Time 3: Sunrise, Sunset and Twilight

Sunrise and sunset change through the year because solar declination changes, and the size of the change grows with latitude.

The ideal pattern

On an imaginary Earth with no axial tilt and no atmosphere, sunrise would occur at 0600 LMT and sunset at 1800 LMT everywhere. On the real Earth, the approximately 23.5 degree axial tilt makes the Sun's declination move north and south during the year. This changes the length of the daylight arc seen from each latitude.

Northern summer and southern winter

Near 21 June the Sun has its greatest northerly declination, about 23.5 degrees north. In northern latitudes sunrise is earlier, sunset is later and day is longer. In southern latitudes sunrise is later, sunset is earlier and day is shorter. Near and north of the Arctic Circle the Sun can remain continuously above the horizon, while corresponding southern latitudes can have continuous night.

Northern winter and southern summer

Near 21 December the pattern reverses. Northern latitudes have a short day and a long night. Southern latitudes have a long day and a short night. The polar day moves to the south and the polar night to the north.

Equinoxes and the equator

At the March and September equinoxes solar declination is approximately zero, so sunrise and sunset occur at broadly similar LMT at all latitudes that experience both events. At the equator, day and night remain nearly equal throughout the year. Refraction and the upper-limb convention make the visible day slightly longer.

The Air Almanac supplies sunrise, sunset, morning civil twilight and evening civil twilight as Local Mean Time for a stated date and latitude.

Sunrise and sunset tables, methodology

Oxford's training extract tabulates sunrise and sunset for every third day and for selected latitudes from 72 degrees north to 60 degrees south. Latitude rows are 10 degrees apart near the equator, 5 degrees apart in middle latitudes and 2 degrees apart in high latitudes. The working answer is interpolated to the nearest minute.

The table entry is LMT at sea level. Longitude is not used to enter the table because, on a given date, points on the same parallel have the same sunrise or sunset LMT. Longitude is used only after the table lookup, when LMT is converted to UTC. Standard Time or IST is then found from UTC.

Two-dimensional interpolation

1. Bracket the required date between the adjacent tabulated dates.
2. Interpolate the event time for each bracketing latitude.
3. Interpolate those results for the required latitude.
4. Round the final event time to the nearest minute.
5. Convert the LMT to UTC using longitude, then apply the required civil time correction.

Worked latitude interpolation

In the supplied training extract for 21 March, sunrise is 0604 LMT at 20 degrees north and 0603 LMT at 30 degrees north. Delhi's latitude, about 28.6 degrees north, lies 86 per cent of the way from 20 to 30 degrees. The one-minute difference gives an interpolated value very close to 0603 LMT.

An Almanac problem has two distinct stages: obtain the event in LMT, then carry out an ordinary time conversion.

The conversion direction

Sunset at Innsbruck

The Air Almanac gives 1833 LMT for sunset at latitude 47 degrees 15 minutes north on 5 September. Longitude 11 degrees 20 minutes east equals 45 minutes 20 seconds of time, rounded to 45 minutes. East LMT is ahead of UTC, so subtract 45 minutes: sunset is 1748 UTC. Adding Austria's one-hour Standard Time correction gives 1848 Standard Time.

Sunrise at Keflavik

At latitude 64 degrees north on 14 October, sunrise is 0645 LMT. Longitude 22 degrees 30 minutes west equals 1 hour 30 minutes. West LMT is behind UTC, so add 1 hour 30 minutes: sunrise is 0815 UTC. With no civil-time correction, this is also 0815 Standard Time.

Sunset and twilight at Karachi

For 18 August at about 25 degrees north, the training extract gives sunset as 1833 LMT and ECT as 1857 LMT. Karachi is at approximately 67 degrees 10 minutes east, equivalent to 4 hours 29 minutes. Subtracting this from 1833 gives 1404 UTC. Evening civil twilight lasts 24 minutes because 1857 minus 1833 equals 24 minutes.

Twilight is the period of useful illumination before sunrise and after sunset while the Sun is below the horizon.

Civil twilight

Civil twilight runs while the Sun's centre is between 0 degrees 50 minutes and 6 degrees below the sensible horizon. There is normally enough natural illumination for ordinary outdoor activity without additional lighting. Morning civil twilight begins when the centre reaches 6 degrees below the horizon and ends at sunrise. Evening civil twilight begins at sunset and ends when the centre reaches 6 degrees below the horizon.

Nautical twilight

Nautical twilight occurs while the Sun's centre is between 6 and 12 degrees below the sensible horizon. General outlines remain discernible and the brighter stars are visible.

Astronomical twilight

Astronomical twilight occurs while the centre is between 12 and 18 degrees below the sensible horizon. Beyond 18 degrees, the Sun no longer contributes significant sky illumination and astronomical darkness is present.

Civil twilight tables in the Air Almanac

The Morning Civil Twilight table gives the LMT at which morning civil twilight begins. The Evening Civil Twilight table gives the LMT at which evening civil twilight ends. Both are sea-level values. They are interpolated for date and latitude in the same way as sunrise and sunset.

Night for operations

When an operational rule uses civil twilight, the night period runs from the end of evening civil twilight to the beginning of morning civil twilight, unless the applicable Indian rule or publication prescribes another period. Pilots must use the definition governing the operation, not assume that sunset alone always begins legal night.

Twilight duration depends on how steeply the Sun's apparent path crosses the horizon. A steep path gives short twilight; a shallow path gives long twilight.

Duration of twilight calculations

At New York, 41 degrees north, on 19 July the training extract gives sunset at 1929 LMT and ECT at 2001 LMT. Evening civil twilight therefore lasts 32 minutes.

Twilight at the equator

Near an equinox, the Sun's path is nearly vertical to the horizon at the equator. From visible sunset, when the centre is 0 degrees 50 minutes below the sensible horizon, to ECT at 6 degrees below, the Sun moves through 5 degrees 10 minutes. At 15 degrees per hour this is approximately 21 minutes, the minimum civil-twilight duration between 60 degrees north and 60 degrees south.

Twilight between the equator and 60 degrees north or south

Away from the equator, the Sun normally cuts the horizon at a shallower angle, so it takes longer to move through the civil-twilight band. Date matters because declination changes the angle of the solar path. The Air Almanac is used rather than a fixed correction.

Twilight in high latitudes

At high latitude the Sun can remain above the horizon all day, remain below it all day, or set without ever reaching 6 degrees below the horizon. In the last case, evening twilight continues until morning twilight and there is no intervening night by the civil-twilight criterion.

Air Almanac times are tabulated for an observer at sea level. Height changes the visible horizon and therefore changes the observed event.

Effect on sunrise and sunset

A higher observer can see farther around Earth's curvature. The visible horizon is depressed below the sea-level tangent. Sunrise is therefore seen earlier than the published sea-level time, and sunset is seen later.

Effect on twilight

Increasing height generally shortens the observed duration of civil twilight. The elevated observer sees sunrise earlier and sunset later, while less atmosphere remains above the observer to refract sunlight during twilight. At very great height the atmospheric twilight interval becomes small.

The safest way to solve an Indian sunrise or twilight question is to keep the astronomical lookup, the longitude conversion and IST as three separate steps.

Worked Delhi sunrise

Use the supplied training extract for 21 March and a Delhi latitude of about 28.6 degrees north. Interpolation between 0604 LMT at 20 degrees north and 0603 LMT at 30 degrees north gives 0603 LMT to the nearest minute.

Delhi longitude is approximately 77 degrees 13 minutes east. This is 5 hours 08 minutes 52 seconds in time, rounded to 5 hours 09 minutes. East LMT is ahead of UTC, so 0603 LMT minus 5 hours 09 minutes gives 0054 UTC. IST is UTC plus 5 hours 30 minutes, giving approximately 0624 IST.

Worked checklist

1. Identify the event: sunrise, sunset, MCT or ECT.
2. Enter the correct table using date and latitude.
3. Interpolate date and latitude to the nearest minute.
4. Record the table answer as LMT.
5. Convert longitude to time and obtain UTC.
6. Add 5 hours 30 minutes for IST when the question asks for Indian Standard Time.
7. Check whether the date changes at midnight.

Final cross-checks