astronomy/source/python/README.md

Astronomy Engine (Python)

This is the complete programming reference for the Python version of Astronomy Engine. Supports Python 3. Does NOT support Python 2. See the home page for more info.

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Quick Start

To get started quickly, here are some examples.

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Contents

• Topic Index
• Classes
• Enumerated Types
• Error Types
• Functions

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Topic Index

Position of Sun, Moon, and planets

Function	Description
HelioVector	Calculates vector with respect to the center of the Sun.
GeoVector	Calculates vector with respect to the center of the Earth.
Equator	Calculates right ascension and declination.
Ecliptic	Converts J2000 equatorial coordinates to J2000 ecliptic coordinates.
EclipticLongitude	Calculates ecliptic longitude of a body in the J2000 system.
Horizon	Calculates horizontal coordinates (azimuth, altitude) for a given observer on the Earth.
LongitudeFromSun	Calculates a body's apparent ecliptic longitude difference from the Sun, as seen by an observer on the Earth.

Rise, set, and culmination times

Function	Description
SearchRiseSet	Finds time of rise or set for a body as seen by an observer on the Earth.
SearchHourAngle	Finds when body reaches a given hour angle for an observer on the Earth. Hour angle = 0 finds culmination, the highest point in the sky.

Moon phases

Function	Description
MoonPhase	Determines the Moon's phase expressed as an ecliptic longitude.
SearchMoonPhase	Finds the next instance of the Moon reaching a specific ecliptic longitude separation from the Sun.
SearchMoonQuarter	Finds the first quarter moon phase after a given date and time.
NextMoonQuarter	Finds the next quarter moon phase after a previous one that has been found.

Lunar perigee and apogee

Function	Description
SearchLunarApsis	Finds the next perigee or apogee of the Moon after a specified date.
NextLunarApsis	Given an already-found apsis, finds the next perigee or apogee of the Moon.

Visual magnitude and elongation

Function	Description
Illumination	Calculates visual magnitude and phase angle of bodies as seen from the Earth.
SearchPeakMagnitude	Searches for the date and time Venus will next appear brightest as seen from the Earth.
AngleFromSun	Returns full angle seen from Earth between body and Sun.
Elongation	Calculates ecliptic longitude angle between a body and the Sun, as seen from the Earth.
SearchMaxElongation	Searches for the next maximum elongation event for Mercury or Venus that occurs after the given date.

Oppositions and conjunctions

Function	Description
SearchRelativeLongitude	Finds oppositions and conjunctions of planets.

Equinoxes, solstices, and apparent solar motion

Function	Description
SearchSunLongitude	Finds the next time the Sun reaches a specified apparent ecliptic longitude in the true equator of date system.
Seasons	Finds the equinoxes and solstices for a given calendar year.
SunPosition	Calculates the Sun's apparent ecliptic coordinates as seen from the Earth.

Coordinate transforms

The following four orientation systems are supported. Astronomy Engine can convert a vector from any of these orientations to any of the others. It also allows converting from a vector to spherical (angular) coordinates and back, within a given orientation. Note the 3-letter codes for each of the orientation systems; these are used in function and type names.

• EQJ = Equatorial J2000: Uses the Earth's equator on January 1, 2000, at noon UTC.
• EQD = Equator of-date: Uses the Earth's equator on a given date and time, adjusted for precession and nutation.
• ECL = Ecliptic: Uses the mean plane of the Earth's orbit around the Sun. The x-axis is referenced against the J2000 equinox.
• HOR = Horizontal: Uses the viewpoint of an observer at a specific location on the Earth at a given date and time.

Function	Description
RotateVector	Applies a rotation matrix to a vector, yielding a vector in another orientation system.
InverseRotation	Given a rotation matrix, finds the inverse rotation matrix that does the opposite transformation.
CombineRotation	Given two rotation matrices, returns a rotation matrix that combines them into a net transformation.
VectorFromSphere	Converts spherical coordinates to Cartesian coordinates.
SphereFromVector	Converts Cartesian coordinates to spherical coordinates.
VectorFromEquator	Given angular equatorial coordinates, calculates equatorial vector.
EquatorFromVector	Given an equatorial vector, calculates equatorial angular coordinates.
VectorFromHorizon	Given apparent angular horizontal coordinates, calculates horizontal vector.
HorizonFromVector	Given a vector in horizontal orientation, calculates horizontal angular coordinates.
Rotation_EQD_EQJ	Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).
Rotation_EQD_ECL	Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).
Rotation_EQD_HOR	Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).
Rotation_EQJ_EQD	Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).
Rotation_EQJ_ECL	Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).
Rotation_EQJ_HOR	Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).
Rotation_ECL_EQD	Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial of-date (EQD).
Rotation_ECL_EQJ	Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).
Rotation_ECL_HOR	Calculates a rotation matrix from ecliptic J2000 (ECL) to horizontal (HOR).
Rotation_HOR_EQD	Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).
Rotation_HOR_EQJ	Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).
Rotation_HOR_ECL	Calculates a rotation matrix from horizontal (HOR) to ecliptic J2000 (ECL).

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Classes

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class Apsis

An event where a satellite is closest to or farthest from the body it orbits.

For the Moon orbiting the Earth, or a planet orbiting the Sun, an apsis is an event where the orbiting body reaches its closest or farthest point from the primary body. The closest approach is called pericenter and the farthest point is apocenter. More specific terminology is common for particular orbiting bodies. The Moon's closest approach to the Earth is called perigee and its furthest point is called apogee. The closest approach of a planet to the Sun is called perihelion and the furthest point is called aphelion. This data structure is returned by SearchLunarApsis and NextLunarApsis to iterate through consecutive alternating perigees and apogees.

Type	Attribute	Description
Time	time	The date and time of the apsis.
ApsisKind	kind	Whether this is a pericenter or apocenter event.
float	dist_au	The distance between the centers of the bodies in astronomical units.
float	dist_km	The distance between the centers of the bodies in kilometers.

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class EclipticCoordinates

Ecliptic angular and Cartesian coordinates.

Coordinates of a celestial body as seen from the center of the Sun (heliocentric), oriented with respect to the plane of the Earth's orbit around the Sun (the ecliptic).

Type	Attribute	Description
float	ex	Cartesian x-coordinate: in the direction of the equinox along the ecliptic plane.
float	ey	Cartesian y-coordinate: in the ecliptic plane 90 degrees prograde from the equinox.
float	ez	Cartesian z-coordinate: perpendicular to the ecliptic plane. Positive is north.
float	elat	Latitude in degrees north (positive) or south (negative) of the ecliptic plane.
float	elon	Longitude in degrees around the ecliptic plane prograde from the equinox.

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class ElongationEvent

Contains information about the visibility of a celestial body at a given date and time.

See the Elongation function for more detailed information about the members of this class. See also SearchMaxElongation for how to search for maximum elongation events.

Type	Attribute	Description
Time	time	The date and time of the observation.
Visibility	visibility	Whether the body is best seen in the morning or the evening.
float	elongation	The angle in degrees between the body and the Sun, as seen from the Earth.
float	ecliptic_separation	The difference between the ecliptic longitudes of the body and the Sun, as seen from the Earth.

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class Equatorial

Equatorial angular coordinates

Coordinates of a celestial body as seen from the Earth. Can be geocentric or topocentric, depending on context. The coordinates are oriented with respect to the Earth's equator projected onto the sky.

Type	Attribute	Description
float	ra	Right ascension in sidereal hours.
float	dec	Declination in degrees.
float	dist	Distance to the celestial body in AU.

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class HorizontalCoordinates

Coordinates of a celestial body as seen by a topocentric observer.

Contains horizontal and equatorial coordinates as seen by an observer on or near the surface of the Earth (a topocentric observer). All coordinates are optionally corrected for atmospheric refraction.

Type	Attribute	Description
float	azimuth	The compass direction laterally around the observer's horizon, measured in degrees. North is 0 degrees, east is 90 degrees, south is 180 degrees, etc.
float	altitude	The angle in degrees above (positive) or below (negative) the observer's horizon.
float	ra	The right ascension in sidereal hours.
float	dec	The declination in degrees.

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class HourAngleEvent

Information about a celestial body crossing a specific hour angle.

Returned by the function SearchHourAngle to report information about a celestial body crossing a certain hour angle as seen by a specified topocentric observer.

Type	Attribute	Description
Time	time	The date and time when the body crosses the specified hour angle.
HorizontalCoordinates	hor	Apparent coordinates of the body at the time it crosses the specified hour angle.

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class IlluminationInfo

Information about the brightness and illuminated shape of a celestial body.

Returned by functions Illumination and SearchPeakMagnitude to report the visual magnitude and illuminated fraction of a celestial body at a given date and time.

Type	Attribute	Description
Time	time	The date and time of the observation.
float	mag	The visual magnitude of the body. Smaller values are brighter.
float	phase_angle	The angle in degrees between the Sun and the Earth, as seen from the body. Indicates the body's phase as seen from the Earth.
float	phase_fraction	A value in the range [0.0, 1.0] indicating what fraction of the body's apparent disc is illuminated, as seen from the Earth.
float	helio_dist	The distance between the Sun and the body at the observation time, in AU.
float	ring_tilt	For Saturn, the tilt angle in degrees of its rings as seen from Earth. When the ring_tilt is very close to 0, it means the rings are edge-on as seen from observers on the Earth, and are thus very difficult to see. For bodies other than Saturn, ring_tilt is None.

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class MoonQuarter

A lunar quarter event along with its date and time.

An object of this type represents one of the four major lunar phases that appear on calendars: new moon, first quarter, full moon, or third quarter. Along with the quarter attribute that specifies the type of quarter, it contains a time field that indicates when the lunar quarter event happens.

Type	Attribute	Description
int	quarter	0=new moon, 1=first quarter, 2=full moon, 3=third quarter.
Time	time	The date and time of the lunar quarter.

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class Observer

Represents the geographic location of an observer on the surface of the Earth.

Type	Parameter	Description
float	latitude	Geographic latitude in degrees north of the equator.
float	longitude	Geographic longitude in degrees east of the prime meridian at Greenwich, England.
float	height	Elevation above sea level in meters.

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class RotationMatrix

Contains a rotation matrix that can be used to transform one coordinate system into another.

Type	Parameter	Description
float[3][3]	rot	A normalized 3x3 rotation matrix.

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class SeasonInfo

The dates and times of changes of season for a given calendar year.

Call Seasons to calculate this data structure for a given year.

Type	Attribute	Description
Time	mar_equinox	The date and time of the March equinox for the specified year.
Time	jun_solstice	The date and time of the June solstice for the specified year.
Time	sep_equinox	The date and time of the September equinox for the specified year.
Time	dec_solstice	The date and time of the December solstice for the specified year.

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class Spherical

Holds spherical coordinates: latitude, longitude, distance.

Type	Parameter	Description
float	lat	The latitude angle: -90..+90 degrees.
float	lon	The longitude angle: 0..360 degrees.
float	dist	Distance in AU.

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class Time

Represents a date and time used for performing astronomy calculations.

All calculations performed by Astronomy Engine are based on dates and times represented by Time objects.

Type	Parameter	Description
float	ut	UT1/UTC number of days since noon on January 1, 2000. See the ut attribute of this class for more details.

Type	Attribute	Description
float	ut	The floating point number of days of Universal Time since noon UTC January 1, 2000. Astronomy Engine approximates UTC and UT1 as being the same thing, although they are not exactly equivalent; UTC and UT1 can disagree by up to 0.9 seconds. This approximation is sufficient for the accuracy requirements of Astronomy Engine. Universal Time Coordinate (UTC) is the international standard for legal and civil timekeeping and replaces the older Greenwich Mean Time (GMT) standard. UTC is kept in sync with unpredictable observed changes in the Earth's rotation by occasionally adding leap seconds as needed. UT1 is an idealized time scale based on observed rotation of the Earth, which gradually slows down in an unpredictable way over time, due to tidal drag by the Moon and Sun, large scale weather events like hurricanes, and internal seismic and convection effects. Conceptually, UT1 drifts from atomic time continuously and erratically, whereas UTC is adjusted by a scheduled whole number of leap seconds as needed. The value in ut is appropriate for any calculation involving the Earth's rotation, such as calculating rise/set times, culumination, and anything involving apparent sidereal time. Before the era of atomic timekeeping, days based on the Earth's rotation were often known as mean solar days.
float	tt	Terrestrial Time days since noon on January 1, 2000. Terrestrial Time is an atomic time scale defined as a number of days since noon on January 1, 2000. In this system, days are not based on Earth rotations, but instead by the number of elapsed SI seconds divided by 86400. Unlike ut, tt increases uniformly without adjustments for changes in the Earth's rotation. The value in tt is used for calculations of movements not involving the Earth's rotation, such as the orbits of planets around the Sun, or the Moon around the Earth. Historically, Terrestrial Time has also been known by the term Ephemeris Time (ET).

member functions

Time.AddDays(self, days)

Calculates the sum or difference of a Time with a specified real-valued number of days.

Sometimes we need to adjust a given Time value by a certain amount of time. This function adds the given real number of days in days to the date and time in the calling object. More precisely, the result's Universal Time field ut is exactly adjusted by days and the Terrestrial Time field tt is adjusted correctly for the resulting UTC date and time, according to the historical and predictive Delta-T model provided by the United States Naval Observatory. The value of the calling object is not modified. This function creates a brand new Time object and returns it.

Type	Parameter	Description
float	days	A floating point number of days by which to adjust time. May be negative, 0, or positive.

Returns: Time

Time.Make(year, month, day, hour, minute, second)

Creates a Time object from a UTC calendar date and time.

Type	Parameter	Description
int	year	The UTC 4-digit year value, e.g. 2019.
int	month	The UTC month in the range 1..12.
int	day	The UTC day of the month, in the range 1..31.
int	hour	The UTC hour, in the range 0..23.
int	minute	The UTC minute, in the range 0..59.
float	second	The real-valued UTC second, in the range [0, 60).

Returns: Time

Time.Now()

Returns the computer's current date and time in the form of a Time object.

Uses the computer's system clock to find the current UTC date and time. Converts that date and time to a Time value and returns the result. Callers can pass this value to other Astronomy Engine functions to calculate current observational conditions.

Returns: Time

Time.Utc(self)

Returns the UTC date and time as a datetime object.

Uses the standard datetime class to represent the date and time in this Time object.

Returns: datetime

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class Vector

A Cartesian vector with 3 space coordinates and 1 time coordinate.

The vector's space coordinates are measured in astronomical units (AU). The coordinate system varies and depends on context. The vector also includes a time stamp.

Type	Attribute	Description
float	x	The x-coordinate of the vector, measured in AU.
float	y	The y-coordinate of the vector, measured in AU.
float	z	The z-coordinate of the vector, measured in AU.
Time	t	The date and time at which the coordinate is valid.

member functions

Vector.Length(self)

Returns the length of the vector in AU.

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Enumerated Types

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enum ApsisKind

Represents whether a satellite is at a closest or farthest point in its orbit.

An apsis is a point in a satellite's orbit that is closest to, or farthest from, the body it orbits (its primary). ApsisKind is an enumerated type that indicates which of these two cases applies to a particular apsis event.

Value	Description
Pericenter	The satellite is at its closest point to its primary.
Apocenter	The satellite is at its farthest point from its primary.
Invalid	A placeholder for an undefined, unknown, or invalid apsis.

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enum Body

The celestial bodies supported by Astronomy Engine calculations.

Value	Description
Invalid	An unknown, invalid, or undefined celestial body.
Mercury	The planet Mercury.
Venus	The planet Venus.
Earth	The planet Earth.
Mars	The planet Mars.
Jupiter	The planet Jupiter.
Saturn	The planet Saturn.
Uranus	The planet Uranus.
Neptune	The planet Neptune.
Pluto	The planet Pluto.
Sun	The Sun.
Moon	The Earth's moon.

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enum Direction

Indicates whether a body is rising above or setting below the horizon.

Specifies the direction of a rising or setting event for a body. For example, Direction.Rise is used to find sunrise times, and Direction.Set is used to find sunset times.

Value	Description
Rise	First appearance of a body as it rises above the horizon.
Set	Last appearance of a body as it sinks below the horizon.

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enum Refraction

Selects if/how to correct for atmospheric refraction.

Some functions allow enabling or disabling atmospheric refraction for the calculated apparent position of a celestial body as seen by an observer on the surface of the Earth.

Value	Description
Airless	No atmospheric refraction correction.
Normal	Recommended correction for standard atmospheric refraction.
JplHorizons	Used only for compatibility testing with JPL Horizons online tool.

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enum Visibility

Indicates whether a body (especially Mercury or Venus) is best seen in the morning or evening.

Value	Description
Morning	The body is best visible in the morning, before sunrise.
Evening	The body is best visible in the evening, after sunset.

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Error Types

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BadVectorError

A vector magnitude is too small to have a direction in space.

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EarthNotAllowedError

The Earth is not allowed as the celestial body in this calculation.

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Error

Indicates an error in an astronomical calculation.

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InternalError

An internal error occured that should be reported as a bug.

Indicates an unexpected and unrecoverable condition occurred. If you encounter this error using Astronomy Engine, it would be very helpful to report it at the Issues page on GitHub. Please include a copy of the stack trace, along with a description of how to reproduce the error. This will help improve the quality of Astronomy Engine for everyone! (Thank you in advance from the author.)

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InvalidBodyError

The celestial body is not allowed for this calculation.

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NoConvergeError

A numeric solver did not converge.

Indicates that there was a failure of a numeric solver to converge. If you encounter this error using Astronomy Engine, it would be very helpful to report it at the Issues page on GitHub. Please include a copy of the stack trace, along with a description of how to reproduce the error. This will help improve the quality of Astronomy Engine for everyone! (Thank you in advance from the author.)

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Functions

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AngleFromSun(body, time)

Returns the angle between the given body and the Sun, as seen from the Earth.

This function calculates the angular separation between the given body and the Sun, as seen from the center of the Earth. This angle is helpful for determining how easy it is to see the body away from the glare of the Sun.

Type	Parameter	Description
Body	body	The celestial body whose angle from the Sun is to be measured. Not allowed to be Body.Earth.
Time	time	The time at which the observation is made.

Returns: float

A numeric value indicating the angle in degrees between the Sun and the specified body as seen from the center of the Earth.

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BodyCode(name)

Finds the Body enumeration value, given the name of a body.

>>> astronomy.BodyCode('Mars')
<Body.Mars: 3>

Type	Parameter	Description
str	name	The common English name of a supported celestial body.

Returns: Body

If name is a valid body name, returns the enumeration value associated with that body. Otherwise, returns Body.Invalid.

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CombineRotation(a, b)

Creates a rotation based on applying one rotation followed by another.

Given two rotation matrices, returns a combined rotation matrix that is equivalent to rotating based on the first matrix, followed by the second. b : RotationMatrix The second rotation to apply.

Type	Parameter	Description
RotationMatrix	a	The first rotation to apply.

Returns: RotationMatrix

The combined rotation matrix.

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Ecliptic(equ)

Converts J2000 equatorial Cartesian coordinates to J2000 ecliptic coordinates.

Given coordinates relative to the Earth's equator at J2000 (the instant of noon UTC on 1 January 2000), this function converts those coordinates to J2000 ecliptic coordinates, which are relative to the plane of the Earth's orbit around the Sun.

Type	Parameter	Description
EquatorialCoordinates	equ	Equatorial coordinates in the J2000 frame of reference.

Returns: EclipticCoordinates

Ecliptic coordinates in the J2000 frame of reference.

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EclipticLongitude(body, time)

Calculates heliocentric ecliptic longitude of a body based on the J2000 equinox.

This function calculates the angle around the plane of the Earth's orbit of a celestial body, as seen from the center of the Sun. The angle is measured prograde (in the direction of the Earth's orbit around the Sun) in degrees from the J2000 equinox. The ecliptic longitude is always in the range [0, 360). time : Time The date and time at which the body's ecliptic longitude is to be calculated.

Type	Parameter	Description
Body	body	A body other than the Sun.

Returns: float

An angular value in degrees indicating the ecliptic longitude of the body.

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Elongation(body, time)

Determines visibility of a celestial body relative to the Sun, as seen from the Earth.

This function returns an ElongationEvent object, which provides the following information about the given celestial body at the given time:

• visibility is an enumerated type that specifies whether the body is more easily seen in the morning before sunrise, or in the evening after sunset.
• elongation is the angle in degrees between two vectors: one from the center of the Earth to the center of the Sun, the other from the center of the Earth to the center of the specified body. This angle indicates how far away the body is from the glare of the Sun. The elongation angle is always in the range [0, 180].
• ecliptic_separation is the absolute value of the difference between the body's ecliptic longitude and the Sun's ecliptic longitude, both as seen from the center of the Earth. This angle measures around the plane of the Earth's orbit, and ignores how far above or below that plane the body is. The ecliptic separation is measured in degrees and is always in the range [0, 180]. time : Time The date and time of the observation.

Type	Parameter	Description
Body	body	The celestial body whose visibility is to be calculated.

Returns: ElongationEvent

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Equator(body, time, observer, ofdate, aberration)

Calculates equatorial coordinates of a celestial body as seen by an observer on the Earth's surface.

Calculates topocentric equatorial coordinates in one of two different systems: J2000 or true-equator-of-date, depending on the value of the ofdate parameter. Equatorial coordinates include right ascension, declination, and distance in astronomical units. This function corrects for light travel time: it adjusts the apparent location of the observed body based on how long it takes for light to travel from the body to the Earth. This function corrects for topocentric parallax, meaning that it adjusts for the angular shift depending on where the observer is located on the Earth. This is most significant for the Moon, because it is so close to the Earth. However, parallax corection has a small effect on the apparent positions of other bodies. Correction for aberration is optional, using the aberration parameter.

Type	Parameter	Description
Body	body	The celestial body to be observed. Not allowed to be Body.Earth.
Time	time	The date and time at which the observation takes place.
Observer	observer	A location on or near the surface of the Earth.
bool	ofdate	Selects the date of the Earth's equator in which to express the equatorial coordinates. If True, returns coordinates using the equator and equinox of date. If False, returns coordinates converted to the J2000 system.
bool	aberration	If True, corrects for aberration of light based on the motion of the Earth with respect to the heliocentric origin. If False, does not correct for aberration.

Returns: EquatorialCoordinates

Equatorial coordinates in the specified frame of reference.

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EquatorFromVector(vec)

Given an equatorial vector, calculates equatorial angular coordinates.

Type	Parameter	Description
Vector	vec	A vector in an equatorial coordinate system.

Returns: Equatorial

Angular coordinates expressed in the same equatorial system as vec.

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GeoMoon(time)

Calculates the geocentric position of the Moon at a given time.

Given a time of observation, calculates the Moon's position as a vector. The vector gives the location of the Moon's center relative to the Earth's center with x-, y-, and z-components measured in astronomical units. This algorithm is based on Nautical Almanac Office's Improved Lunar Ephemeris of 1954, which in turn derives from E. W. Brown's lunar theories from the early twentieth century. It is adapted from Turbo Pascal code from the book Astronomy on the Personal Computer by Montenbruck and Pfleger.

Type	Parameter	Description
Time	time	The date and time for which to calculate the Moon's position.

Returns: Vector

The Moon's position as a vector in J2000 Cartesian equatorial coordinates.

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GeoVector(body, time, aberration)

Calculates geocentric Cartesian coordinates of a body in the J2000 equatorial system.

This function calculates the position of the given celestial body as a vector, using the center of the Earth as the origin. The result is expressed as a Cartesian vector in the J2000 equatorial system: the coordinates are based on the mean equator of the Earth at noon UTC on 1 January 2000. If given an invalid value for body, or the body is Body.Pluto and the time is outside the year range 1700..2200, this function will raise an exception. Unlike HelioVector, this function always corrects for light travel time. This means the position of the body is "back-dated" by the amount of time it takes light to travel from that body to an observer on the Earth. Also, the position can optionally be corrected for aberration, an effect causing the apparent direction of the body to be shifted due to transverse movement of the Earth with respect to the rays of light coming from that body.

Type	Parameter	Description
Body	body	A body for which to calculate a heliocentric position: the Sun, Moon, or any of the planets.
Time	time	The date and time for which to calculate the position.
bool	aberration	A boolean value indicating whether to correct for aberration.

Returns: Vector

A geocentric position vector of the center of the given body.

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HelioVector(body, time)

Calculates heliocentric Cartesian coordinates of a body in the J2000 equatorial system.

This function calculates the position of the given celestial body as a vector, using the center of the Sun as the origin. The result is expressed as a Cartesian vector in the J2000 equatorial system: the coordinates are based on the mean equator of the Earth at noon UTC on 1 January 2000. The position is not corrected for light travel time or aberration. This is different from the behavior of GeoVector. If given an invalid value for body, or the body is Body.Pluto and time is outside the year range 1700..2200, this function raise an exception.

Type	Parameter	Description
Body	body	The celestial body whose heliocentric position is to be calculated: The Sun, Moon, or any of the planets.
Time	time	The time at which to calculate the heliocentric position.

Returns: Vector

A heliocentric position vector of the center of the given body at the given time.

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Horizon(time, observer, ra, dec, refraction)

Calculates the apparent location of a body relative to the local horizon of an observer on the Earth.

Given a date and time, the geographic location of an observer on the Earth, and equatorial coordinates (right ascension and declination) of a celestial body, this function returns horizontal coordinates (azimuth and altitude angles) for the body relative to the horizon at the geographic location. The right ascension ra and declination dec passed in must be equator of date coordinates, based on the Earth's true equator at the date and time of the observation. Otherwise the resulting horizontal coordinates will be inaccurate. Equator of date coordinates can be obtained by calling Equator, passing in True as its ofdate parameter. It is also recommended to enable aberration correction by passing in True for the aberration parameter. This function optionally corrects for atmospheric refraction. For most uses, it is recommended to pass Refraction.Normal in the refraction parameter to correct for optical lensing of the Earth's atmosphere that causes objects to appear somewhat higher above the horizon than they actually are. However, callers may choose to avoid this correction by passing in Refraction.Airless. If refraction correction is enabled, the azimuth, altitude, right ascension, and declination in the HorizontalCoordinates object returned by this function will all be corrected for refraction. If refraction is disabled, none of these four coordinates will be corrected; in that case, the right ascension and declination in the returned object will be numerically identical to the respective ra and dec values passed in.

Type	Parameter	Description
Time	time	The date and time for which to find horizontal coordinates.
Observer	observer	The location of the observer for which to find horizontal coordinates.
float	ra	Right ascension in sidereal hours of the celestial object, referred to the mean equinox of date for the J2000 epoch.
float	dec	Declination in degrees of the celestial object, referred to the mean equator of date for the J2000 epoch. Positive values are north of the celestial equator and negative values are south of it.
Refraction	refraction	The option for selecting whether to correct for atmospheric lensing. If Refraction.Normal, a well-behaved refraction model is used. If Refraction.None, no refraction correct is performed. Refraction.JplHorizons is used only for compatibility testing with the JPL Horizons online tool.

Returns: HorizontalCoordinates

The horizontal coordinates (altitude and azimuth), along with equatorial coordinates (right ascension and declination), all optionally corrected for atmospheric refraction. See remarks above for more details.

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HorizonFromVector(vector, refraction)

Converts Cartesian coordinates to horizontal coordinates.

Given a horizontal Cartesian vector, returns horizontal azimuth and altitude. IMPORTANT: This function differs from SphereFromVector in two ways:

• SphereFromVector returns a lon value that represents azimuth defined counterclockwise from north (e.g., west = +90), but this function represents a clockwise rotation (e.g., east = +90). The difference is because SphereFromVector is intended to preserve the vector "right-hand rule", while this function defines azimuth in a more traditional way as used in navigation and cartography.
• This function optionally corrects for atmospheric refraction, while SphereFromVector does not. The returned object contains the azimuth in lon. It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees. The altitude is stored in lat. The distance to the observed object is stored in dist, and is expressed in astronomical units (AU).

Type	Parameter	Description
Vector	vector	Cartesian vector to be converted to horizontal angular coordinates.
Refraction	refraction	See comments in the RefractionAngle function.

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Illumination(body, time)

Finds visual magnitude, phase angle, and other illumination information about a celestial body.

This function calculates information about how bright a celestial body appears from the Earth, reported as visual magnitude, which is a smaller (or even negative) number for brighter objects, and a larger number for dimmer objects. For bodies other than the Sun, it reports a phase angle, which is the angle in degrees between the Sun and the Earth, as seen from the center of the body. Phase angle indicates what fraction of the body appears illuminated as seen from the Earth. For example, when the phase angle is near zero, it means the body appears "full" as seen from the Earth. A phase angle approaching 180 degrees means the body appears as a thin crescent as seen from the Earth. A phase angle of 90 degrees means the body appears "half full". For the Sun, the phase angle is always reported as 0; the Sun emits light rather than reflecting it, so it doesn't have a phase angle. When the body is Saturn, the returned object contains a field ring_tilt that holds the tilt angle in degrees of Saturn's rings as seen from the Earth. A value of 0 means the rings appear edge-on, and are thus nearly invisible from the Earth. The ring_tilt holds 0 for all bodies other than Saturn.

Type	Parameter	Description
Body	body	The Sun, Moon, or any planet other than the Earth.
Time	time	The date and time of the observation.

Returns: IlluminationInfo

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InverseRefractionAngle(refraction, bent_altitude)

Calculates the inverse of an atmospheric refraction angle.

Given an observed altitude angle that includes atmospheric refraction, calculate the negative angular correction to obtain the unrefracted altitude. This is useful for cases where observed horizontal coordinates are to be converted to another orientation system, but refraction first must be removed from the observed position.

Type	Parameter	Description
Refraction	refraction	Refraction.Normal - corrects for atmospheric refraction (recommended). Refraction.Airless - no correction is performed. Refraction.JplHorizons - For JPL Horizons compatibility testing only.
float	bent_altitude	The apparent altitude that includes atmospheric refraction.

Returns: float

The angular adjustment in degrees, to be added to the altitude angle to correct for atmospheric lensing. This will be less than or equal to zero.

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InverseRotation(rotation)

Calculates the inverse of a rotation matrix.

Given a rotation matrix that performs some coordinate transform, this function returns the matrix that reverses that trasnform.

Type	Parameter	Description
RotationMatrix	rotation	The rotation matrix to be inverted.

Returns: RotationMatrix

The inverse rotation matrix.

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LongitudeFromSun(body, time)

Returns a body's ecliptic longitude with respect to the Sun, as seen from the Earth.

This function can be used to determine where a planet appears around the ecliptic plane (the plane of the Earth's orbit around the Sun) as seen from the Earth, relative to the Sun's apparent position. The angle starts at 0 when the body and the Sun are at the same ecliptic longitude as seen from the Earth. The angle increases in the prograde direction (the direction that the planets orbit the Sun and the Moon orbits the Earth). When the angle is 180 degrees, it means the Sun and the body appear on opposite sides of the sky for an Earthly observer. When body is a planet whose orbit around the Sun is farther than the Earth's, 180 degrees indicates opposition. For the Moon, it indicates a full moon. The angle keeps increasing up to 360 degrees as the body's apparent prograde motion continues relative to the Sun. When the angle reaches 360 degrees, it starts over at 0 degrees. Values between 0 and 180 degrees indicate that the body is visible in the evening sky after sunset. Values between 180 degrees and 360 degrees indicate that the body is visible in the morning sky before sunrise. time : Time The date and time of the observation.

Type	Parameter	Description
Body	body	The celestial body for which to find longitude from the Sun.

Returns: float

An angle in degrees in the range [0, 360).

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MoonPhase(time)

Returns the Moon's phase as an angle from 0 to 360 degrees.

This function determines the phase of the Moon using its apparent ecliptic longitude relative to the Sun, as seen from the center of the Earth. Certain values of the angle have conventional definitions:

• 0 = new moon
• 90 = first quarter
• 180 = full moon
• 270 = third quarter

Type	Parameter	Description
Time	time	The date and time of the observation.

Returns: float

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NextLunarApsis(apsis)

Finds the next lunar perigee or apogee in a series.

This function requires an Apsis value obtained from a call to SearchLunarApsis or NextLunarApsis. Given an apogee event, this function finds the next perigee event, and vice versa. See SearchLunarApsis for more details.

Type	Parameter	Description
Apsis	apsis

Returns: Apsis

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NextMoonQuarter(mq)

Continues searching for lunar quarters from a previous search.

After calling SearchMoonQuarter, this function can be called one or more times to continue finding consecutive lunar quarters. This function finds the next consecutive moon quarter event after the one passed in as the parameter mq.

Type	Parameter	Description
MoonQuarter	mq	A value returned by a prior call to SearchMoonQuarter or NextMoonQuarter.

Returns: MoonQuarter

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RefractionAngle(refraction, altitude)

Calculates the amount of "lift" to an altitude angle caused by atmospheric refraction.

Given an altitude angle and a refraction option, calculates the amount of "lift" caused by atmospheric refraction. This is the number of degrees higher in the sky an object appears due to lensing of the Earth's atmosphere.

Type	Parameter	Description
Refraction	refraction	The option for selecting whether to correct for atmospheric lensing. If Refraction.Normal, a well-behaved refraction model is used. If Refraction.Airless, no refraction correct is performed. Refraction.JplHorizons is used only for compatibility testing with the JPL Horizons online tool.
float	altitude	The number of degrees above (positive) or below (negative) the horizon an object is, before being corrected for refraction.

Returns: float

The number of additional degrees of altitude an object appears to have, due to atmospheric refraction, depending on the option selected by the refraction parameter.

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RotateVector(rotation, vector)

Applies a rotation to a vector, yielding a rotated vector.

This function transforms a vector in one orientation to a vector in another orientation.

Type	Parameter	Description
RotationMatrix	rotation	A rotation matrix that specifies how the orientation of the vector is to be changed.
Vector	vector	The vector whose orientation is to be changed.

Returns: Vector

A vector in the orientation specified by rotation.

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Rotation_ECL_EQD(time)

Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: EQD = equatorial system, using equator of date.

Type	Parameter	Description
Time	time	The date and time of the desired equator.

Returns: RotationMatrix

A rotation matrix that converts ECL to EQD.

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Rotation_ECL_EQJ()

Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: EQJ = equatorial system, using equator at J2000 epoch.

Returns: RotationMatrix

A rotation matrix that converts ECL to EQJ.

---

Rotation_ECL_HOR(time, observer)

Calculates a rotation matrix from ecliptic J2000 (ECL) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type	Parameter	Description
Time	time	The date and time of the desired horizontal orientation.
Observer	observer	A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix

A rotation matrix that converts ECL to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

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Rotation_EQD_ECL(time)

Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of date. Target: ECL = ecliptic system, using equator at J2000 epoch.

Type	Parameter	Description
Time	time	The date and time of the source equator.

Returns: RotationMatrix

A rotation matrix that converts EQD to ECL.

---

Rotation_EQD_EQJ(time)

Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of the specified date/time. Target: EQJ = equatorial system, using equator at J2000 epoch.

Type	Parameter	Description
Time	time	The date and time at which the Earth's equator defines the source orientation.

Returns: RotationMatrix

A rotation matrix that converts EQD at time to EQJ.

---

Rotation_EQD_HOR(time, observer)

Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of the specified date/time. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type	Parameter	Description
Time	time	The date and time at which the Earth's equator applies.
Observer	observer	A location near the Earth's mean sea level that defines the observer's location.

Returns: RotationMatrix

A rotation matrix that converts EQD to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

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Rotation_EQJ_ECL()

Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using equator at J2000 epoch. Target: ECL = ecliptic system, using equator at J2000 epoch.

Returns: RotationMatrix

A rotation matrix that converts EQJ to ECL.

---

Rotation_EQJ_EQD(time)

Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using equator at J2000 epoch. Target: EQD = equatorial system, using equator of the specified date/time.

Type	Parameter	Description
Time	time	The date and time at which the Earth's equator defines the target orientation.

Returns: RotationMatrix

A rotation matrix that converts EQJ to EQD at time.

---

Rotation_EQJ_HOR(time, observer)

Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using the equator at the J2000 epoch. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type	Parameter	Description
Time	time	The date and time of the desired horizontal orientation.
Observer	observer	A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix

A rotation matrix that converts EQJ to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

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Rotation_HOR_ECL(time, observer)

Calculates a rotation matrix from horizontal (HOR) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system. Target: ECL = ecliptic system, using equator at J2000 epoch.

Type	Parameter	Description
Time	time	The date and time of the horizontal observation.
Observer	observer	The location of the horizontal observer.

Returns: RotationMatrix

A rotation matrix that converts HOR to ECL.

---

Rotation_HOR_EQD(time, observer)

Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system (x=North, y=West, z=Zenith). Target: EQD = equatorial system, using equator of the specified date/time.

Type	Parameter	Description
Time	time	The date and time at which the Earth's equator applies.
Observer	observer	A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix

A rotation matrix that converts HOR to EQD at time and for observer.

---

Rotation_HOR_EQJ(time, observer)

Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system (x=North, y=West, z=Zenith). Target: EQJ = equatorial system, using equator at the J2000 epoch.

Type	Parameter	Description
Time	time	The date and time of the observation.
Observer	observer	A location near the Earth's mean sea level that define's the observer's horizon.

Returns: RotationMatrix

A rotation matrix that converts HOR to EQD at time and for observer.

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Search(func, context, t1, t2, dt_tolerance_seconds)

Searches for a time at which a function's value increases through zero.

Certain astronomy calculations involve finding a time when an event occurs. Often such events can be defined as the root of a function: the time at which the function's value becomes zero. Search finds the ascending root of a function: the time at which the function's value becomes zero while having a positive slope. That is, as time increases, the function transitions from a negative value, through zero at a specific moment, to a positive value later. The goal of the search is to find that specific moment. The search function is specified by two parameters: func and context. The func parameter is a function itself that accepts a time and a context containing any other arguments needed to evaluate the function. The context parameter supplies that context for the given search. As an example, a caller may wish to find the moment a celestial body reaches a certain ecliptic longitude. In that case, the caller might create a type (class, tuple, whatever) that contains a Body member to specify the body and a numeric value to hold the target longitude. A different function might use a completely different context type. Every time it is called, func returns a float value or it raises an exception. If func raises an exception, the search immediately fails and the exception is propagated back to the caller. Otherwise, the search proceeds until it either finds the ascending root or fails for some reason. The search calls func repeatedly to rapidly narrow in on any ascending root within the time window specified by t1 and t2. The search never reports a solution outside this time window. Search uses a combination of bisection and quadratic interpolation to minimize the number of function calls. However, it is critical that the supplied time window be small enough that there cannot be more than one root (ascedning or descending) within it; otherwise the search can fail. Beyond that, it helps to make the time window as small as possible, ideally such that the function itself resembles a smooth parabolic curve within that window. If an ascending root is not found, or more than one root (ascending and/or descending) exists within the window t1..t2, Search will return None to indicate a normal search failure. If the search does not converge within 20 iterations, it will raise an Error exception. context : object An arbitrary data structure needed to be passed to the function func every time it is called. t1 : float The lower time bound of the search window. See remarks above for more details. t2 : float The upper time bound of the search window. See remarks above for more details. dt_tolerance_seconds : float Specifies an amount of time in seconds within which a bounded ascending root is considered accurate enough to stop. A typical value is 1 second.

Type	Parameter	Description
function(context, Time)	func	A function that takes an arbitrary context parameter and a Time parameter. Returns a float value. See remarks above for more details.

Returns: Time or None

If the search is successful, returns a #Time object that is within dt_tolerance_seconds of an ascending root. In this case, the returned time value will always be within the inclusive range [t1, t2]. If there is no ascending root, or there is more than one ascending root, the function returns None.

---

SearchHourAngle(body, observer, hourAngle, startTime)

Searches for the time when a celestial body reaches a specified hour angle as seen by an observer on the Earth.

The hour angle of a celestial body indicates its position in the sky with respect to the Earth's rotation. The hour angle depends on the location of the observer on the Earth. The hour angle is 0 when the body reaches its highest angle above the horizon in a given day. The hour angle increases by 1 unit for every sidereal hour that passes after that point, up to 24 sidereal hours when it reaches the highest point again. So the hour angle indicates the number of hours that have passed since the most recent time that the body has culminated, or reached its highest point. This function searches for the next time a celestial body reaches the given hour angle after the date and time specified by startTime. To find when a body culminates, pass 0 for hourAngle. To find when a body reaches its lowest point in the sky, pass 12 for hourAngle. Note that, especially close to the Earth's poles, a body as seen on a given day may always be above the horizon or always below the horizon, so the caller cannot assume that a culminating object is visible nor that an object is below the horizon at its minimum altitude. On success, the function reports the date and time, along with the horizontal coordinates of the body at that time, as seen by the given observer.

Type	Parameter	Description
Body	body	The celestial body, which can the Sun, the Moon, or any planet other than the Earth.
Observer	observer	Indicates a location on or near the surface of the Earth where the observer is located.
float	hourAngle	An hour angle value in the range [0.0, 24.0) indicating the number of sidereal hours after the body's most recent culmination.
Time	startTime	The date and time at which to start the search.

Returns: HourAngleEvent

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SearchLunarApsis(startTime)

Finds the time of the first lunar apogee or perigee after the given time.

Given a date and time to start the search in startTime, this function finds the next date and time that the center of the Moon reaches the closest or farthest point in its orbit with respect to the center of the Earth, whichever comes first after startTime. The return value (of type Apsis) also contains an indicator of whether the event is apogee or perigee. The closest point is called perigee and the farthest point is called apogee. The word apsis refers to either event. To iterate through consecutive alternating perigee and apogee events, call SearchLunarApsis once, then use the return value to call NextLunarApsis. After that, keep feeding the previous return value from NextLunarApsis into another call of NextLunarApsis as many times as desired.

Type	Parameter	Description
Time	startTime	The date and time at which to start searching for the next perigee or apogee.

Returns: Apsis

---

SearchMaxElongation(body, startTime)

Finds a date and time when Mercury or Venus reaches its maximum angle from the Sun as seen from the Earth.

Mercury and Venus are are often difficult to observe because they are closer to the Sun than the Earth is. Mercury especially is almost always impossible to see because it gets lost in the Sun's glare. The best opportunities for spotting Mercury, and the best opportunities for viewing Venus through a telescope without atmospheric interference, are when these planets reach maximum elongation. These are events where the planets reach the maximum angle from the Sun as seen from the Earth. This function solves for those times, reporting the next maximum elongation event's date and time, the elongation value itself, the relative longitude with the Sun, and whether the planet is best observed in the morning or evening. See ElongationEvent for more details about the returned object.

Type	Parameter	Description
Body	body	Either Body.Mercury or Body.Venus. Any other value will result in an exception. To find the best viewing opportunities for planets farther from the Sun than the Earth is (Mars through Pluto), use SearchRelativeLongitude to find the next opposition event.
Time	startTime	The date and time at which to begin the search. The maximum elongation event found will always be the first one that occurs after this date and time.

Returns: ElongationEvent

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SearchMoonPhase(targetLon, startTime, limitDays)

Searches for the time that the Moon reaches a specified phase.

Lunar phases are conventionally defined in terms of the Moon's geocentric ecliptic longitude with respect to the Sun's geocentric ecliptic longitude. When the Moon and the Sun have the same longitude, that is defined as a new moon. When their longitudes are 180 degrees apart, that is defined as a full moon. This function searches for any value of the lunar phase expressed as an angle in degrees in the range [0, 360). If you want to iterate through lunar quarters (new moon, first quarter, full moon, third quarter) it is much easier to call the functions SearchMoonQuarter and NextMoonQuarter. This function is useful for finding general phase angles outside those four quarters.

Type	Parameter	Description
float	targetLon	The difference in geocentric longitude between the Sun and Moon that specifies the lunar phase being sought. This can be any value in the range [0, 360). Certain values have conventional names: 0 = new moon, 90 = first quarter, 180 = full moon, 270 = third quarter.
Time	startTime	The beginning of the time window in which to search for the Moon reaching the specified phase.
float	limitDays	The number of days after startTime that limits the time window for the search.

Returns: Time or None

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SearchMoonQuarter(startTime)

Finds the first lunar quarter after the specified date and time.

A lunar quarter is one of the following four lunar phase events: new moon, first quarter, full moon, third quarter. This function finds the lunar quarter that happens soonest after the specified date and time. To continue iterating through consecutive lunar quarters, call this function once, followed by calls to NextMoonQuarter as many times as desired.

Type	Parameter	Description
Time	startTime	The date and time at which to start the search.

Returns: MoonQuarter

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SearchPeakMagnitude(body, startTime)

Searches for the date and time Venus will next appear brightest as seen from the Earth.

This function searches for the date and time Venus appears brightest as seen from the Earth. Currently only Venus is supported for the body parameter, though this could change in the future. Mercury's peak magnitude occurs at superior conjunction, when it is virtually impossible to see from the Earth, so peak magnitude events have little practical value for that planet. Planets other than Venus and Mercury reach peak magnitude at opposition, which can be found using SearchRelativeLongitude. The Moon reaches peak magnitude at full moon, which can be found using SearchMoonQuarter or SearchMoonPhase. The Sun reaches peak magnitude at perihelion, which occurs each year in January. However, the difference is minor and has little practical value.

Type	Parameter	Description
Body	body	Currently only Body.Venus is allowed. Any other value results in an exception. See remarks above for more details.
Time	startTime	The date and time to start searching for the next peak magnitude event.

Returns: IlluminationInfo

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SearchRelativeLongitude(body, targetRelLon, startTime)

Searches for when the Earth and another planet are separated by a certain ecliptic longitude.

Searches for the time when the Earth and another planet are separated by a specified angle in ecliptic longitude, as seen from the Sun. A relative longitude is the angle between two bodies measured in the plane of the Earth's orbit (the ecliptic plane). The distance of the bodies above or below the ecliptic plane is ignored. If you imagine the shadow of the body cast onto the ecliptic plane, and the angle measured around that plane from one body to the other in the direction the planets orbit the Sun, you will get an angle somewhere between 0 and 360 degrees. This is the relative longitude. Given a planet other than the Earth in body and a time to start the search in startTime, this function searches for the next time that the relative longitude measured from the planet to the Earth is targetRelLon. Certain astronomical events are defined in terms of relative longitude between the Earth and another planet:

• When the relative longitude is 0 degrees, it means both planets are in the same direction from the Sun. For planets that orbit closer to the Sun (Mercury and Venus), this is known as inferior conjunction, a time when the other planet becomes very difficult to see because of being lost in the Sun's glare. (The only exception is in the rare event of a transit, when we see the silhouette of the planet passing between the Earth and the Sun.)
• When the relative longitude is 0 degrees and the other planet orbits farther from the Sun, this is known as opposition. Opposition is when the planet is closest to the Earth, and also when it is visible for most of the night, so it is considered the best time to observe the planet.
• When the relative longitude is 180 degrees, it means the other planet is on the opposite side of the Sun from the Earth. This is called superior conjunction. Like inferior conjunction, the planet is very difficult to see from the Earth. Superior conjunction is possible for any planet other than the Earth.

Type	Parameter	Description
Body	body	A planet other than the Earth. If body is not a planet, or if it is Body.Earth, an error occurs.
float	targetRelLon	The desired relative longitude, expressed in degrees. Must be in the range [0, 360).
Time	startTime	The date and time at which to begin the search.

Returns: Time

The date and time of the relative longitude event.

---

SearchRiseSet(body, observer, direction, startTime, limitDays)

Searches for the next time a celestial body rises or sets as seen by an observer on the Earth.

This function finds the next rise or set time of the Sun, Moon, or planet other than the Earth. Rise time is when the body first starts to be visible above the horizon. For example, sunrise is the moment that the top of the Sun first appears to peek above the horizon. Set time is the moment when the body appears to vanish below the horizon. This function corrects for typical atmospheric refraction, which causes celestial bodies to appear higher above the horizon than they would if the Earth had no atmosphere. It also adjusts for the apparent angular radius of the observed body (significant only for the Sun and Moon). Note that rise or set may not occur in every 24 hour period. For example, near the Earth's poles, there are long periods of time where the Sun stays below the horizon, never rising. Also, it is possible for the Moon to rise just before midnight but not set during the subsequent 24-hour day. This is because the Moon sets nearly an hour later each day due to orbiting the Earth a significant amount during each rotation of the Earth. Therefore callers must not assume that the function will always succeed.

Type	Parameter	Description
Body	body	The Sun, Moon, or any planet other than the Earth.
Observer	observer	The location where observation takes place.
Direction	direction	Either Direction.Rise to find a rise time or Direction.Set to find a set time.
Time	startTime	The date and time at which to start the search.
float	limitDays	Limits how many days to search for a rise or set time. To limit a rise or set time to the same day, you can use a value of 1 day. In cases where you want to find the next rise or set time no matter how far in the future (for example, for an observer near the south pole), you can pass in a larger value like 365.

Returns: Time or None

If the rise or set time is found within the specified time window, this function returns that time. Otherwise, it returns None.

---

SearchSunLongitude(targetLon, startTime, limitDays)

Searches for the time when the Sun reaches an apparent ecliptic longitude as seen from the Earth.

This function finds the moment in time, if any exists in the given time window, that the center of the Sun reaches a specific ecliptic longitude as seen from the center of the Earth. This function can be used to determine equinoxes and solstices. However, it is usually more convenient and efficient to call Seasons to calculate all equinoxes and solstices for a given calendar year. The function searches the window of time specified by startTime and startTime+limitDays. The search will return None if the Sun never reaches the longitude targetLon or if the window is so large that the longitude ranges more than 180 degrees within it. It is recommended to keep the window smaller than 10 days when possible. targetLon : float The desired ecliptic longitude in degrees, relative to the true equinox of date. This may be any value in the range [0, 360), although certain values have conventional meanings: 0 = March equinox, 90 = June solstice, 180 = September equinox, 270 = December solstice. startTime : Time The date and time for starting the search for the desired longitude event. limitDays : float The real-valued number of days, which when added to startTime, limits the range of time over which the search looks. It is recommended to keep this value between 1 and 10 days. See remarks above for more details.

Returns: Time or None

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Seasons(year)

Finds both equinoxes and both solstices for a given calendar year.

The changes of seasons are defined by solstices and equinoxes. Given a calendar year number, this function calculates the March and September equinoxes and the June and December solstices. The equinoxes are the moments twice each year when the plane of the Earth's equator passes through the center of the Sun. In other words, the Sun's declination is zero at both equinoxes. The March equinox defines the beginning of spring in the northern hemisphere and the beginning of autumn in the southern hemisphere. The September equinox defines the beginning of autumn in the northern hemisphere and the beginning of spring in the southern hemisphere. The solstices are the moments twice each year when one of the Earth's poles is most tilted toward the Sun. More precisely, the Sun's declination reaches its minimum value at the December solstice, which defines the beginning of winter in the northern hemisphere and the beginning of summer in the southern hemisphere. The Sun's declination reaches its maximum value at the June solstice, which defines the beginning of summer in the northern hemisphere and the beginning of winter in the southern hemisphere.

Type	Parameter	Description
int	year	The calendar year number for which to calculate equinoxes and solstices. The value may be any integer, but only the years 1800 through 2100 have been validated for accuracy: unit testing against data from the United States Naval Observatory confirms that all equinoxes and solstices for that range of years are within 2 minutes of the correct time.

Returns: SeasonInfo

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SphereFromVector(vector)

Converts Cartesian coordinates to spherical coordinates.

Given a Cartesian vector, returns latitude, longitude, and distance.

Type	Parameter	Description
Vector	vector	Cartesian vector to be converted to spherical coordinates.

Returns: Spherical

Spherical coordinates that are equivalent to the given vector.

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SunPosition(time)

Calculates geocentric ecliptic coordinates for the Sun.

This function calculates the position of the Sun as seen from the Earth. The returned value includes both Cartesian and spherical coordinates. The x-coordinate and longitude values in the returned object are based on the true equinox of date: one of two points in the sky where the instantaneous plane of the Earth's equator at the given date and time (the equatorial plane) intersects with the plane of the Earth's orbit around the Sun (the ecliptic plane). By convention, the apparent location of the Sun at the March equinox is chosen as the longitude origin and x-axis direction, instead of the one for September. SunPosition corrects for precession and nutation of the Earth's axis in order to obtain the exact equatorial plane at the given time. This function can be used for calculating changes of seasons: equinoxes and solstices. In fact, the function Seasons does use this function for that purpose.

Type	Parameter	Description
Time	time	The date and time for which to calculate the Sun's position.

Returns: EclipticCoordinates

The ecliptic coordinates of the Sun using the Earth's true equator of date.

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VectorFromEquator(equ, time)

Given angular equatorial coordinates in equ, calculates equatorial vector.

Type	Parameter	Description
Equatorial	equ	Angular equatorial coordinates to be converted to a vector.
Time	time	The date and time of the observation. This is needed because the returned vector object requires a valid time value when passed to certain other functions.

Returns: Vector

A vector in the equatorial system.

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VectorFromHorizon(sphere, time, refraction)

Given apparent angular horizontal coordinates in sphere, calculate horizontal vector.

Type	Parameter	Description
Spherical	sphere	A structure that contains apparent horizontal coordinates: lat holds the refracted azimuth angle, lon holds the azimuth in degrees clockwise from north, and dist holds the distance from the observer to the object in AU.
Time	time	The date and time of the observation. This is needed because the returned vector object requires a valid time value when passed to certain other functions.
Refraction	refraction	See remarks in function RefractionAngle.

Returns: Vector

A vector in the horizontal system: x = north, y = west, and z = zenith (up).

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VectorFromSphere(sphere, time)

Converts spherical coordinates to Cartesian coordinates.

Given spherical coordinates and a time at which they are valid, returns a vector of Cartesian coordinates. The returned value includes the time, as required by all Time objects.

Type	Parameter	Description
Spherical	sphere	Spherical coordinates to be converted.
Time	time	The time that should be included in the returned vector.

Returns: Vector

The vector form of the supplied spherical coordinates.