@spec equation_of_time(float()) :: float()

Returns the equation of time in minutes.

Arguments

• julian_centuries is any moment in time expressed as Julian centuries from J2000.0.

Returns

• the discrepancy between apparent solar time and mean solar time in minutes as a float. A positive value means the sundial is ahead of the clock.

Notes

The equation of time describes the discrepancy between apparent solar time (which directly tracks the Sun's diurnal motion) and mean solar time (which tracks a theoretical mean Sun with uniform motion).

During a year the equation of time ranges from about +16 min 33 s (around 3 November) to −14 min 6 s (around 11 February), with zeros near 15 April, 13 June, 1 September, and 25 December.

The two principal causes are the obliquity of the ecliptic (~23.44°) and the eccentricity of the Earth's orbit (~0.0167).

Examples

iex> Astro.Solar.equation_of_time(0.0)
-3.244441990189671

@spec equinox_and_solstice(pos_integer(), :march | :june | :september | :december) ::
  {:ok, DateTime.t()}

Returns the UTC datetime of an equinox or solstice.

Arguments

• year is a positive integer Gregorian year.

• event is one of :march, :june, :september, or :december identifying the equinox or solstice.

Returns

• {:ok, datetime} where datetime is a DateTime.t() in UTC.

Notes

The :march and :september events are the equinoxes (Sun's ecliptic longitude 0° and 180° respectively). The :june and :december events are the solstices (ecliptic longitude 90° and 270°).

Examples

iex> {:ok, dt} = Astro.Solar.equinox_and_solstice(2024, :march)
iex> dt.year
2024
iex> dt.month
3
iex> dt.day
20

Returns an approximate moment at or before t when the solar ecliptic longitude just exceeded lambda degrees.

Arguments

• lambda is the target solar ecliptic longitude in degrees.

• t is any moment in time expressed as a moment (fractional days since the epoch).

Returns

• the approximate moment (fractional days since the epoch) at or before t when the solar ecliptic longitude last exceeded lambda degrees.

Examples

# Estimate when the Sun last passed 90° before the June solstice
iex> moment = Astro.Time.date_time_to_moment(~D[2024-06-21])
iex> result = Astro.Solar.estimate_prior_solar_ecliptic_longitude(90, moment)
iex> {:ok, dt} = Astro.Time.date_time_from_moment(result)
iex> dt.year
2024
iex> dt.month
6

Returns the solar ecliptic longitude in degrees.

Arguments

• t is any moment in time expressed as a moment (fractional days since the epoch).

Returns

• the solar ecliptic longitude in degrees as a float, in the range 0..360.

Notes

The solar ecliptic longitude is the position of the Sun on the celestial sphere along the ecliptic. It is also an effective measure of the position of the Earth in its orbit around the Sun, taken as 0° at the moment of the vernal equinox.

Since it is based on how far the Earth has moved in its orbit since the equinox, it is a measure of what time of the tropical year (the year of seasons) has elapsed, without the inaccuracies of a calendar date which is perturbed by leap years and calendar imperfections.

For a moment the loaded ephemeris does not cover, the longitude is computed from the Meeus series, accurate to about 0.01°, as Astro 2.7 computed it for every moment. Calendars that count months by the Sun's longitude, such as the Chinese and Japanese lunisolar calendars, find their solar terms for dates of any era this way.

Examples

iex> moment = Astro.Time.date_time_to_moment(~D[2024-03-20])
iex> Astro.Solar.solar_ecliptic_longitude(moment)
359.87145169401623

iex> moment = Astro.Time.date_time_to_moment(~D[1000-06-01])
iex> Astro.Solar.solar_ecliptic_longitude(moment) |> Float.round(4)
69.5887

@spec solar_ecliptic_longitude_after(number(), Astro.Time.time()) :: Astro.Time.time()

Returns the moment (UT) of the first time at or after moment t when the solar ecliptic longitude will be lambda degrees.

Arguments

• lambda is the target solar ecliptic longitude in degrees.

• t is any moment in time expressed as a moment (fractional days since the epoch).

Returns

• the moment (fractional days since the epoch) when the solar ecliptic longitude reaches lambda degrees.

Examples

# Find the June solstice (longitude 90°) in 2024
iex> moment = Astro.Time.date_time_to_moment(~D[2024-05-22])
iex> result = Astro.Solar.solar_ecliptic_longitude_after(90, moment)
iex> {:ok, dt} = Astro.Time.date_time_from_moment(result)
iex> dt.year
2024
iex> dt.month
6

@spec solar_noon_utc(float(), Astro.longitude()) :: float()

Returns solar noon as minutes since midnight UTC.

Arguments

• julian_centuries is any moment in time expressed as Julian centuries from J2000.0.

• longitude is the longitude in degrees of the location from which solar noon is to be measured. West is negative.

Returns

• solar noon as a float number of minutes since midnight UTC.

Notes

Solar noon is the moment when the Sun passes a location's meridian and reaches its highest position in the sky. In most cases it does not occur at 12:00 local time.

Examples

iex> Astro.Solar.solar_noon_utc(0.0, 151.2093)
1328.2818354717708

@spec sun_geometric_mean_longitude(float()) :: float()

Returns the Sun's geometric mean longitude in degrees.

Arguments

• julian_centuries is any moment in time expressed as Julian centuries from J2000.0.

Returns

• the mean solar longitude in degrees as a float, in the range 0..360.

Notes

Mean longitude is a convenient uniform measure of how far around its orbit a body has progressed since passing the reference direction. While mean longitude assumes constant speed, true longitude accounts for the body's actual speed which varies around its elliptical orbit. The difference between the two is the equation of the centre.

Examples

iex> Astro.Solar.sun_geometric_mean_longitude(0.0)
280.46646