Altitude Calculation

When determining the rising and setting of an object, the effect of atmospheric refraction is usually considered, making the object’s rising time slightly earlier and the setting time later than they would be when there is no refraction. In this project, the atmosphere model used in calculating the altitude of a target is the same as in computing the star’s apparent positions. The atmospheric pressure in this model is the sea-level standard and the temperature is set to 10°C, deriving a negative angle of approximately 34 arcminutes at the horizon. For more details, please refer to the computing your own refraction angle section in the documentation of Skyfield — the key scientific Python package we use in this project.

Sunrise and Sunset

Both the atmospheric refraction and the radius of the sun are taken into account in defining sunrise and sunset. Skyfield uses the official definition of sunrise and sunset from the United States Naval Observatory (USNO):

For computational purposes, sunrise or sunset is defined to occur when … the center of the Sun is geometrically 50 arcminutes below a horizontal plane … The 50-arcminute geometric depression of the Sun’s center used for the computations is obtained by adding the average apparent radius of the Sun (16 arcminutes) to the average amount of atmospheric refraction at the horizon (34 arcminutes).

Star Visibility During Twilights

According to Tousey and Koomen (1953), the visibility of stars and planets during twilights are as follows:

• Sunrise/sunset: At this time, only the brightest stars or planets, such as Venus and Jupiter, may be visible to the naked eye.
• Civil dawn starts starts/ends: At this time, stars brighter than magnitude 1 are visible to the naked eye in most parts of the sky.
• Nautical twilight starts/ends: At this time, stars brighter than magnitude 4 are visible to the naked eye in most parts of the sky.

Time Zone

The time zone ID dataset invoked in this project is the “Same since 1970” from Timezone Boundary Builder. According to the IANA time zone database, this database attempts to record historical time zones and all civil changes since 1970 (the Unix time epoch).

The time zone IDs and standard offsets in this project represent the current time zone of a specific location. This is for deriving stable and unambiguous IDs while providing more familiar and intuitive local time reference for users. These time zone IDs are only used for deriving equinox/solstice dates, the time window determination for the rising/setting calculation, and the displayed Standard Time column in the result table.

Symbols of Arcminute and Arcsecond

Arcminutes and arcseconds are marked with the ASCII straight single quote ' and straight double quote " to adapt to various systems and media.

Date Format

ISO 8601

ISO 8601: Date and time format

# ISO 8601-2:2019
Date and time: YYYY-MM-DDThh:mm:ss[.sss][Z|±hh:mm]
Time range: YYYY-MM-DD/YYYY-MM-DD

Common Era

Year Dating Conventions from NASA explaining using BCE/CE instead of BC/AD:

In recent years, some historical scholars have advocated the use of the religiously neutral abbreviations BCE (for “Before Common Era”) to substitute for “BC,” and “CE” (for “Common Era”) to replace “AD.” These secular terms are both used as suffixes making them better suited to computer generated tables.