times: IANA zones Europe/Paris and Australia/Sydney from the browser. Map: Natural Earth 1:110m land (public domain). A teaching animation: the irradiance shown is extraterrestrial, not a measurement or a forecast.

Further: solar forecasting basics, with the equations · the forecast comparison · complex-valued forecasting.