Solar time, sunrise and twilight

Why is apparent solar time different from mean solar time?

A real Sun and a fictitious uniform mean Sun do not cross the meridian together every day.

Two effects disturb uniform apparent motion

The Earth’s orbit is elliptical, so orbital angular speed varies. The Earth’s axis is tilted relative to the orbital plane, so equal movement along the ecliptic does not project into equal movement along the celestial equator. Together these effects produce the equation of time.

Here define E=apparent solar time−local mean solar time. If LMT is 12:00 and E=+8 min, apparent solar time is 12:08. Definitions in tables can reverse the sign, so read the table convention instead of memorising an unqualified addition rule.

Declination drives the seasonal pattern

Solar declination is the Sun’s angular distance north or south of the celestial equator. It is near zero at equinoxes and near±23.4° at solstices. Northern positive declination gives longer northern days and shorter southern days.

Local apparent noon occurs when the Sun crosses the observer’s meridian. It need not occur at 12:00 on the civil clock: longitude within the time zone, legal time offset and equation of time all contribute. Do not use a schematic noon to infer an operational sunrise.

Find when apparent noon occurs on a mean clock

Under E = apparent − mean, let the supplied equation of time be +12 minutes. Apparent noon occurs at apparent solar time 12:00, so the local mean clock then reads 11:48. At 15°E, approximate Greenwich mean time is another hour earlier, 10:48. The order of the two conversions matters less than keeping their reference labels.

If a civil zone offset were supplied, convert that Greenwich/UTC approximation to the legal clock separately. This inverse task explains why a sundial’s noon, local mean noon and civil 12:00 need not coincide. The equation of time changes with date; the laboratory deliberately supplies it as an input to isolate the sign convention, not to substitute for an astronomical almanac.

What sets the length of day and twilight?

Latitude and solar declination determine how the Sun crosses the horizon.

Follow the tilted daily circle

A simple geometric horizon model gives cos H0=−tan(latitude)tan(declination), where H0 is the sunset hour angle. Daylight≈2 H0/15 hours. At 45°N and declination+20°, H0≈111.3°, giving 14.84 hours. If the right-hand side lies outside−1 to+1, the model indicates continuous day or night.

This model uses the Sun’s centre at a geometric horizon. Published sunrise/sunset tables include their stated refraction and solar-disc conventions and may use a standard altitude near−0.833°. Terrain, observer height and actual refraction alter what is seen. Use authoritative operational tables and the applicable legal definitions.

Twilight is a depression angle

Civil, nautical and astronomical twilight correspond conventionally to the Sun’s centre 6°, 12° and 18° below the horizon. Their duration depends on the angle at which the solar path meets the horizon; high latitudes can have very long twilight or no occurrence of a specified boundary.

Do not treat the word night as a universal fixed depression angle. Licensing and operating rules can define it differently. A schedule calculation must identify which boundary the question or rule uses and the date, latitude, longitude and time reference of the table.

Compare equal daylight with unequal twilight

At an equinox, the geometric model gives about 12 hours of daylight at many latitudes, yet twilight duration differs. Near the equator the Sun’s daily path crosses the horizon more steeply; at high latitude it crosses at a shallow angle and takes longer to descend through a fixed depression angle. Equal day length therefore does not imply equal twilight length.

For the 45°N, +20° declination example, the geometric sunset is around 19.42 local apparent solar time and sunrise around 04.58. These decimal hours are about 19:25 and 04:35, not 19:42 and 04:58. Converting decimal hours into minutes is a separate step. Published sunrise tables should be used for an operational timing task, with their own definitions and refraction assumptions.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.