Solar position

SolarPosition(azimuth, elevation, apparent_elevation)

Represents the position of the Sun relative to an observer.

Fields

• azimuth::Real: solar azimuth angle (degrees, measured clockwise from north)
• elevation::Real: solar elevation angle above the horizon (degrees)
• apparent_elevation::Real: elevation corrected for atmospheric refraction (degrees)

aberration_correction(heliocentric_radius)

An adjustment applied to celestial coordinates to account for the apparent displacement caused by Earth’s motion through space.

apparent_sidereal_greenwich_time(
    mean_sidereal_greenwich_time,
    nutation_longitude, 
    elliptic_obliquity
)

Greenwich sidereal time corrected for the effects of nutation giving the true rotation angle relative to the apparent equinox.

apparent_sun_longitude(geocentric_longitude, nutation_longitude, aberration_correction)

The Sun’s ecliptic longitude after applying corrections for nutation and aberration.

apparent_zenith(solpos::SolarPosition)

The complementary to 90° (degrees) of the Sun's apparent elevation.

ascending_moon_longitude(julian_ephemeris_century)

The ecliptic longitude referenced to the mean equinox of the date, of the point where the Moon’s mean orbit crosses northward through the ecliptic.

delta_T(month::Int, year::Int)

Computes the difference between Terrestrial Dynamical Time (TD) and Universal Time (UT).

It is evaluated as a piecewise polynomial, as per NASA, which in turn refer to [2, 3]. Note that $\Delta T$ is unknown for years before -1999 and after 3000. Values could be calculated for such intervals, although they are not intended to be used for these years.

elliptic_obliquity(mean_elliptic_obliquity, nutation_obliquity)

The angle between Earth’s equator and the mean ecliptic defined as an ideal, unperturbed ellipse.

geocentric_latitude(heliocentric_latitude)

A celestial object's angular distance north or south of the ecliptic plane as measured from Earth’s center.

geocentric_longitude(heliocentric_longitude)

A celestial object's ecliptic longitude as measured from Earth’s center, referenced to the ecliptic plane and the vernal equinox.

geocentric_sun_ascension(
    apparent_sun_longitude,
    elliptic_obliquity,
    geocentric_latitude
)

The angle measured eastward from the geocentric meridian, that locates a direction or point relative to Earth’s ellipsoid rather than its rotational axis.

geocentric_sun_declination(
    apparent_sun_longitude,
    elliptic_obliquity,
    geocentric_latitude
)

The Sun’s angular distance, north or south of Earth’s equatorial plane as measured from Earth’s center.

heliocentric_latitude(julian_ephemeris_millenium)

A celestial object's angular position around the Sun measured in the ecliptic plane from a defined reference direction.

heliocentric_longitude(julian_ephemeris_millenium)

A celestial object's angular distance north or south of the ecliptic plane as measured from the Sun.

heliocentric_polynomial(julian_ephemeris_millenium, coefficients)

Polynomial approximation for the heliocentric longitude, latitude, radius.

heliocentric_radius(julian_ephemeris_millenium)

The distance from the Sun to the celestial object in a chosen heliocentric coordinate system. In this case, it corresponds to the Earth-Sun distance.

julian_century(julian_day)

A time interval of exactly 36,525 days (365.25 days × 100) used as a standard unit in astronomy.

julian_ephemeris_century(julian_ephemeris_day)

A 36,525-day interval measured specifically in Ephemeris Time (or its modern dynamical time scales) for high-precision astronomical modeling.

julian_ephemeris_day(julian_day, ΔT)

A continuous count of days measured in uniform Ephemeris Time (or its successors).

julian_ephemeris_millenium(julian_ephemeris_century)

A 1,000-year interval equal to 365,250 ephemeris days, defined within Ephemeris Time for long-term astronomical calculations.

mean_elliptic_obliquity(julian_ephemeris_millenium)

The angle between Earth’s equator and the mean (long-term averaged) ecliptic defined by an unperturbed elliptical Earth orbit.

mean_moon_anomaly(julian_ephemeris_century)

The uniformly increasing angular position of the Moon in its elliptical orbit measured from perigee.

mean_moon_elongation_from_sun(julian_ephemeris_century)

The average angular separation between the Moon and the Sun as measured along the ecliptic.

mean_sidereal_greenwich_time(julian_day, julian_century)

The hour angle of the mean vernal equinox at the Greenwich meridian reflecting Earth’s rotation relative to the fixed stars without nutation effects.

mean_sun_anomaly(julian_ephemeris_century)

The angular position of the Sun in its elliptical orbit, measured from perihelion and increasing uniformly in time.

mean_sun_longitude(julian_ephemeris_millenium)

The Sun’s ecliptic longitude calculated from a uniformly moving fictitious Sun on the ecliptic.

moon_latitude_argument(julian_ephemeris_century)

The angle from the Moon’s ascending node to its position measured along its orbit, using mean (unperturbed) orbital elements.

nutation_coefficients(julian_ephemeris_century)

Constructs the vector of weights for evaluating the nutation_longitude and nutation_obliquity.

nutation_longitude(julian_ephemeris_century, nutation_coefficients)

The small periodic variation in Earth’s ecliptic longitude caused by gravitational torques from the Moon and Sun.

nutation_obliquity(julian_ephemeris_century, nutation_coefficients)

The small periodic variation in Earth’s axial tilt (obliquity) resulting from gravitational perturbations.

observer_local_hour(
    observer_longitude, 
    apparent_sidereal_greenwich_time, 
    geocentric_sun_ascension
)

The angle between the observer’s local meridian and a celestial object measured westward on the celestial sphere.

radial_distance_equatorial_plane(
    observer_latitude,
    observer_altitude,
    reduced_observer_latitude
)

The perpendicular distance of a point from Earth’s equatorial plane.

radial_distance_rotational_axis(
    observer_latitude, 
    observer_altitude,
    reduced_observer_latitude
)

The perpendicular distance of a point from Earth’s spin axis.

reduced_observer_latitude(observer_latitude)

The angle whose tangent equals the tangent of the geodetic latitude scaled by Earth’s polar-to-equatorial radius ratio, representing the point’s projection onto the surface of the reference ellipsoid.

spa(location::Location, datetime::DateTime)

Computes the solar position in terms of Solar azimuth, elevation, and apparent elevation, following the solar position algorithm [4].

sun_ascension_parallax(
    radial_distance_equatorial_plane, 
    sun_equatorial_horizontal_parallax, 
    geocentric_sun_declination, 
    observer_local_hour
)

The correction to the Sun’s right ascension due to the difference between geocentric and topocentric perspectives.

sun_equatorial_horizontal_parallax(heliocentric_radius)

The angle between the Sun’s direction as seen from Earth’s center and from a point on the equator at sea level when the Sun is on the horizon.

sunray(solpos::SolarPosition)

The unit vector defining the direction of the Sun's rays, with respect to an observer on the Earth's surface. Conventionally, it points from the observer towards the Sun [5].

topocentric_apparent_elevation(
    observer_latitude,
    topocentric_sun_declination,
    topocentric_local_hour
)

Topocentric elevation angle without atmospheric refraction correction.

topocentric_astronomical_azimuth(
    observer_latitude, 
    topocentric_sun_declination, 
    topocentric_local_hour
)

The Sun’s azimuth measured from true north eastward as seen from the observer’s location, based on astronomical (not navigational) convention.

topocentric_azimuth(topocentric_astronomical_azimuth)

The Sun’s azimuth from the observer’s location relative to a defined reference direction, typically true north, on the horizon.

topocentric_elevation(topocentric_apparent_elevation, topocentric_elevation_correction)

The angle between the Sun and the observer’s local horizon, measured at the observer’s location.

topocentric_elevation_correction(
    temperature,
    pressure,
    topocentric_apparent_elevation
)

The adjustment applied to an object’s observed altitude to account for the bending of its light as it passes through Earth’s atmosphere.

topocentric_local_hour(observer_local_hour, sun_ascension_parallax)

The hour angle of a celestial object as seen from the observer’s exact location on Earth’s surface rather than its center.

topocentric_sun_ascension(geocentric_sun_ascension, sun_ascension_parallax)

The Sun’s right ascension as viewed from the observer’s actual location on Earth’s surface.

topocentric_sun_declination(
    radial_distance_equatorial_plane, 
    radial_distance_rotational_axis, 
    sun_equatorial_horizontal_parallax, 
    geocentric_sun_declination, 
    observer_local_hour, 
    sun_ascension_parallax
)

The Sun’s declination as viewed from the observer’s actual location on Earth’s surface.

zenith(solpos::SolarPosition)

The complementary to 90° (degrees) of the Sun's elevation.