mozilla-central/third_party/rust/calendrical_calculations/src/astronomy.rs

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// This file is part of ICU4X.
//
// The contents of this file implement algorithms from Calendrical Calculations
// by Reingold & Dershowitz, Cambridge University Press, 4th edition (2018),
// which have been released as Lisp code at <https://github.com/EdReingold/calendar-code2/>
// under the Apache-2.0 license. Accordingly, this file is released under
// the Apache License, Version 2.0 which can be found at the calendrical_calculations
//! This file contains important structs and functions relating to location,
//! time, and astronomy; these are intended for calender calculations and based off
//! _Calendrical Calculations_ by Reingold & Dershowitz.
//!
//! TODO(#3709): Address inconcistencies with existing ICU code for extreme dates.
use crate::error::LocationOutOfBoundsError;
use crate::helpers::{binary_search, i64_to_i32, invert_angular, next_moment, poly};
use crate::rata_die::{Moment, RataDie};
use core::f64::consts::PI;
#[allow(unused_imports)]
use core_maths::*;
// TODO: this isn't f64::div_euclid as defined in std. Figure out what the call sites
// mean to do.
fn div_euclid_f64(n: f64, d: f64) -> f64 {
debug_assert!(d > 0.0);
let (a, b) = (n / d, n % d);
if n >= 0.0 || b == 0.0 {
a
} else {
a - 1.0
}
}
#[derive(Debug, Copy, Clone, Default)]
/// A Location on the Earth given as a latitude, longitude, elevation, and standard time zone.
/// Latitude is given in degrees from -90 to 90, longitude in degrees from -180 to 180,
/// elevation in meters, and zone as a UTC offset in fractional days (ex. UTC+1 would have zone = 1.0 / 24.0)
#[allow(clippy::exhaustive_structs)] // This is all that is needed by the book algorithms
pub struct Location {
/// latitude from -90 to 90
pub latitude: f64,
/// longitude from -180 to 180
pub longitude: f64,
/// elevation in meters
pub elevation: f64,
/// UTC timezone offset in fractional days (1 hr = 1.0 / 24.0 day)
pub zone: f64,
}
/// The location of Mecca; used for Islamic calendar calculations.
#[allow(dead_code)]
pub const MECCA: Location = Location {
latitude: 6427.0 / 300.0,
longitude: 11947.0 / 300.0,
elevation: 298.0,
zone: (1_f64 / 8_f64),
};
/// The mean synodic month in days of 86400 atomic seconds
/// (86400 seconds = 24 hours * 60 minutes/hour * 60 seconds/minute)
///
/// This is defined in _Calendrical Calculations_ by Reingold & Dershowitz.
pub const MEAN_SYNODIC_MONTH: f64 = 29.530588861;
/// The Moment of noon on January 1, 2000
pub const J2000: Moment = Moment::new(730120.5);
/// The mean tropical year in days
///
/// This is defined in _Calendrical Calculations_ by Reingold & Dershowitz.
pub const MEAN_TROPICAL_YEAR: f64 = 365.242189;
/// The minimum allowable UTC offset (-12 hours) in fractional days (-0.5 days)
pub const MIN_UTC_OFFSET: f64 = -0.5;
/// The maximum allowable UTC offset (+14 hours) in fractional days (14.0 / 24.0 days)
pub const MAX_UTC_OFFSET: f64 = 14.0 / 24.0;
/// The angle of winter for the purposes of solar calculations
pub const WINTER: f64 = 270.0;
/// The moment of the first new moon of the CE, which occurred on January 11, 1 CE.
pub const NEW_MOON_ZERO: Moment = Moment::new(11.458922815770109);
impl Location {
/// Create a location; latitude is from -90 to 90, and longitude is from -180 to 180;
/// attempting to create a location outside of these bounds will result in a LocationOutOfBoundsError.
#[allow(dead_code)] // TODO: Remove dead_code tag after use
pub fn try_new(
latitude: f64,
longitude: f64,
elevation: f64,
zone: f64,
) -> Result<Location, LocationOutOfBoundsError> {
if !(-90.0..=90.0).contains(&latitude) {
return Err(LocationOutOfBoundsError::Latitude(latitude));
}
if !(-180.0..=180.0).contains(&longitude) {
return Err(LocationOutOfBoundsError::Longitude(longitude));
}
if !(MIN_UTC_OFFSET..=MAX_UTC_OFFSET).contains(&zone) {
return Err(LocationOutOfBoundsError::Offset(
zone,
MIN_UTC_OFFSET,
MAX_UTC_OFFSET,
));
}
Ok(Location {
latitude,
longitude,
elevation,
zone,
})
}
/// Create a new Location without checking for bounds
pub const fn new_unchecked(
latitude: f64,
longitude: f64,
elevation: f64,
zone: f64,
) -> Location {
Location {
latitude,
longitude,
elevation,
zone,
}
}
/// Get the longitude of a Location
#[allow(dead_code)]
pub fn longitude(&self) -> f64 {
self.longitude
}
/// Get the latitude of a Location
#[allow(dead_code)]
pub fn latitude(&self) -> f64 {
self.latitude
}
/// Get the elevation of a Location
#[allow(dead_code)]
pub fn elevation(&self) -> f64 {
self.elevation
}
/// Get the utc-offset of a Location
#[allow(dead_code)]
pub fn zone(&self) -> f64 {
self.zone
}
/// Convert a longitude into a mean time zone;
/// this yields the difference in Moment given a longitude
/// e.g. a longitude of 90 degrees is 0.25 (90 / 360) days ahead
/// of a location with a longitude of 0 degrees.
pub fn zone_from_longitude(longitude: f64) -> f64 {
longitude / (360.0)
}
/// Convert standard time to local mean time given a location and a time zone with given offset
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
#[allow(dead_code)]
pub fn standard_from_local(standard_time: Moment, location: Location) -> Moment {
Self::standard_from_universal(
Self::universal_from_local(standard_time, location),
location,
)
}
/// Convert from local mean time to universal time given a location
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn universal_from_local(local_time: Moment, location: Location) -> Moment {
local_time - Self::zone_from_longitude(location.longitude)
}
/// Convert from universal time to local time given a location
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
#[allow(dead_code)] // TODO: Remove dead_code tag after use
pub fn local_from_universal(universal_time: Moment, location: Location) -> Moment {
universal_time + Self::zone_from_longitude(location.longitude)
}
/// Given a UTC-offset in hours and a Moment in standard time,
/// return the Moment in universal time from the time zone with the given offset.
/// The field utc_offset should be within the range of possible offsets given by
/// the constand fields `MIN_UTC_OFFSET` and `MAX_UTC_OFFSET`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn universal_from_standard(standard_moment: Moment, location: Location) -> Moment {
debug_assert!(location.zone > MIN_UTC_OFFSET && location.zone < MAX_UTC_OFFSET, "UTC offset {0} was not within the possible range of offsets (see astronomy::MIN_UTC_OFFSET and astronomy::MAX_UTC_OFFSET)", location.zone);
standard_moment - location.zone
}
/// Given a Moment in standard time and UTC-offset in hours,
/// return the Moment in standard time from the time zone with the given offset.
/// The field utc_offset should be within the range of possible offsets given by
/// the constand fields `MIN_UTC_OFFSET` and `MAX_UTC_OFFSET`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
#[allow(dead_code)]
pub fn standard_from_universal(standard_time: Moment, location: Location) -> Moment {
debug_assert!(location.zone > MIN_UTC_OFFSET && location.zone < MAX_UTC_OFFSET, "UTC offset {0} was not within the possible range of offsets (see astronomy::MIN_UTC_OFFSET and astronomy::MAX_UTC_OFFSET)", location.zone);
standard_time + location.zone
}
}
#[derive(Debug)]
/// The Astronomical struct provides functions which support astronomical
/// calculations used by many observational calendars.
#[allow(clippy::exhaustive_structs)] // only exists to collect methods
pub struct Astronomical;
impl Astronomical {
/// Function for the ephemeris correction, which corrects the
/// somewhat-unpredictable discrepancy between dynamical time
/// and universal time
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus (1991) with data from NASA.
pub fn ephemeris_correction(moment: Moment) -> f64 {
// TODO: Change this to directly convert from moment to Gregorian year through a separate fn
let year = moment.inner() / 365.2425;
// Note: Converting to int handles negative number Euclidean division skew.
let year_int = (if year > 0.0 { year + 1.0 } else { year }) as i32;
let fixed_mid_year = crate::iso::fixed_from_iso(year_int, 7, 1);
let c = ((fixed_mid_year.to_i64_date() as f64) - 693596.0) / 36525.0;
let y2000 = (year_int - 2000) as f64;
let y1700 = (year_int - 1700) as f64;
let y1600 = (year_int - 1600) as f64;
let y1000 = ((year_int - 1000) as f64) / 100.0;
let y0 = year_int as f64 / 100.0;
let y1820 = ((year_int - 1820) as f64) / 100.0;
if (2051..=2150).contains(&year_int) {
(-20.0
+ 32.0 * (((year_int - 1820) * (year_int - 1820)) as f64 / 10000.0)
+ 0.5628 * (2150 - year_int) as f64)
/ 86400.0
} else if (2006..=2050).contains(&year_int) {
(62.92 + 0.32217 * y2000 + 0.005589 * y2000 * y2000) / 86400.0
} else if (1987..=2005).contains(&year_int) {
// This polynomial is written out manually instead of using pow for optimization, see #3743
(63.86 + 0.3345 * y2000 - 0.060374 * y2000 * y2000
+ 0.0017275 * y2000 * y2000 * y2000
+ 0.000651814 * y2000 * y2000 * y2000 * y2000
+ 0.00002373599 * y2000 * y2000 * y2000 * y2000 * y2000)
/ 86400.0
} else if (1900..=1986).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
-0.00002 + 0.000297 * c + 0.025184 * c * c - 0.181133 * c * c * c
+ 0.553040 * c * c * c * c
- 0.861938 * c * c * c * c * c
+ 0.677066 * c * c * c * c * c * c
- 0.212591 * c * c * c * c * c * c * c
} else if (1800..=1899).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
-0.000009
+ 0.003844 * c
+ 0.083563 * c * c
+ 0.865736 * c * c * c
+ 4.867575 * c * c * c * c
+ 15.845535 * c * c * c * c * c
+ 31.332267 * c * c * c * c * c * c
+ 38.291999 * c * c * c * c * c * c * c
+ 28.316289 * c * c * c * c * c * c * c * c
+ 11.636204 * c * c * c * c * c * c * c * c * c
+ 2.043794 * c * c * c * c * c * c * c * c * c * c
} else if (1700..=1799).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(8.118780842 - 0.005092142 * y1700 + 0.003336121 * y1700 * y1700
- 0.0000266484 * y1700 * y1700 * y1700)
/ 86400.0
} else if (1600..=1699).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(120.0 - 0.9808 * y1600 - 0.01532 * y1600 * y1600
+ 0.000140272128 * y1600 * y1600 * y1600)
/ 86400.0
} else if (500..=1599).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(1574.2 - 556.01 * y1000 + 71.23472 * y1000 * y1000 + 0.319781 * y1000 * y1000 * y1000
- 0.8503463 * y1000 * y1000 * y1000 * y1000
- 0.005050998 * y1000 * y1000 * y1000 * y1000 * y1000
+ 0.0083572073 * y1000 * y1000 * y1000 * y1000 * y1000 * y1000)
/ 86400.0
} else if (-499..=499).contains(&year_int) {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(10583.6 - 1014.41 * y0 + 33.78311 * y0 * y0
- 5.952053 * y0 * y0 * y0
- 0.1798452 * y0 * y0 * y0 * y0
+ 0.022174192 * y0 * y0 * y0 * y0 * y0
+ 0.0090316521 * y0 * y0 * y0 * y0 * y0 * y0)
/ 86400.0
} else {
(-20.0 + 32.0 * y1820 * y1820) / 86400.0
}
}
/// Include the ephemeris correction to universal time, yielding dynamical time
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn dynamical_from_universal(universal: Moment) -> Moment {
// TODO: Determine correct naming scheme for "dynamical"
universal + Self::ephemeris_correction(universal)
}
/// Remove the ephemeris correction from dynamical time, yielding universal time
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn universal_from_dynamical(dynamical: Moment) -> Moment {
// TODO: Determine correct naming scheme for "dynamical"
dynamical - Self::ephemeris_correction(dynamical)
}
/// The number of uniform length centuries (36525 days measured in dynamical time)
/// before or after noon on January 1, 2000
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn julian_centuries(moment: Moment) -> f64 {
let intermediate = Self::dynamical_from_universal(moment);
(intermediate - J2000) / 36525.0
}
/// The equation of time, which approximates the difference between apparent solar time and
/// mean time; for example, the difference between when the sun is highest in the sky (solar noon)
/// and noon as measured by a clock adjusted to the local longitude. This varies throughout the
/// year and the difference is given by the equation of time.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, p. 185.
pub fn equation_of_time(moment: Moment) -> f64 {
let c = Self::julian_centuries(moment);
let lambda = poly(c, &[280.46645, 36000.76983, 0.0003032]);
let anomaly = poly(c, &[357.52910, 35999.05030, -0.0001559, -0.00000048]);
let eccentricity = poly(c, &[0.016708617, -0.000042037, -0.0000001236]);
let varepsilon = Self::obliquity(moment);
let y = (varepsilon / 2.0).to_radians().tan();
let y = y * y;
let equation = (y * (2.0 * lambda).to_radians().sin()
- 2.0 * eccentricity * anomaly.to_radians().sin()
+ 4.0
* eccentricity
* y
* anomaly.to_radians().sin()
* (2.0 * lambda).to_radians().cos()
- 0.5 * y * y * (4.0 * lambda).to_radians().sin()
- 1.25 * eccentricity * eccentricity * (2.0 * anomaly).to_radians().sin())
/ (2.0 * PI);
equation.signum() * equation.abs().min(12.0 / 24.0)
}
/// The standard time of dusk at a given location on a given date, or `None` if there is no
/// dusk on that date.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn dusk(date: f64, location: Location, alpha: f64) -> Option<Moment> {
let evening = false;
let moment_of_depression = Self::moment_of_depression(
Moment::new(date + (18.0 / 24.0)),
location,
alpha,
evening,
)?;
Some(Location::standard_from_local(
moment_of_depression,
location,
))
}
/// Calculates the obliquity of the ecliptic at a given moment, meaning the angle of the Earth's
/// axial tilt with respect to the plane of its orbit around the sun (currently ~23.4 deg)
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn obliquity(moment: Moment) -> f64 {
let c = Self::julian_centuries(moment);
let angle = 23.0 + 26.0 / 60.0 + 21.448 / 3600.0;
let coefs = &[0.0, -46.8150 / 3600.0, -0.00059 / 3600.0, 0.001813 / 3600.0];
angle + poly(c, coefs)
}
/// Calculates the declination at a given [`Moment`] of UTC time of an object at ecliptic latitude `beta` and ecliptic longitude `lambda`; all angles are in degrees.
/// the declination is the angular distance north or south of an object in the sky with respect to the plane
/// of the Earth's equator; analogous to latitude.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn declination(moment: Moment, beta: f64, lambda: f64) -> f64 {
let varepsilon = Self::obliquity(moment);
(beta.to_radians().sin() * varepsilon.to_radians().cos()
+ beta.to_radians().cos() * varepsilon.to_radians().sin() * lambda.to_radians().sin())
.asin()
.to_degrees()
.rem_euclid(360.0)
}
/// Calculates the right ascension at a given [`Moment`] of UTC time of an object at ecliptic latitude `beta` and ecliptic longitude `lambda`; all angles are in degrees.
/// the right ascension is the angular distance east or west of an object in the sky with respect to the plane
/// of the vernal equinox, which is the celestial coordinate point at which the ecliptic intersects the celestial
/// equator marking spring in the northern hemisphere; analogous to longitude.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn right_ascension(moment: Moment, beta: f64, lambda: f64) -> f64 {
let varepsilon = Self::obliquity(moment);
let y = lambda.to_radians().sin() * varepsilon.to_radians().cos()
- beta.to_radians().tan() * varepsilon.to_radians().sin();
let x = lambda.to_radians().cos();
// Arctangent of y/x in degrees, handling zero cases
y.atan2(x).to_degrees().rem_euclid(360.0)
}
/// Local time from apparent solar time at a given location
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn local_from_apparent(moment: Moment, location: Location) -> Moment {
moment - Self::equation_of_time(Location::universal_from_local(moment, location))
}
/// Approx moment in local time near `moment` at which the depression angle of the sun is `alpha` (negative if
/// the sun is above the horizon) at the given location; since the same angle of depression of the sun
/// can exist twice in a day, early is set to true to specify the morning moment, and false for the
/// evening. Returns `None` if the specified angle is not reached.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn approx_moment_of_depression(
moment: Moment,
location: Location,
alpha: f64,
early: bool, /* TODO: Replace this bool with an enum with Morning and Evening, or Early and Late */
) -> Option<Moment> {
let date = moment.as_rata_die().to_f64_date().floor();
let alt = if alpha >= 0.0 {
if early {
date
} else {
date + 1.0
}
} else {
date + 12.0 / 24.0
};
let value = if Self::sine_offset(moment, location, alpha).abs() > 1.0 {
Self::sine_offset(Moment::new(alt), location, alpha)
} else {
Self::sine_offset(moment, location, alpha)
};
if value.abs() <= 1.0 {
let offset =
(value.asin().to_degrees().rem_euclid(360.0) / 360.0 + 0.5).rem_euclid(1.0) - 0.5;
let moment = Moment::new(
date + if early {
(6.0 / 24.0) - offset
} else {
(18.0 / 24.0) + offset
},
);
Some(Self::local_from_apparent(moment, location))
} else {
None
}
}
/// Moment in local time near `approx` at which the depression angle of the sun is `alpha` (negative if
/// the sun is above the horizon) at the given location; since the same angle of depression of the sun
/// can exist twice in a day, early is set to true to specify the morning moment, and false for the
/// evening. Returns `None` if the specified angle is not reached.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn moment_of_depression(
approx: Moment,
location: Location,
alpha: f64,
early: bool, /* TODO: Replace this bool with an enum with Morning and Evening, or Early and Late */
) -> Option<Moment> {
let moment = Self::approx_moment_of_depression(approx, location, alpha, early)?;
if (approx - moment).abs() < 30.0 {
Some(moment)
} else {
Self::moment_of_depression(moment, location, alpha, early)
}
}
/// The angle of refraction caused by Earth's atmosphere at a given location.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn refraction(location: Location) -> f64 {
// The moment is not used.
let h = location.elevation.max(0.0);
let earth_r = 6.372e6; // Radius of Earth.
let dip = (earth_r / (earth_r + h)).acos().to_degrees();
(34.0 / 60.0) + dip + ((19.0 / 3600.0) * h.sqrt())
}
/// The moment (in universal time) of the nth new moon after
/// (or before if n is negative) the new moon of January 11, 1 CE,
/// which is the first new moon after R.D. 0.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, corrected 2nd edn., 2005.
pub fn nth_new_moon(n: i32) -> Moment {
// The following polynomials are written out instead of using pow for optimization, see #3743
let n0 = 24724.0;
let k = (n as f64) - n0;
let c = k / 1236.85;
let approx = J2000
+ (5.09766 + (MEAN_SYNODIC_MONTH * 1236.85 * c) + (0.00015437 * c * c)
- (0.00000015 * c * c * c)
+ (0.00000000073 * c * c * c * c));
let e = 1.0 - (0.002516 * c) - (0.0000074 * c * c);
let solar_anomaly =
2.5534 + (1236.85 * 29.10535670 * c) - (0.0000014 * c * c) - (0.00000011 * c * c * c);
let lunar_anomaly = 201.5643
+ (385.81693528 * 1236.85 * c)
+ (0.0107582 * c * c)
+ (0.00001238 * c * c * c)
- (0.000000058 * c * c * c * c);
let moon_argument = 160.7108 + (390.67050284 * 1236.85 * c)
- (0.0016118 * c * c)
- (0.00000227 * c * c * c)
+ (0.000000011 * c * c * c * c);
let omega =
124.7746 + (-1.56375588 * 1236.85 * c) + (0.0020672 * c * c) + (0.00000215 * c * c * c);
let mut st = (
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
);
let [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23] = [
-0.40720, 0.17241, 0.01608, 0.01039, 0.00739, -0.00514, 0.00208, -0.00111, -0.00057,
0.00056, -0.00042, 0.00042, 0.00038, -0.00024, -0.00007, 0.00004, 0.00004, 0.00003,
0.00003, -0.00003, 0.00003, -0.00002, -0.00002, 0.00002,
];
let [x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23] = [
0.0, 1.0, 0.0, 0.0, -1.0, 1.0, 2.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, -1.0, 2.0, 0.0, 3.0,
1.0, 0.0, 1.0, -1.0, -1.0, 1.0, 0.0,
];
let [y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18, y19, y20, y21, y22, y23] = [
1.0, 0.0, 2.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 2.0, 3.0, 0.0, 0.0, 2.0, 1.0, 2.0, 0.0,
1.0, 2.0, 1.0, 1.0, 1.0, 3.0, 4.0,
];
let [z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23] = [
0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, -2.0, 2.0, 0.0, 0.0, 2.0, -2.0, 0.0, 0.0, -2.0, 0.0,
-2.0, 2.0, 2.0, 2.0, -2.0, 0.0, 0.0,
];
let mut at = (
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
);
let [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] = [
251.88, 251.83, 349.42, 84.66, 141.74, 207.14, 154.84, 34.52, 207.19, 291.34, 161.72,
239.56, 331.55,
];
let [j0, j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12] = [
0.016321, 26.651886, 36.412478, 18.206239, 53.303771, 2.453732, 7.306860, 27.261239,
0.121824, 1.844379, 24.198154, 25.513099, 3.592518,
];
let [l0, l1, l2, l3, l4, l5, l6, l7, l8, l9, l10, l11, l12] = [
0.000165, 0.000164, 0.000126, 0.000110, 0.000062, 0.000060, 0.000056, 0.000047,
0.000042, 0.000040, 0.000037, 0.000035, 0.000023,
];
let mut correction = -0.00017 * omega.to_radians().sin();
// This summation is unrolled for optimization, see #3743
st.0 = v0
* (x0 * solar_anomaly + y0 * lunar_anomaly + z0 * moon_argument)
.to_radians()
.sin();
st.1 = v1
* e
* (x1 * solar_anomaly + y1 * lunar_anomaly + z1 * moon_argument)
.to_radians()
.sin();
st.2 = v2
* (x2 * solar_anomaly + y2 * lunar_anomaly + z2 * moon_argument)
.to_radians()
.sin();
st.3 = v3
* (x3 * solar_anomaly + y3 * lunar_anomaly + z3 * moon_argument)
.to_radians()
.sin();
st.4 = v4
* e
* (x4 * solar_anomaly + y4 * lunar_anomaly + z4 * moon_argument)
.to_radians()
.sin();
st.5 = v5
* e
* (x5 * solar_anomaly + y5 * lunar_anomaly + z5 * moon_argument)
.to_radians()
.sin();
st.6 = v6
* e
* e
* (x6 * solar_anomaly + y6 * lunar_anomaly + z6 * moon_argument)
.to_radians()
.sin();
st.7 = v7
* (x7 * solar_anomaly + y7 * lunar_anomaly + z7 * moon_argument)
.to_radians()
.sin();
st.8 = v8
* (x8 * solar_anomaly + y8 * lunar_anomaly + z8 * moon_argument)
.to_radians()
.sin();
st.9 = v9
* e
* (x9 * solar_anomaly + y9 * lunar_anomaly + z9 * moon_argument)
.to_radians()
.sin();
st.10 = v10
* (x10 * solar_anomaly + y10 * lunar_anomaly + z10 * moon_argument)
.to_radians()
.sin();
st.11 = v11
* e
* (x11 * solar_anomaly + y11 * lunar_anomaly + z11 * moon_argument)
.to_radians()
.sin();
st.12 = v12
* e
* (x12 * solar_anomaly + y12 * lunar_anomaly + z12 * moon_argument)
.to_radians()
.sin();
st.13 = v13
* e
* (x13 * solar_anomaly + y13 * lunar_anomaly + z13 * moon_argument)
.to_radians()
.sin();
st.14 = v14
* (x14 * solar_anomaly + y14 * lunar_anomaly + z14 * moon_argument)
.to_radians()
.sin();
st.15 = v15
* (x15 * solar_anomaly + y15 * lunar_anomaly + z15 * moon_argument)
.to_radians()
.sin();
st.16 = v16
* (x16 * solar_anomaly + y16 * lunar_anomaly + z16 * moon_argument)
.to_radians()
.sin();
st.17 = v17
* (x17 * solar_anomaly + y17 * lunar_anomaly + z17 * moon_argument)
.to_radians()
.sin();
st.18 = v18
* (x18 * solar_anomaly + y18 * lunar_anomaly + z18 * moon_argument)
.to_radians()
.sin();
st.19 = v19
* (x19 * solar_anomaly + y19 * lunar_anomaly + z19 * moon_argument)
.to_radians()
.sin();
st.20 = v20
* (x20 * solar_anomaly + y20 * lunar_anomaly + z20 * moon_argument)
.to_radians()
.sin();
st.21 = v21
* (x21 * solar_anomaly + y21 * lunar_anomaly + z21 * moon_argument)
.to_radians()
.sin();
st.22 = v22
* (x22 * solar_anomaly + y22 * lunar_anomaly + z22 * moon_argument)
.to_radians()
.sin();
st.23 = v23
* (x23 * solar_anomaly + y23 * lunar_anomaly + z23 * moon_argument)
.to_radians()
.sin();
let sum = st.0
+ st.1
+ st.2
+ st.3
+ st.4
+ st.5
+ st.6
+ st.7
+ st.8
+ st.9
+ st.10
+ st.11
+ st.12
+ st.13
+ st.14
+ st.15
+ st.16
+ st.17
+ st.18
+ st.19
+ st.20
+ st.21
+ st.22
+ st.23;
correction += sum;
let extra = 0.000325
* (299.77 + (132.8475848 * c) - (0.009173 * c * c))
.to_radians()
.sin();
at.0 = l0 * (i0 + j0 * k).to_radians().sin();
at.1 = l1 * (i1 + j1 * k).to_radians().sin();
at.2 = l2 * (i2 + j2 * k).to_radians().sin();
at.3 = l3 * (i3 + j3 * k).to_radians().sin();
at.4 = l4 * (i4 + j4 * k).to_radians().sin();
at.5 = l5 * (i5 + j5 * k).to_radians().sin();
at.6 = l6 * (i6 + j6 * k).to_radians().sin();
at.7 = l7 * (i7 + j7 * k).to_radians().sin();
at.8 = l8 * (i8 + j8 * k).to_radians().sin();
at.9 = l9 * (i9 + j9 * k).to_radians().sin();
at.10 = l10 * (i10 + j10 * k).to_radians().sin();
at.11 = l11 * (i11 + j11 * k).to_radians().sin();
at.12 = l12 * (i12 + j12 * k).to_radians().sin();
let additional = at.0
+ at.1
+ at.2
+ at.3
+ at.4
+ at.5
+ at.6
+ at.7
+ at.8
+ at.9
+ at.10
+ at.11
+ at.12;
Self::universal_from_dynamical(approx + correction + extra + additional)
}
/// Sidereal time, as the hour angle between the meridian and the vernal equinox,
/// from a given moment.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Meeus, 2nd edition (1988), p. 88.
#[allow(dead_code)] // TODO: Remove dead code tag after use
pub fn sidereal_from_moment(moment: Moment) -> f64 {
let c = (moment - J2000) / 36525.0;
let coefficients = &[
(280.46061837),
(36525.0 * 360.98564736629),
(0.000387933),
(-1.0 / 38710000.0),
];
let angle = poly(c, coefficients);
angle.rem_euclid(360.0)
}
/// Ecliptic (aka celestial) latitude of the moon (in degrees)
///
/// This is not a geocentric or geodetic latitude, it does not take into account the
/// rotation of the Earth and is instead measured from the ecliptic.
///
/// `julian_centuries` is the result of calling `Self::julian_centuries(moment)`.
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, pp. 338-342.
pub fn lunar_latitude(julian_centuries: f64) -> f64 {
let c = julian_centuries;
let l = Self::mean_lunar_longitude(c);
let d = Self::lunar_elongation(c);
let ms = Self::solar_anomaly(c);
let ml = Self::lunar_anomaly(c);
let f = Self::moon_node(c);
let e = 1.0 - (0.002516 * c) - (0.0000074 * c * c);
let mut ct = (
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
);
let [w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50, w51, w52, w53, w54, w55, w56, w57, w58, w59] = [
0.0, 0.0, 0.0, 2.0, 2.0, 2.0, 2.0, 0.0, 2.0, 0.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0,
0.0, 4.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 4.0, 4.0, 0.0, 4.0, 2.0, 2.0,
2.0, 2.0, 0.0, 2.0, 2.0, 2.0, 2.0, 4.0, 2.0, 2.0, 0.0, 2.0, 1.0, 1.0, 0.0, 2.0, 1.0,
2.0, 0.0, 4.0, 4.0, 1.0, 4.0, 1.0, 4.0, 2.0,
];
let [x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59] = [
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, -1.0, -1.0,
-1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, -1.0, -2.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0,
0.0, -1.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0, -1.0, -2.0,
];
let [y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18, y19, y20, y21, y22, y23, y24, y25, y26, y27, y28, y29, y30, y31, y32, y33, y34, y35, y36, y37, y38, y39, y40, y41, y42, y43, y44, y45, y46, y47, y48, y49, y50, y51, y52, y53, y54, y55, y56, y57, y58, y59] = [
0.0, 1.0, 1.0, 0.0, -1.0, -1.0, 0.0, 2.0, 1.0, 2.0, 0.0, -2.0, 1.0, 0.0, -1.0, 0.0,
-1.0, -1.0, -1.0, 0.0, 0.0, -1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 3.0, 0.0, -1.0, 1.0, -2.0,
0.0, 2.0, 1.0, -2.0, 3.0, 2.0, -3.0, -1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0,
-2.0, -1.0, 1.0, -2.0, 2.0, -2.0, -1.0, 1.0, 1.0, -1.0, 0.0, 0.0,
];
let [z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23, z24, z25, z26, z27, z28, z29, z30, z31, z32, z33, z34, z35, z36, z37, z38, z39, z40, z41, z42, z43, z44, z45, z46, z47, z48, z49, z50, z51, z52, z53, z54, z55, z56, z57, z58, z59] = [
1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0,
-1.0, -1.0, -1.0, 1.0, 3.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -3.0, 1.0,
-3.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 1.0, 1.0, 1.0, -1.0, 3.0, -1.0, -1.0, 1.0,
-1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0,
];
let [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59] = [
5128122.0, 280602.0, 277693.0, 173237.0, 55413.0, 46271.0, 32573.0, 17198.0, 9266.0,
8822.0, 8216.0, 4324.0, 4200.0, -3359.0, 2463.0, 2211.0, 2065.0, -1870.0, 1828.0,
-1794.0, -1749.0, -1565.0, -1491.0, -1475.0, -1410.0, -1344.0, -1335.0, 1107.0, 1021.0,
833.0, 777.0, 671.0, 607.0, 596.0, 491.0, -451.0, 439.0, 422.0, 421.0, -366.0, -351.0,
331.0, 315.0, 302.0, -283.0, -229.0, 223.0, 223.0, -220.0, -220.0, -185.0, 181.0,
-177.0, 176.0, 166.0, -164.0, 132.0, -119.0, 115.0, 107.0,
];
// This summation is unrolled for optimization, see #3743
ct.0 = v0 * (w0 * d + x0 * ms + y0 * ml + z0 * f).to_radians().sin();
ct.1 = v1 * (w1 * d + x1 * ms + y1 * ml + z1 * f).to_radians().sin();
ct.2 = v2 * (w2 * d + x2 * ms + y2 * ml + z2 * f).to_radians().sin();
ct.3 = v3 * (w3 * d + x3 * ms + y3 * ml + z3 * f).to_radians().sin();
ct.4 = v4 * (w4 * d + x4 * ms + y4 * ml + z4 * f).to_radians().sin();
ct.5 = v5 * (w5 * d + x5 * ms + y5 * ml + z5 * f).to_radians().sin();
ct.6 = v6 * (w6 * d + x6 * ms + y6 * ml + z6 * f).to_radians().sin();
ct.7 = v7 * (w7 * d + x7 * ms + y7 * ml + z7 * f).to_radians().sin();
ct.8 = v8 * (w8 * d + x8 * ms + y8 * ml + z8 * f).to_radians().sin();
ct.9 = v9 * (w9 * d + x9 * ms + y9 * ml + z9 * f).to_radians().sin();
ct.10 = v10 * e * (w10 * d + x10 * ms + y10 * ml + z10 * f).to_radians().sin();
ct.11 = v11 * (w11 * d + x11 * ms + y11 * ml + z11 * f).to_radians().sin();
ct.12 = v12 * (w12 * d + x12 * ms + y12 * ml + z12 * f).to_radians().sin();
ct.13 = v13 * e * (w13 * d + x13 * ms + y13 * ml + z13 * f).to_radians().sin();
ct.14 = v14 * e * (w14 * d + x14 * ms + y14 * ml + z14 * f).to_radians().sin();
ct.15 = v15 * e * (w15 * d + x15 * ms + y15 * ml + z15 * f).to_radians().sin();
ct.16 = v16 * e * (w16 * d + x16 * ms + y16 * ml + z16 * f).to_radians().sin();
ct.17 = v17 * e * (w17 * d + x17 * ms + y17 * ml + z17 * f).to_radians().sin();
ct.18 = v18 * (w18 * d + x18 * ms + y18 * ml + z18 * f).to_radians().sin();
ct.19 = v19 * e * (w19 * d + x19 * ms + y19 * ml + z19 * f).to_radians().sin();
ct.20 = v20 * (w20 * d + x20 * ms + y20 * ml + z20 * f).to_radians().sin();
ct.21 = v21 * e * (w21 * d + x21 * ms + y21 * ml + z21 * f).to_radians().sin();
ct.22 = v22 * (w22 * d + x22 * ms + y22 * ml + z22 * f).to_radians().sin();
ct.23 = v23 * e * (w23 * d + x23 * ms + y23 * ml + z23 * f).to_radians().sin();
ct.24 = v24 * e * (w24 * d + x24 * ms + y24 * ml + z24 * f).to_radians().sin();
ct.25 = v25 * e * (w25 * d + x25 * ms + y25 * ml + z25 * f).to_radians().sin();
ct.26 = v26 * (w26 * d + x26 * ms + y26 * ml + z26 * f).to_radians().sin();
ct.27 = v27 * (w27 * d + x27 * ms + y27 * ml + z27 * f).to_radians().sin();
ct.28 = v28 * (w28 * d + x28 * ms + y28 * ml + z28 * f).to_radians().sin();
ct.29 = v29 * (w29 * d + x29 * ms + y29 * ml + z29 * f).to_radians().sin();
ct.30 = v30 * (w30 * d + x30 * ms + y30 * ml + z30 * f).to_radians().sin();
ct.31 = v31 * (w31 * d + x31 * ms + y31 * ml + z31 * f).to_radians().sin();
ct.32 = v32 * (w32 * d + x32 * ms + y32 * ml + z32 * f).to_radians().sin();
ct.33 = v33 * (w33 * d + x33 * ms + y33 * ml + z33 * f).to_radians().sin();
ct.34 = v34 * e * (w34 * d + x34 * ms + y34 * ml + z34 * f).to_radians().sin();
ct.35 = v35 * (w35 * d + x35 * ms + y35 * ml + z35 * f).to_radians().sin();
ct.36 = v36 * (w36 * d + x36 * ms + y36 * ml + z36 * f).to_radians().sin();
ct.37 = v37 * (w37 * d + x37 * ms + y37 * ml + z37 * f).to_radians().sin();
ct.38 = v38 * (w38 * d + x38 * ms + y38 * ml + z38 * f).to_radians().sin();
ct.39 = v39 * e * (w39 * d + x39 * ms + y39 * ml + z39 * f).to_radians().sin();
ct.40 = v40 * e * (w40 * d + x40 * ms + y40 * ml + z40 * f).to_radians().sin();
ct.41 = v41 * (w41 * d + x41 * ms + y41 * ml + z41 * f).to_radians().sin();
ct.42 = v42 * e * (w42 * d + x42 * ms + y42 * ml + z42 * f).to_radians().sin();
ct.43 = v43 * e * e * (w43 * d + x43 * ms + y43 * ml + z43 * f).to_radians().sin();
ct.44 = v44 * (w44 * d + x44 * ms + y44 * ml + z44 * f).to_radians().sin();
ct.45 = v45 * e * (w45 * d + x45 * ms + y45 * ml + z45 * f).to_radians().sin();
ct.46 = v46 * e * (w46 * d + x46 * ms + y46 * ml + z46 * f).to_radians().sin();
ct.47 = v47 * e * (w47 * d + x47 * ms + y47 * ml + z47 * f).to_radians().sin();
ct.48 = v48 * e * (w48 * d + x48 * ms + y48 * ml + z48 * f).to_radians().sin();
ct.49 = v49 * e * (w49 * d + x49 * ms + y49 * ml + z49 * f).to_radians().sin();
ct.50 = v50 * (w50 * d + x50 * ms + y50 * ml + z50 * f).to_radians().sin();
ct.51 = v51 * e * (w51 * d + x51 * ms + y51 * ml + z51 * f).to_radians().sin();
ct.52 = v52 * e * (w52 * d + x52 * ms + y52 * ml + z52 * f).to_radians().sin();
ct.53 = v53 * (w53 * d + x53 * ms + y53 * ml + z53 * f).to_radians().sin();
ct.54 = v54 * e * (w54 * d + x54 * ms + y54 * ml + z54 * f).to_radians().sin();
ct.55 = v55 * (w55 * d + x55 * ms + y55 * ml + z55 * f).to_radians().sin();
ct.56 = v56 * (w56 * d + x56 * ms + y56 * ml + z56 * f).to_radians().sin();
ct.57 = v57 * (w57 * d + x57 * ms + y57 * ml + z57 * f).to_radians().sin();
ct.58 = v58 * e * (w58 * d + x58 * ms + y58 * ml + z58 * f).to_radians().sin();
ct.59 = v59 * e * e * (w59 * d + x59 * ms + y59 * ml + z59 * f).to_radians().sin();
let mut correction = ct.0
+ ct.1
+ ct.2
+ ct.3
+ ct.4
+ ct.5
+ ct.6
+ ct.7
+ ct.8
+ ct.9
+ ct.10
+ ct.11
+ ct.12
+ ct.13
+ ct.14
+ ct.15
+ ct.16
+ ct.17
+ ct.18
+ ct.19
+ ct.20
+ ct.21
+ ct.22
+ ct.23
+ ct.24
+ ct.25
+ ct.26
+ ct.27
+ ct.28
+ ct.29
+ ct.30
+ ct.31
+ ct.32
+ ct.33
+ ct.34
+ ct.35
+ ct.36
+ ct.37
+ ct.38
+ ct.39
+ ct.40
+ ct.41
+ ct.42
+ ct.43
+ ct.44
+ ct.45
+ ct.46
+ ct.47
+ ct.48
+ ct.49
+ ct.50
+ ct.51
+ ct.52
+ ct.53
+ ct.54
+ ct.55
+ ct.56
+ ct.57
+ ct.58
+ ct.59;
correction /= 1_000_000.0;
let venus = (175.0
* ((119.75 + c * 131.849 + f).to_radians().sin()
+ (119.75 + c * 131.849 - f).to_radians().sin()))
/ 1_000_000.0;
let flat_earth = (-2235.0 * l.to_radians().sin()
+ 127.0 * (l - ml).to_radians().sin()
+ -115.0 * (l + ml).to_radians().sin())
/ 1_000_000.0;
let extra = (382.0 * (313.45 + (c * 481266.484)).to_radians().sin()) / 1_000_000.0;
correction + venus + flat_earth + extra
}
/// Ecliptic (aka celestial) longitude of the moon (in degrees)
///
/// This is not a geocentric or geodetic longitude, it does not take into account the
/// rotation of the Earth and is instead measured from the ecliptic and the vernal equinox.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, pp. 338-342.
pub fn lunar_longitude(julian_centuries: f64) -> f64 {
let c = julian_centuries;
let l = Self::mean_lunar_longitude(c);
let d = Self::lunar_elongation(c);
let ms = Self::solar_anomaly(c);
let ml = Self::lunar_anomaly(c);
let f = Self::moon_node(c);
let e = 1.0 - (0.002516 * c) - (0.0000074 * c * c);
let mut ct = (
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
);
let [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58] = [
6288774.0, 1274027.0, 658314.0, 213618.0, -185116.0, -114332.0, 58793.0, 57066.0,
53322.0, 45758.0, -40923.0, -34720.0, -30383.0, 15327.0, -12528.0, 10980.0, 10675.0,
10034.0, 8548.0, -7888.0, -6766.0, -5163.0, 4987.0, 4036.0, 3994.0, 3861.0, 3665.0,
-2689.0, -2602.0, 2390.0, -2348.0, 2236.0, -2120.0, -2069.0, 2048.0, -1773.0, -1595.0,
1215.0, -1110.0, -892.0, -810.0, 759.0, -713.0, -700.0, 691.0, 596.0, 549.0, 537.0,
520.0, -487.0, -399.0, -381.0, 351.0, -340.0, 330.0, 327.0, -323.0, 299.0, 294.0,
];
let [w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19, w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32, w33, w34, w35, w36, w37, w38, w39, w40, w41, w42, w43, w44, w45, w46, w47, w48, w49, w50, w51, w52, w53, w54, w55, w56, w57, w58] = [
0.0, 2.0, 2.0, 0.0, 0.0, 0.0, 2.0, 2.0, 2.0, 2.0, 0.0, 1.0, 0.0, 2.0, 0.0, 0.0, 4.0,
0.0, 4.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 4.0, 2.0, 0.0, 2.0, 2.0, 1.0, 2.0, 0.0, 0.0,
2.0, 2.0, 2.0, 4.0, 0.0, 3.0, 2.0, 4.0, 0.0, 2.0, 2.0, 2.0, 4.0, 0.0, 4.0, 1.0, 2.0,
0.0, 1.0, 3.0, 4.0, 2.0, 0.0, 1.0, 2.0,
];
let [x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58] = [
0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0, -1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 1.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, -1.0, 0.0, -2.0, 1.0, 2.0,
-2.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, -1.0, 2.0, 2.0, 1.0, -1.0, 0.0, 0.0, -1.0, 0.0,
1.0, 0.0, 1.0, 0.0, 0.0, -1.0, 2.0, 1.0, 0.0,
];
let [y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18, y19, y20, y21, y22, y23, y24, y25, y26, y27, y28, y29, y30, y31, y32, y33, y34, y35, y36, y37, y38, y39, y40, y41, y42, y43, y44, y45, y46, y47, y48, y49, y50, y51, y52, y53, y54, y55, y56, y57, y58] = [
1.0, -1.0, 0.0, 2.0, 0.0, 0.0, -2.0, -1.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 1.0,
-1.0, 3.0, -2.0, -1.0, 0.0, -1.0, 0.0, 1.0, 2.0, 0.0, -3.0, -2.0, -1.0, -2.0, 1.0, 0.0,
2.0, 0.0, -1.0, 1.0, 0.0, -1.0, 2.0, -1.0, 1.0, -2.0, -1.0, -1.0, -2.0, 0.0, 1.0, 4.0,
0.0, -2.0, 0.0, 2.0, 1.0, -2.0, -3.0, 2.0, 1.0, -1.0, 3.0,
];
let [z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23, z24, z25, z26, z27, z28, z29, z30, z31, z32, z33, z34, z35, z36, z37, z38, z39, z40, z41, z42, z43, z44, z45, z46, z47, z48, z49, z50, z51, z52, z53, z54, z55, z56, z57, z58] = [
0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -2.0, 2.0, -2.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, -2.0, 2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0, -2.0,
-2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
];
// This summation is unrolled for optimization, see #3743
ct.0 = v0 * (w0 * d + x0 * ms + y0 * ml + z0 * f).to_radians().sin();
ct.1 = v1 * (w1 * d + x1 * ms + y1 * ml + z1 * f).to_radians().sin();
ct.2 = v2 * (w2 * d + x2 * ms + y2 * ml + z2 * f).to_radians().sin();
ct.3 = v3 * (w3 * d + x3 * ms + y3 * ml + z3 * f).to_radians().sin();
ct.4 = v4 * e * (w4 * d + x4 * ms + y4 * ml + z4 * f).to_radians().sin();
ct.5 = v5 * (w5 * d + x5 * ms + y5 * ml + z5 * f).to_radians().sin();
ct.6 = v6 * (w6 * d + x6 * ms + y6 * ml + z6 * f).to_radians().sin();
ct.7 = v7 * e * (w7 * d + x7 * ms + y7 * ml + z7 * f).to_radians().sin();
ct.8 = v8 * (w8 * d + x8 * ms + y8 * ml + z8 * f).to_radians().sin();
ct.9 = v9 * e * (w9 * d + x9 * ms + y9 * ml + z9 * f).to_radians().sin();
ct.10 = v10 * e * (w10 * d + x10 * ms + y10 * ml + z10 * f).to_radians().sin();
ct.11 = v11 * (w11 * d + x11 * ms + y11 * ml + z11 * f).to_radians().sin();
ct.12 = v12 * e * (w12 * d + x12 * ms + y12 * ml + z12 * f).to_radians().sin();
ct.13 = v13 * (w13 * d + x13 * ms + y13 * ml + z13 * f).to_radians().sin();
ct.14 = v14 * (w14 * d + x14 * ms + y14 * ml + z14 * f).to_radians().sin();
ct.15 = v15 * (w15 * d + x15 * ms + y15 * ml + z15 * f).to_radians().sin();
ct.16 = v16 * (w16 * d + x16 * ms + y16 * ml + z16 * f).to_radians().sin();
ct.17 = v17 * (w17 * d + x17 * ms + y17 * ml + z17 * f).to_radians().sin();
ct.18 = v18 * (w18 * d + x18 * ms + y18 * ml + z18 * f).to_radians().sin();
ct.19 = v19 * e * (w19 * d + x19 * ms + y19 * ml + z19 * f).to_radians().sin();
ct.20 = v20 * e * (w20 * d + x20 * ms + y20 * ml + z20 * f).to_radians().sin();
ct.21 = v21 * (w21 * d + x21 * ms + y21 * ml + z21 * f).to_radians().sin();
ct.22 = v22 * e * (w22 * d + x22 * ms + y22 * ml + z22 * f).to_radians().sin();
ct.23 = v23 * e * (w23 * d + x23 * ms + y23 * ml + z23 * f).to_radians().sin();
ct.24 = v24 * (w24 * d + x24 * ms + y24 * ml + z24 * f).to_radians().sin();
ct.25 = v25 * (w25 * d + x25 * ms + y25 * ml + z25 * f).to_radians().sin();
ct.26 = v26 * (w26 * d + x26 * ms + y26 * ml + z26 * f).to_radians().sin();
ct.27 = v27 * e * (w27 * d + x27 * ms + y27 * ml + z27 * f).to_radians().sin();
ct.28 = v28 * (w28 * d + x28 * ms + y28 * ml + z28 * f).to_radians().sin();
ct.29 = v29 * e * (w29 * d + x29 * ms + y29 * ml + z29 * f).to_radians().sin();
ct.30 = v30 * (w30 * d + x30 * ms + y30 * ml + z30 * f).to_radians().sin();
ct.31 = v31 * e * e * (w31 * d + x31 * ms + y31 * ml + z31 * f).to_radians().sin();
ct.32 = v32 * e * (w32 * d + x32 * ms + y32 * ml + z32 * f).to_radians().sin();
ct.33 = v33 * e * e * (w33 * d + x33 * ms + y33 * ml + z33 * f).to_radians().sin();
ct.34 = v34 * e * e * (w34 * d + x34 * ms + y34 * ml + z34 * f).to_radians().sin();
ct.35 = v35 * (w35 * d + x35 * ms + y35 * ml + z35 * f).to_radians().sin();
ct.36 = v36 * (w36 * d + x36 * ms + y36 * ml + z36 * f).to_radians().sin();
ct.37 = v37 * e * (w37 * d + x37 * ms + y37 * ml + z37 * f).to_radians().sin();
ct.38 = v38 * (w38 * d + x38 * ms + y38 * ml + z38 * f).to_radians().sin();
ct.39 = v39 * (w39 * d + x39 * ms + y39 * ml + z39 * f).to_radians().sin();
ct.40 = v40 * e * (w40 * d + x40 * ms + y40 * ml + z40 * f).to_radians().sin();
ct.41 = v41 * e * (w41 * d + x41 * ms + y41 * ml + z41 * f).to_radians().sin();
ct.42 = v42 * e * e * (w42 * d + x42 * ms + y42 * ml + z42 * f).to_radians().sin();
ct.43 = v43 * e * e * (w43 * d + x43 * ms + y43 * ml + z43 * f).to_radians().sin();
ct.44 = v44 * e * (w44 * d + x44 * ms + y44 * ml + z44 * f).to_radians().sin();
ct.45 = v45 * e * (w45 * d + x45 * ms + y45 * ml + z45 * f).to_radians().sin();
ct.46 = v46 * (w46 * d + x46 * ms + y46 * ml + z46 * f).to_radians().sin();
ct.47 = v47 * (w47 * d + x47 * ms + y47 * ml + z47 * f).to_radians().sin();
ct.48 = v48 * e * (w48 * d + x48 * ms + y48 * ml + z48 * f).to_radians().sin();
ct.49 = v49 * (w49 * d + x49 * ms + y49 * ml + z49 * f).to_radians().sin();
ct.50 = v50 * e * (w50 * d + x50 * ms + y50 * ml + z50 * f).to_radians().sin();
ct.51 = v51 * (w51 * d + x51 * ms + y51 * ml + z51 * f).to_radians().sin();
ct.52 = v52 * e * (w52 * d + x52 * ms + y52 * ml + z52 * f).to_radians().sin();
ct.53 = v53 * (w53 * d + x53 * ms + y53 * ml + z53 * f).to_radians().sin();
ct.54 = v54 * (w54 * d + x54 * ms + y54 * ml + z54 * f).to_radians().sin();
ct.55 = v55 * e * (w55 * d + x55 * ms + y55 * ml + z55 * f).to_radians().sin();
ct.56 = v56 * e * e * (w56 * d + x56 * ms + y56 * ml + z56 * f).to_radians().sin();
ct.57 = v57 * e * (w57 * d + x57 * ms + y57 * ml + z57 * f).to_radians().sin();
ct.58 = v58 * (w58 * d + x58 * ms + y58 * ml + z58 * f).to_radians().sin();
let mut correction = ct.0
+ ct.1
+ ct.2
+ ct.3
+ ct.4
+ ct.5
+ ct.6
+ ct.7
+ ct.8
+ ct.9
+ ct.10
+ ct.11
+ ct.12
+ ct.13
+ ct.14
+ ct.15
+ ct.16
+ ct.17
+ ct.18
+ ct.19
+ ct.20
+ ct.21
+ ct.22
+ ct.23
+ ct.24
+ ct.25
+ ct.26
+ ct.27
+ ct.28
+ ct.29
+ ct.30
+ ct.31
+ ct.32
+ ct.33
+ ct.34
+ ct.35
+ ct.36
+ ct.37
+ ct.38
+ ct.39
+ ct.40
+ ct.41
+ ct.42
+ ct.43
+ ct.44
+ ct.45
+ ct.46
+ ct.47
+ ct.48
+ ct.49
+ ct.50
+ ct.51
+ ct.52
+ ct.53
+ ct.54
+ ct.55
+ ct.56
+ ct.57
+ ct.58;
correction /= 1000000.0;
let venus = 3958.0 / 1000000.0 * (119.75 + c * 131.849).to_radians().sin();
let jupiter = 318.0 / 1000000.0 * (53.09 + c * 479264.29).to_radians().sin();
let flat_earth = 1962.0 / 1000000.0 * (l - f).to_radians().sin();
(l + correction + venus + jupiter + flat_earth + Self::nutation(julian_centuries))
.rem_euclid(360.0)
}
/// Mean longitude of the moon (in degrees) at a given Moment in Julian centuries.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, pp. 336-340.
fn mean_lunar_longitude(c: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
let n = 218.3164477
+ c * (481267.88123421 - 0.0015786 * c + c * c / 538841.0 - c * c * c / 65194000.0);
n.rem_euclid(360.0)
}
/// Closest fixed date on or after `date` on the eve of which crescent moon first became visible at `location`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn phasis_on_or_after(
date: RataDie,
location: Location,
lunar_phase: Option<f64>,
) -> RataDie {
let lunar_phase =
lunar_phase.unwrap_or_else(|| Self::calculate_new_moon_at_or_before(date));
let age = date.to_f64_date() - lunar_phase;
let tau = if age <= 4.0 || Self::visible_crescent((date - 1).as_moment(), location) {
lunar_phase + 29.0 // Next new moon
} else {
date.to_f64_date()
};
next_moment(Moment::new(tau), location, Self::visible_crescent)
}
/// Closest fixed date on or before `date` when crescent moon first became visible at `location`.
/// Lunar phase is the result of calling `lunar_phase(moment, julian_centuries) in an earlier function.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn phasis_on_or_before(
date: RataDie,
location: Location,
lunar_phase: Option<f64>,
) -> RataDie {
let lunar_phase =
lunar_phase.unwrap_or_else(|| Self::calculate_new_moon_at_or_before(date));
let age = date.to_f64_date() - lunar_phase;
let tau = if age <= 3.0 && !Self::visible_crescent((date).as_moment(), location) {
lunar_phase - 30.0 // Previous new moon
} else {
lunar_phase
};
next_moment(Moment::new(tau), location, Self::visible_crescent)
}
/// Calculate the day that the new moon occurred on or before the given date.
pub fn calculate_new_moon_at_or_before(date: RataDie) -> f64 {
Self::lunar_phase_at_or_before(0.0, date.as_moment())
.inner()
.floor()
}
/// Length of the lunar month containing `date` in days, based on observability at `location`.
/// Calculates the month length for the Islamic Observational Calendar
/// Can return 31 days due to the imprecise nature of trying to approximate an observational calendar. (See page 294 of the Calendrical Calculations book)
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn month_length(date: RataDie, location: Location) -> u8 {
let moon = Self::phasis_on_or_after(date + 1, location, None);
let prev = Self::phasis_on_or_before(date, location, None);
debug_assert!(moon > prev);
debug_assert!(moon - prev < u8::MAX.into());
(moon - prev) as u8
}
/// Lunar elongation (the moon's angular distance east of the Sun) at a given Moment in Julian centuries
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, p. 338.
fn lunar_elongation(c: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(297.85019021 + 445267.1114034 * c - 0.0018819 * c * c + c * c * c / 545868.0
- c * c * c * c / 113065000.0)
.rem_euclid(360.0)
}
/// Altitude of the moon (in degrees) at a given moment
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998.
pub fn lunar_altitude(moment: Moment, location: Location) -> f64 {
let phi = location.latitude;
let psi = location.longitude;
let c = Self::julian_centuries(moment);
let lambda = Self::lunar_longitude(c);
let beta = Self::lunar_latitude(c);
let alpha = Self::right_ascension(moment, beta, lambda);
let delta = Self::declination(moment, beta, lambda);
let theta0 = Self::sidereal_from_moment(moment);
let cap_h = (theta0 + psi - alpha).rem_euclid(360.0);
let altitude = (phi.to_radians().sin() * delta.to_radians().sin()
+ phi.to_radians().cos() * delta.to_radians().cos() * cap_h.to_radians().cos())
.asin()
.to_degrees();
(altitude + 180.0).rem_euclid(360.0) - 180.0
}
/// Distance to the moon in meters at the given moment.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, pp. 338-342.
#[allow(dead_code)]
pub fn lunar_distance(moment: Moment) -> f64 {
let c = Self::julian_centuries(moment);
let cap_d = Self::lunar_elongation(c);
let cap_m = Self::solar_anomaly(c);
let cap_m_prime = Self::lunar_anomaly(c);
let cap_f = Self::moon_node(c);
let cap_e = 1.0 - (0.002516 * c) - (0.0000074 * c * c);
let args_lunar_elongation = [
0.0, 2.0, 2.0, 0.0, 0.0, 0.0, 2.0, 2.0, 2.0, 2.0, 0.0, 1.0, 0.0, 2.0, 0.0, 0.0, 4.0,
0.0, 4.0, 2.0, 2.0, 1.0, 1.0, 2.0, 2.0, 4.0, 2.0, 0.0, 2.0, 2.0, 1.0, 2.0, 0.0, 0.0,
2.0, 2.0, 2.0, 4.0, 0.0, 3.0, 2.0, 4.0, 0.0, 2.0, 2.0, 2.0, 4.0, 0.0, 4.0, 1.0, 2.0,
0.0, 1.0, 3.0, 4.0, 2.0, 0.0, 1.0, 2.0, 2.0,
];
let args_solar_anomaly = [
0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, -1.0, 0.0, -1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 1.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, -1.0, 0.0, -2.0, 1.0, 2.0,
-2.0, 0.0, 0.0, -1.0, 0.0, 0.0, 1.0, -1.0, 2.0, 2.0, 1.0, -1.0, 0.0, 0.0, -1.0, 0.0,
1.0, 0.0, 1.0, 0.0, 0.0, -1.0, 2.0, 1.0, 0.0, 0.0,
];
let args_lunar_anomaly = [
1.0, -1.0, 0.0, 2.0, 0.0, 0.0, -2.0, -1.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 1.0, 1.0,
-1.0, 3.0, -2.0, -1.0, 0.0, -1.0, 0.0, 1.0, 2.0, 0.0, -3.0, -2.0, -1.0, -2.0, 1.0, 0.0,
2.0, 0.0, -1.0, 1.0, 0.0, -1.0, 2.0, -1.0, 1.0, -2.0, -1.0, -1.0, -2.0, 0.0, 1.0, 4.0,
0.0, -2.0, 0.0, 2.0, 1.0, -2.0, -3.0, 2.0, 1.0, -1.0, 3.0, -1.0,
];
let args_moon_node = [
0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -2.0, 2.0, -2.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, -2.0, 2.0, 0.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0, -2.0,
-2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -2.0,
];
let cosine_coeff = [
-20905355.0,
-3699111.0,
-2955968.0,
-569925.0,
48888.0,
-3149.0,
246158.0,
-152138.0,
-170733.0,
-204586.0,
-129620.0,
108743.0,
104755.0,
10321.0,
0.0,
79661.0,
-34782.0,
-23210.0,
-21636.0,
24208.0,
30824.0,
-8379.0,
-16675.0,
-12831.0,
-10445.0,
-11650.0,
14403.0,
-7003.0,
0.0,
10056.0,
6322.0,
-9884.0,
5751.0,
0.0,
-4950.0,
4130.0,
0.0,
-3958.0,
0.0,
3258.0,
2616.0,
-1897.0,
-2117.0,
2354.0,
0.0,
0.0,
-1423.0,
-1117.0,
-1571.0,
-1739.0,
0.0,
-4421.0,
0.0,
0.0,
0.0,
0.0,
1165.0,
0.0,
0.0,
8752.0,
];
let correction: f64 = cosine_coeff
.iter()
.zip(args_lunar_elongation.iter())
.zip(args_solar_anomaly.iter())
.zip(args_lunar_anomaly.iter())
.zip(args_moon_node.iter())
.map(|((((&v, &w), &x), &y), &z)| {
v * cap_e.powf(x.abs())
* (w * cap_d + x * cap_m + y * cap_m_prime + z * cap_f)
.to_radians()
.cos()
})
.sum();
385000560.0 + correction
}
/// The parallax of the moon, meaning the difference in angle of the direction of the moon
/// as measured from a given location and from the center of the Earth, in degrees.
/// Note: the location is encoded as the `lunar_altitude_val` which is the result of `lunar_altitude(moment,location)`.
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998.
pub fn lunar_parallax(lunar_altitude_val: f64, moment: Moment) -> f64 {
let cap_delta = Self::lunar_distance(moment);
let alt = 6378140.0 / cap_delta;
let arg = alt * lunar_altitude_val.to_radians().cos();
arg.asin().to_degrees().rem_euclid(360.0)
}
/// Topocentric altitude of the moon.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn topocentric_lunar_altitude(moment: Moment, location: Location) -> f64 {
let lunar_altitude = Self::lunar_altitude(moment, location);
lunar_altitude - Self::lunar_parallax(lunar_altitude, moment)
}
/// Observed altitude of upper limb of moon at moment at location.
/// /// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn observed_lunar_altitude(moment: Moment, location: Location) -> f64 {
let r = Self::topocentric_lunar_altitude(moment, location);
let y = Self::refraction(location);
let z = 16.0 / 60.0;
r + y + z
}
/// Average anomaly of the sun (in degrees) at a given Moment in Julian centuries.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, p. 338.
fn solar_anomaly(c: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(357.5291092 + 35999.0502909 * c - 0.0001536 * c * c + c * c * c / 24490000.0)
.rem_euclid(360.0)
}
/// Average anomaly of the moon (in degrees) at a given Moment in Julian centuries
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, p. 338.
fn lunar_anomaly(c: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(134.9633964 + 477198.8675055 * c + 0.0087414 * c * c + c * c * c / 69699.0
- c * c * c * c / 14712000.0)
.rem_euclid(360.0)
}
/// The moon's argument of latitude, in degrees, at the moment given by `c` in Julian centuries.
/// The argument of latitude is used to define the position of a body moving in a Kepler orbit.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from _Astronomical Algorithms_ by Jean Meeus, 2nd edn., 1998, p. 338.
fn moon_node(c: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
(93.2720950 + 483202.0175233 * c - 0.0036539 * c * c - c * c * c / 3526000.0
+ c * c * c * c / 863310000.0)
.rem_euclid(360.0)
}
/// Standard time of moonset on the date of the given moment and at the given location.
/// Returns `None` if there is no such moonset.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
#[allow(dead_code)] // TODO: Remove dead code tag after use
fn moonset(date: Moment, location: Location) -> Option<Moment> {
let moment = Location::universal_from_standard(date, location);
let waxing = Self::lunar_phase(date, Self::julian_centuries(date)) < 180.0;
let alt = Self::observed_lunar_altitude(moment, location);
let lat = location.latitude;
let offset = alt / (4.0 * (90.0 - lat.abs()));
let approx = if waxing {
if offset > 0.0 {
moment + offset
} else {
moment + 1.0 + offset
}
} else {
moment - offset + 0.5
};
let set = Moment::new(binary_search(
approx.inner() - (6.0 / 24.0),
approx.inner() + (6.0 / 24.0),
|x| Self::observed_lunar_altitude(Moment::new(x), location) < 0.0,
1.0 / 24.0 / 60.0,
));
if set < moment + 1.0 {
let std = Moment::new(
Location::standard_from_universal(set, location)
.inner()
.max(date.inner()),
);
debug_assert!(std >= date, "std should not be less than date");
if std < date {
return None;
}
Some(std)
} else {
None
}
}
/// Standard time of sunset on the date of the given moment and at the given location.
/// Returns `None` if there is no such sunset.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
#[allow(dead_code)]
pub fn sunset(date: Moment, location: Location) -> Option<Moment> {
let alpha = Self::refraction(location) + (16.0 / 60.0);
Self::dusk(date.inner(), location, alpha)
}
/// Time between sunset and moonset on the date of the given moment at the given location.
/// Returns `None` if there is no such sunset.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn moonlag(date: Moment, location: Location) -> Option<f64> {
if let Some(sun) = Self::sunset(date, location) {
if let Some(moon) = Self::moonset(date, location) {
Some(moon - sun)
} else {
Some(1.0)
}
} else {
None
}
}
/// Longitudinal nutation (periodic variation in the inclination of the Earth's axis) at a given Moment.
/// Argument comes from the result of calling `Self::julian_centuries(moment)` in an earlier function.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn nutation(julian_centuries: f64) -> f64 {
// This polynomial is written out manually instead of using a fn like pow for optimization, see #3743
let c = julian_centuries;
let a = 124.90 - 1934.134 * c + 0.002063 * c * c;
let b = 201.11 + 72001.5377 * c + 0.00057 * c * c;
-0.004778 * a.to_radians().sin() - 0.0003667 * b.to_radians().sin()
}
/// The phase of the moon at a given Moment, defined as the difference in longitudes
/// of the sun and the moon.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn lunar_phase(moment: Moment, julian_centuries: f64) -> f64 {
let t0 = NEW_MOON_ZERO;
let maybe_n = i64_to_i32(div_euclid_f64(moment - t0, MEAN_SYNODIC_MONTH).round() as i64);
debug_assert!(
maybe_n.is_ok(),
"Lunar phase moment should be in range of i32"
);
let n = maybe_n.unwrap_or_else(|e| e.saturate());
let a = (Self::lunar_longitude(julian_centuries) - Self::solar_longitude(julian_centuries))
.rem_euclid(360.0);
let b = 360.0 * ((moment - Self::nth_new_moon(n)) / MEAN_SYNODIC_MONTH).rem_euclid(1.0);
if (a - b).abs() > 180.0 {
b
} else {
a
}
}
/// Moment in universal time of the last time at or before the given moment when the lunar phase
/// was equal to the `phase` given.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn lunar_phase_at_or_before(phase: f64, moment: Moment) -> Moment {
let julian_centuries = Self::julian_centuries(moment);
let tau = moment.inner()
- (MEAN_SYNODIC_MONTH / 360.0)
* ((Self::lunar_phase(moment, julian_centuries) - phase) % 360.0);
let a = tau - 2.0;
let b = moment.inner().min(tau + 2.0);
let lunar_phase_f64 = |x: f64| -> f64 {
Self::lunar_phase(Moment::new(x), Self::julian_centuries(Moment::new(x)))
};
Moment::new(invert_angular(lunar_phase_f64, phase, (a, b)))
}
/// The longitude of the Sun at a given Moment in degrees.
/// Moment is not directly used but is enconded from the argument `julian_centuries` which is the result of calling `Self::julian_centuries(moment) in an earlier function`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz,
/// originally from "Planetary Programs and Tables from -4000 to +2800" by Bretagnon & Simon, 1986.
pub fn solar_longitude(julian_centuries: f64) -> f64 {
let c: f64 = julian_centuries;
let mut lt = (
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
);
let [x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48] = [
403406.0, 195207.0, 119433.0, 112392.0, 3891.0, 2819.0, 1721.0, 660.0, 350.0, 334.0,
314.0, 268.0, 242.0, 234.0, 158.0, 132.0, 129.0, 114.0, 99.0, 93.0, 86.0, 78.0, 72.0,
68.0, 64.0, 46.0, 38.0, 37.0, 32.0, 29.0, 28.0, 27.0, 27.0, 25.0, 24.0, 21.0, 21.0,
20.0, 18.0, 17.0, 14.0, 13.0, 13.0, 13.0, 12.0, 10.0, 10.0, 10.0, 10.0,
];
let [y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18, y19, y20, y21, y22, y23, y24, y25, y26, y27, y28, y29, y30, y31, y32, y33, y34, y35, y36, y37, y38, y39, y40, y41, y42, y43, y44, y45, y46, y47, y48] = [
270.54861, 340.19128, 63.91854, 331.26220, 317.843, 86.631, 240.052, 310.26, 247.23,
260.87, 297.82, 343.14, 166.79, 81.53, 3.50, 132.75, 182.95, 162.03, 29.8, 266.4,
249.2, 157.6, 257.8, 185.1, 69.9, 8.0, 197.1, 250.4, 65.3, 162.7, 341.5, 291.6, 98.5,
146.7, 110.0, 5.2, 342.6, 230.9, 256.1, 45.3, 242.9, 115.2, 151.8, 285.3, 53.3, 126.6,
205.7, 85.9, 146.1,
];
let [z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23, z24, z25, z26, z27, z28, z29, z30, z31, z32, z33, z34, z35, z36, z37, z38, z39, z40, z41, z42, z43, z44, z45, z46, z47, z48] = [
0.9287892,
35999.1376958,
35999.4089666,
35998.7287385,
71998.20261,
71998.4403,
36000.35726,
71997.4812,
32964.4678,
-19.4410,
445267.1117,
45036.8840,
3.1008,
22518.4434,
-19.9739,
65928.9345,
9038.0293,
3034.7684,
33718.148,
3034.448,
-2280.773,
29929.992,
31556.493,
149.588,
9037.750,
107997.405,
-4444.176,
151.771,
67555.316,
31556.080,
-4561.540,
107996.706,
1221.655,
62894.167,
31437.369,
14578.298,
-31931.757,
34777.243,
1221.999,
62894.511,
-4442.039,
107997.909,
119.066,
16859.071,
-4.578,
26895.292,
-39.127,
12297.536,
90073.778,
];
// This summation is unrolled for optimization, see #3743
lt.0 = x0 * (y0 + z0 * c).to_radians().sin();
lt.1 = x1 * (y1 + z1 * c).to_radians().sin();
lt.2 = x2 * (y2 + z2 * c).to_radians().sin();
lt.3 = x3 * (y3 + z3 * c).to_radians().sin();
lt.4 = x4 * (y4 + z4 * c).to_radians().sin();
lt.5 = x5 * (y5 + z5 * c).to_radians().sin();
lt.6 = x6 * (y6 + z6 * c).to_radians().sin();
lt.7 = x7 * (y7 + z7 * c).to_radians().sin();
lt.8 = x8 * (y8 + z8 * c).to_radians().sin();
lt.9 = x9 * (y9 + z9 * c).to_radians().sin();
lt.10 = x10 * (y10 + z10 * c).to_radians().sin();
lt.11 = x11 * (y11 + z11 * c).to_radians().sin();
lt.12 = x12 * (y12 + z12 * c).to_radians().sin();
lt.13 = x13 * (y13 + z13 * c).to_radians().sin();
lt.14 = x14 * (y14 + z14 * c).to_radians().sin();
lt.15 = x15 * (y15 + z15 * c).to_radians().sin();
lt.16 = x16 * (y16 + z16 * c).to_radians().sin();
lt.17 = x17 * (y17 + z17 * c).to_radians().sin();
lt.18 = x18 * (y18 + z18 * c).to_radians().sin();
lt.19 = x19 * (y19 + z19 * c).to_radians().sin();
lt.20 = x20 * (y20 + z20 * c).to_radians().sin();
lt.21 = x21 * (y21 + z21 * c).to_radians().sin();
lt.22 = x22 * (y22 + z22 * c).to_radians().sin();
lt.23 = x23 * (y23 + z23 * c).to_radians().sin();
lt.24 = x24 * (y24 + z24 * c).to_radians().sin();
lt.25 = x25 * (y25 + z25 * c).to_radians().sin();
lt.26 = x26 * (y26 + z26 * c).to_radians().sin();
lt.27 = x27 * (y27 + z27 * c).to_radians().sin();
lt.28 = x28 * (y28 + z28 * c).to_radians().sin();
lt.29 = x29 * (y29 + z29 * c).to_radians().sin();
lt.30 = x30 * (y30 + z30 * c).to_radians().sin();
lt.31 = x31 * (y31 + z31 * c).to_radians().sin();
lt.32 = x32 * (y32 + z32 * c).to_radians().sin();
lt.33 = x33 * (y33 + z33 * c).to_radians().sin();
lt.34 = x34 * (y34 + z34 * c).to_radians().sin();
lt.35 = x35 * (y35 + z35 * c).to_radians().sin();
lt.36 = x36 * (y36 + z36 * c).to_radians().sin();
lt.37 = x37 * (y37 + z37 * c).to_radians().sin();
lt.38 = x38 * (y38 + z38 * c).to_radians().sin();
lt.39 = x39 * (y39 + z39 * c).to_radians().sin();
lt.40 = x40 * (y40 + z40 * c).to_radians().sin();
lt.41 = x41 * (y41 + z41 * c).to_radians().sin();
lt.42 = x42 * (y42 + z42 * c).to_radians().sin();
lt.43 = x43 * (y43 + z43 * c).to_radians().sin();
lt.44 = x44 * (y44 + z44 * c).to_radians().sin();
lt.45 = x45 * (y45 + z45 * c).to_radians().sin();
lt.46 = x46 * (y46 + z46 * c).to_radians().sin();
lt.47 = x47 * (y47 + z47 * c).to_radians().sin();
lt.48 = x48 * (y48 + z48 * c).to_radians().sin();
let mut lambda = lt.0
+ lt.1
+ lt.2
+ lt.3
+ lt.4
+ lt.5
+ lt.6
+ lt.7
+ lt.8
+ lt.9
+ lt.10
+ lt.11
+ lt.12
+ lt.13
+ lt.14
+ lt.15
+ lt.16
+ lt.17
+ lt.18
+ lt.19
+ lt.20
+ lt.21
+ lt.22
+ lt.23
+ lt.24
+ lt.25
+ lt.26
+ lt.27
+ lt.28
+ lt.29
+ lt.30
+ lt.31
+ lt.32
+ lt.33
+ lt.34
+ lt.35
+ lt.36
+ lt.37
+ lt.38
+ lt.39
+ lt.40
+ lt.41
+ lt.42
+ lt.43
+ lt.44
+ lt.45
+ lt.46
+ lt.47
+ lt.48;
lambda *= 0.000005729577951308232;
lambda += 282.7771834 + 36000.76953744 * c;
(lambda + Self::aberration(c) + Self::nutation(julian_centuries)).rem_euclid(360.0)
}
/// The best viewing time (UT) in the evening for viewing the young moon from `location` on `date`. This is defined as
/// the time when the sun is 4.5 degrees below the horizon, or `date + 1` if there is no such time.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn simple_best_view(date: RataDie, location: Location) -> Moment {
let dark = Self::dusk(date.to_f64_date(), location, 4.5);
let best = dark.unwrap_or((date + 1).as_moment());
Location::universal_from_standard(best, location)
}
/// Angular separation of the sun and moon at `moment`, for the purposes of determining the likely
/// visibility of the crescent moon.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn arc_of_light(moment: Moment) -> f64 {
let julian_centuries = Self::julian_centuries(moment);
(Self::lunar_latitude(julian_centuries).to_radians().cos()
* Self::lunar_phase(moment, julian_centuries)
.to_radians()
.cos())
.acos()
.to_degrees()
}
/// Criterion for likely visibility of the crescent moon on the eve of `date` at `location`,
/// not intended for high altitudes or polar regions, as defined by S.K. Shaukat.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn shaukat_criterion(date: Moment, location: Location) -> bool {
let tee = Self::simple_best_view((date - 1.0).as_rata_die(), location);
let phase = Self::lunar_phase(tee, Self::julian_centuries(tee));
let h = Self::lunar_altitude(tee, location);
let cap_arcl = Self::arc_of_light(tee);
let new = 0.0;
let first_quarter = 90.0;
let deg_10_6 = 10.6;
let deg_90 = 90.0;
let deg_4_1 = 4.1;
if phase > new
&& phase < first_quarter
&& cap_arcl >= deg_10_6
&& cap_arcl <= deg_90
&& h > deg_4_1
{
return true;
}
false
}
/// Criterion for possible visibility of crescent moon on the eve of `date` at `location`;
/// currently, this calls `shaukat_criterion`, but this can be replaced with another implementation.
pub fn visible_crescent(date: Moment, location: Location) -> bool {
Self::shaukat_criterion(date, location)
}
/// Given an `angle` and a [`Moment`] `moment`, approximate the `Moment` at or before moment
/// at which solar longitude exceeded the given angle.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn estimate_prior_solar_longitude(angle: f64, moment: Moment) -> Moment {
let rate = MEAN_TROPICAL_YEAR / 360.0;
let julian_centuries = Self::julian_centuries(moment);
let tau =
moment - rate * (Self::solar_longitude(julian_centuries) - angle).rem_euclid(360.0);
let delta = (Self::solar_longitude(Self::julian_centuries(tau)) - angle + 180.0)
.rem_euclid(360.0)
- 180.0;
let result_rhs = tau - rate * delta;
if moment < result_rhs {
moment
} else {
result_rhs
}
}
/// Aberration at the time given in Julian centuries.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
fn aberration(c: f64) -> f64 {
// This code differs from the lisp/book code by taking in a julian centuries value instead of
// a Moment; this is because aberration is only ever called in the fn solar_longitude, which
// already converts moment to julian centuries. Thus this function takes the julian centuries
// to avoid unnecessarily calculating the same value twice.
0.0000974 * (177.63 + 35999.01848 * c).to_radians().cos() - 0.005575
}
/// Find the time of the new moon preceding a given Moment (the last new moon before the moment)
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
/// Most of the math performed in the equivalent book/lisp function is done in [`Self::num_of_new_moon_at_or_after`].
pub fn new_moon_before(moment: Moment) -> Moment {
Self::nth_new_moon(Self::num_of_new_moon_at_or_after(moment) - 1)
}
/// Find the time of the new moon following a given Moment (the first new moon before the moment)
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
/// Most of the math performed in the equivalent book/lisp function is done in [`Self::num_of_new_moon_at_or_after`].
pub fn new_moon_at_or_after(moment: Moment) -> Moment {
Self::nth_new_moon(Self::num_of_new_moon_at_or_after(moment))
}
/// Function to find the number of the new moon at or after a given moment;
/// helper function for `new_moon_before` and `new_moon_at_or_after`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
/// This function incorporates code from the book/lisp equivalent functions
/// of [`Self::new_moon_before`] and [`Self::new_moon_at_or_after`].
pub fn num_of_new_moon_at_or_after(moment: Moment) -> i32 {
let t0: Moment = NEW_MOON_ZERO;
let phi = Self::lunar_phase(moment, Self::julian_centuries(moment));
let maybe_n = i64_to_i32(
(div_euclid_f64(moment - t0, MEAN_SYNODIC_MONTH) - phi / 360.0).round() as i64,
);
debug_assert!(maybe_n.is_ok(), "Num of new moon should be in range of i32");
let n = maybe_n.unwrap_or_else(|e| e.saturate());
let mut result = n;
let mut iters = 0;
let max_iters = 31;
while iters < max_iters && Self::nth_new_moon(result) < moment {
iters += 1;
result += 1;
}
result
}
/// Sine of angle between the position of the sun at the given moment in local time and the moment
/// at which the angle of depression of the sun from the given location is equal to `alpha`.
///
/// Based on functions from _Calendrical Calculations_ by Reingold & Dershowitz.
pub fn sine_offset(moment: Moment, location: Location, alpha: f64) -> f64 {
let phi = location.latitude;
let tee_prime = Location::universal_from_local(moment, location);
let delta = Self::declination(
tee_prime,
0.0,
Self::solar_longitude(Self::julian_centuries(tee_prime)),
);
phi.to_radians().tan() * delta.to_radians().tan()
+ alpha.to_radians().sin() / (delta.to_radians().cos() * phi.to_radians().cos())
}
}
#[cfg(test)]
mod tests {
use super::*;
// Constants applied to provide a margin of error when comparing floating-point values in tests.
const TEST_LOWER_BOUND_FACTOR: f64 = 0.9999999;
const TEST_UPPER_BOUND_FACTOR: f64 = 1.0000001;
macro_rules! assert_eq_f64 {
($expected_value:expr, $value:expr, $moment:expr) => {
if $expected_value > 0.0 {
assert!($value > $expected_value * TEST_LOWER_BOUND_FACTOR,
"calculation failed for the test case:\n\n\tMoment: {:?} with expected: {} and calculated: {}\n\n",
$moment, $expected_value, $value);
assert!($value < $expected_value * TEST_UPPER_BOUND_FACTOR,
"calculation failed for the test case:\n\n\tMoment: {:?} with expected: {} and calculated: {}\n\n",
$moment, $expected_value, $value);
} else {
assert!($value > $expected_value * TEST_UPPER_BOUND_FACTOR,
"calculation failed for the test case:\n\n\tMoment: {:?} with expected: {} and calculated: {}\n\n",
$moment, $expected_value, $value);
assert!($value < $expected_value * TEST_LOWER_BOUND_FACTOR,
"calculation failed for the test case:\n\n\tMoment: {:?} with expected: {} and calculated: {}\n\n",
$moment, $expected_value, $value);
}
}
}
#[test]
// Checks that ephemeris_correction gives the same values as the lisp reference code for the given RD test cases
// (See function definition for lisp reference)
fn check_ephemeris_correction() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_ephemeris = [
0.2141698518518519,
0.14363257367091617,
0.11444429141515931,
0.10718320232694657,
0.06949806372337948,
0.05750681225096574,
0.04475812294339828,
0.017397257248984357,
0.012796798891589713,
0.008869421568656596,
0.007262628304956149,
0.005979700330107665,
0.005740181544555194,
0.0038756713829057486,
0.0031575183970409424,
0.0023931271439193596,
0.0017316532690131062,
0.0016698814624679225,
6.150149905066665E-4,
1.7716816592592584E-4,
1.016458530046296E-4,
1.7152348357870364E-4,
1.3696411598154996E-4,
6.153868613872005E-5,
1.4168812498149138E-5,
2.767107192307865E-4,
2.9636802723679223E-4,
3.028239003387824E-4,
3.028239003387824E-4,
6.75088347496296E-4,
7.128242445629627E-4,
9.633446296296293E-4,
0.0029138888888888877,
];
for (rd, expected_ephemeris) in rd_vals.iter().zip(expected_ephemeris.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let ephemeris = Astronomical::ephemeris_correction(moment);
let expected_ephemeris_value = expected_ephemeris;
assert!(ephemeris > expected_ephemeris_value * TEST_LOWER_BOUND_FACTOR, "Ephemeris correction calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_ephemeris_value} and calculated: {ephemeris}\n\n");
assert!(ephemeris < expected_ephemeris_value * TEST_UPPER_BOUND_FACTOR, "Ephemeris correction calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_ephemeris_value} and calculated: {ephemeris}\n\n");
}
}
#[test]
// Checks that solar_longitude gives the same values as the lisp reference code for the given RD test cases
// (See function definition for lisp reference)
fn check_solar_longitude() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_solar_long = [
119.47343190503307,
254.2489611345809,
181.43599673954304,
188.66392267483752,
289.0915666249348,
59.11974154849304,
228.31455470912624,
34.46076992887538,
63.18799596698955,
2.4575913259759545,
350.475934906397,
13.498220866371412,
37.403920329437824,
81.02813003520714,
313.86049865107634,
19.95443016415811,
176.05943166351062,
344.92295174632454,
79.96492181924987,
99.30231774304411,
121.53530416596914,
88.56742889029556,
129.289884101192,
6.146910693067184,
28.25199345351575,
151.7806330331332,
185.94586701843946,
28.55560762159439,
193.3478921554779,
357.15125499424175,
336.1706924761211,
228.18487947607719,
116.43935225951282,
];
for (rd, expected_solar_long) in rd_vals.iter().zip(expected_solar_long.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let solar_long =
Astronomical::solar_longitude(Astronomical::julian_centuries(moment + 0.5));
let expected_solar_long_value = expected_solar_long;
assert!(solar_long > expected_solar_long_value * TEST_LOWER_BOUND_FACTOR, "Solar longitude calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_solar_long_value} and calculated: {solar_long}\n\n");
assert!(solar_long < expected_solar_long_value * TEST_UPPER_BOUND_FACTOR, "Solar longitude calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_solar_long_value} and calculated: {solar_long}\n\n");
}
}
#[test]
// Checks that lunar_latitude gives the same values as the lisp reference code for the given RD test cases
// (See function definition for lisp reference)
fn check_lunar_latitude() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_lunar_lat = [
2.4527590208461576,
-4.90223034654341,
-2.9394693592610484,
5.001904508580623,
-3.208909826304433,
0.894361559890105,
-3.8633355687979827,
-2.5224444701068927,
1.0320696124422062,
3.005689926794408,
1.613842956502888,
4.766740664556875,
4.899202930916035,
4.838473946607273,
2.301475724501815,
-0.8905637199828537,
4.7657836433468495,
-2.737358003826797,
-4.035652608005429,
-3.157214517184652,
-1.8796147336498752,
-3.379519408995276,
-4.398341468078228,
2.099198567294447,
5.268746128633113,
-1.6722994521634027,
4.6820126551666865,
3.705518210116447,
2.493964063649065,
-4.167774638752936,
-2.873757531859998,
-4.667251128743298,
5.138562328560728,
];
for (rd, expected_lunar_lat) in rd_vals.iter().zip(expected_lunar_lat.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let lunar_lat = Astronomical::lunar_latitude(Astronomical::julian_centuries(moment));
let expected_lunar_lat_value = *expected_lunar_lat;
assert_eq_f64!(expected_lunar_lat_value, lunar_lat, moment)
}
}
#[test]
// Checks that lunar_longitude gives the same values as the lisp reference code for the given RD test cases
// (See function definition for lisp reference)
fn check_lunar_longitude() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_lunar_long = [
244.85390528515035,
208.85673853696503,
213.74684265158967,
292.04624333935743,
156.81901407583166,
108.0556329349528,
39.35609790324581,
98.56585102192106,
332.95829627335894,
92.25965175091615,
78.13202909213766,
274.9469953879383,
128.3628442664409,
89.51845094326185,
24.607322526832988,
53.4859568448797,
187.89852001941696,
320.1723620959754,
314.0425667275923,
145.47406514043587,
185.03050779751646,
142.18913274552065,
253.74337531953228,
151.64868501335397,
287.9877436469169,
25.626707154435444,
290.28830064619893,
189.91314245171338,
284.93173002623826,
152.3390442635215,
51.66226507971774,
26.68206023138705,
175.5008226195208,
];
for (rd, expected_lunar_long) in rd_vals.iter().zip(expected_lunar_long.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let lunar_long = Astronomical::lunar_longitude(Astronomical::julian_centuries(moment));
let expected_lunar_long_value = *expected_lunar_long;
assert_eq_f64!(expected_lunar_long_value, lunar_long, moment)
}
}
#[test]
fn check_lunar_altitude() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_altitude_deg: [f64; 33] = [
-13.163184128188277,
-7.281425833096932,
-77.1499009115812,
-30.401178593900795,
71.84857827681589,
-43.79857984753659,
40.65320421851649,
-40.2787255279427,
29.611156512065406,
-19.973178784428228,
-23.740743779700097,
30.956688013173505,
-18.88869091014726,
-32.16116202243495,
-45.68091943596022,
-50.292110029959986,
-54.3453056090807,
-34.56600009726776,
44.13198955291821,
-57.539862986917285,
-62.08243959461623,
-54.07209109276471,
-16.120452006695814,
23.864594681196934,
32.95014668614863,
72.69165128891194,
-29.849481790038908,
31.610644151367637,
-42.21968940776054,
28.6478092363985,
-38.95055354031621,
27.601977078963245,
-54.85468160086816,
];
for (rd, expected_alt) in rd_vals.iter().zip(expected_altitude_deg.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let lunar_alt = Astronomical::lunar_altitude(moment, MECCA);
let expected_alt_value = *expected_alt;
assert_eq_f64!(expected_alt_value, lunar_alt, moment)
}
}
#[test]
fn check_lunar_distance() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_distances = [
387624532.22874624,
393677431.9167689,
402232943.80299366,
392558548.8426357,
366799795.8707107,
365107305.3822873,
401995197.0122423,
404025417.6150537,
377671971.8515077,
403160628.6150732,
375160036.9057225,
369934038.34809774,
402543074.28064245,
374847147.6967837,
403469151.42100906,
386211365.4436033,
385336015.6086019,
400371744.7464432,
395970218.00750065,
383858113.5538787,
389634540.7722341,
390868707.6609328,
368015493.693663,
399800095.77937233,
404273360.3039046,
382777325.7053601,
378047375.3350678,
385774023.9948239,
371763698.0990588,
362461692.8996066,
394214466.3812425,
405787977.04490376,
404202826.42484397,
];
for (rd, expected_distance) in rd_vals.iter().zip(expected_distances.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let distance = Astronomical::lunar_distance(moment);
let expected_distance_val = *expected_distance;
assert_eq_f64!(expected_distance_val, distance, moment)
}
}
#[test]
fn check_lunar_parallax() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_parallax = [
0.9180377088277034,
0.9208275970231943,
0.20205836298974478,
0.8029475944705559,
0.3103764190238057,
0.7224552232666479,
0.6896953754669151,
0.6900664438899986,
0.8412721901635796,
0.8519504336914271,
0.8916972264563727,
0.8471706468502866,
0.8589744596828851,
0.8253387743371953,
0.6328154405175959,
0.60452566100182,
0.5528114670829496,
0.7516491660573382,
0.6624140811593374,
0.5109678575066725,
0.4391324179474404,
0.5486027633624313,
0.9540023420545446,
0.835939538308717,
0.7585615249134946,
0.284040095327141,
0.8384425157447107,
0.8067682261382678,
0.7279971552035109,
0.8848306274359499,
0.720943806048675,
0.7980998225232075,
0.5204553405568378,
];
for (rd, parallax) in rd_vals.iter().zip(expected_parallax.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let lunar_altitude_val = Astronomical::lunar_altitude(moment, MECCA);
let parallax_val = Astronomical::lunar_parallax(lunar_altitude_val, moment);
let expected_parallax_val = *parallax;
assert_eq_f64!(expected_parallax_val, parallax_val, moment);
}
}
#[test]
fn check_moonset() {
let rd_vals = [
-214193.0, -61387.0, 25469.0, 49217.0, 171307.0, 210155.0, 253427.0, 369740.0,
400085.0, 434355.0, 452605.0, 470160.0, 473837.0, 507850.0, 524156.0, 544676.0,
567118.0, 569477.0, 601716.0, 613424.0, 626596.0, 645554.0, 664224.0, 671401.0,
694799.0, 704424.0, 708842.0, 709409.0, 709580.0, 727274.0, 728714.0, 744313.0,
764652.0,
];
let expected_values = [
-214192.91577491348,
-61386.372392431986,
25469.842646633304,
49217.03030766261,
171307.41988615665,
210155.96578468647,
253427.2528524993,
0.0,
400085.5281194299,
434355.0524936674,
452605.0379962325,
470160.4931771927,
473837.06032208423,
507850.8560177605,
0.0,
544676.908706548,
567118.8180096536,
569477.7141856537,
601716.4168627897,
613424.9325031227,
626596.9563783304,
645554.9526297608,
664224.070965863,
671401.2004198332,
694799.4892001058,
704424.4299627786,
708842.0314145002,
709409.2245215117,
0.0,
727274.2148254914,
0.0,
744313.2118589033,
764652.9631741203,
];
for (rd, expected_val) in rd_vals.iter().zip(expected_values.iter()) {
let moment: Moment = Moment::new(*rd);
let moonset_val = Astronomical::moonset(moment, MECCA);
let expected_moonset_val = *expected_val;
#[allow(clippy::unnecessary_unwrap)]
if moonset_val.is_none() {
assert_eq!(expected_moonset_val, 0.0);
} else {
assert_eq_f64!(expected_moonset_val, moonset_val.unwrap().inner(), moment);
}
}
}
#[test]
fn check_sunset() {
let rd_vals = [
-214193.0, -61387.0, 25469.0, 49217.0, 171307.0, 210155.0, 253427.0, 369740.0,
400085.0, 434355.0, 452605.0, 470160.0, 473837.0, 507850.0, 524156.0, 544676.0,
567118.0, 569477.0, 601716.0, 613424.0, 626596.0, 645554.0, 664224.0, 671401.0,
694799.0, 704424.0, 708842.0, 709409.0, 709580.0, 727274.0, 728714.0, 744313.0,
764652.0,
];
let expected_values = [
-214192.2194436165,
-61386.30267524347,
25469.734889564967,
49217.72851448112,
171307.70878832813,
210155.77420199668,
253427.70087725233,
369740.7627365203,
400085.77677703864,
434355.74808897293,
452605.7425360138,
470160.75310216413,
473837.76440251875,
507850.7840412511,
524156.7225351998,
544676.7561346035,
567118.7396585084,
569477.7396636717,
601716.784057734,
613424.7870863203,
626596.781969136,
645554.7863087669,
664224.778132625,
671401.7496876866,
694799.7602310368,
704424.7619096127,
708842.730647343,
709409.7603906896,
709580.7240122546,
727274.745361792,
728714.734750938,
744313.699821144,
764652.7844809336,
];
let jerusalem = Location {
latitude: 31.78,
longitude: 35.24,
elevation: 740.0,
zone: (1_f64 / 12_f64),
};
for (rd, expected_sunset_value) in rd_vals.iter().zip(expected_values.iter()) {
let moment = Moment::new(*rd);
let sunset_value = Astronomical::sunset(moment, jerusalem).unwrap();
let expected_sunset_val = *expected_sunset_value;
assert_eq_f64!(expected_sunset_val, sunset_value.inner(), moment)
}
}
#[test]
// Checks that next_new_moon gives the same values as the lisp reference code for the given RD test cases
// (See function definition for lisp reference)
fn check_next_new_moon() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_next_new_moon = [
-214174.60582868298,
-61382.99532831192,
25495.80977675628,
49238.50244808781,
171318.43531326813,
210180.69184966758,
253442.85936730343,
369763.74641362444,
400091.5783431683,
434376.5781067696,
452627.1919724953,
470167.57836052414,
473858.8532764285,
507878.6668429224,
524179.2470620894,
544702.7538732041,
567146.5131819838,
569479.2032589674,
601727.0335578924,
613449.7621296605,
626620.3698017383,
645579.0767485882,
664242.8867184789,
671418.970538101,
694807.5633711396,
704433.4911827276,
708863.5970001582,
709424.4049294397,
709602.0826867367,
727291.2094001573,
728737.4476913146,
744329.5739998783,
764676.1912733881,
];
for (rd, expected_next_new_moon) in rd_vals.iter().zip(expected_next_new_moon.iter()) {
let moment: Moment = Moment::new(*rd as f64);
let next_new_moon = Astronomical::new_moon_at_or_after(moment);
let expected_next_new_moon_moment = Moment::new(*expected_next_new_moon);
if *expected_next_new_moon > 0.0 {
assert!(expected_next_new_moon_moment.inner() > next_new_moon.inner() * TEST_LOWER_BOUND_FACTOR, "New moon calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_next_new_moon_moment:?} and calculated: {next_new_moon:?}\n\n");
assert!(expected_next_new_moon_moment.inner() < next_new_moon.inner() * TEST_UPPER_BOUND_FACTOR, "New moon calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_next_new_moon_moment:?} and calculated: {next_new_moon:?}\n\n");
} else {
assert!(expected_next_new_moon_moment.inner() > next_new_moon.inner() * TEST_UPPER_BOUND_FACTOR, "New moon calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_next_new_moon_moment:?} and calculated: {next_new_moon:?}\n\n");
assert!(expected_next_new_moon_moment.inner() < next_new_moon.inner() * TEST_LOWER_BOUND_FACTOR, "New moon calculation failed for the test case:\n\n\tMoment: {moment:?} with expected: {expected_next_new_moon_moment:?} and calculated: {next_new_moon:?}\n\n");
}
}
}
#[test]
fn check_astronomy_0th_new_moon() {
// Checks the accuracy of the 0th new moon to be on January 11th
let zeroth_new_moon = Astronomical::nth_new_moon(0);
assert_eq!(
zeroth_new_moon.inner() as i32,
11,
"0th new moon check failed with nth_new_moon(0) = {zeroth_new_moon:?}"
);
}
#[test]
fn check_num_of_new_moon_0() {
// Tests the function num_of_new_moon_at_or_after() returns 0 for moment 0
assert_eq!(
Astronomical::num_of_new_moon_at_or_after(Moment::new(0.0)),
0
);
}
#[test]
fn check_new_moon_directionality() {
// Checks that new_moon_before is less than new_moon_at_or_after for a large number of Moments
let mut moment: Moment = Moment::new(-15500.0);
let max_moment = Moment::new(15501.0);
let mut iters: i32 = 0;
let max_iters = 10000;
while iters < max_iters && moment < max_moment {
let before = Astronomical::new_moon_before(moment);
let at_or_after = Astronomical::new_moon_at_or_after(moment);
assert!(before < at_or_after, "Directionality of fns new_moon_before and new_moon_at_or_after failed for Moment: {moment:?}");
iters += 1;
moment += 31.0;
}
assert!(
iters > 500,
"Testing failed: less than the expected number of testing iterations"
);
assert!(
iters < max_iters,
"Testing failed: more than the expected number of testing iterations"
);
}
#[test]
fn check_location_valid_case() {
// Checks that location construction and functions work for various valid lats and longs
let mut long = -180.0;
let mut lat = -90.0;
let zone = 0.0;
while long <= 180.0 {
while lat <= 90.0 {
let location: Location = Location::try_new(lat, long, 1000.0, zone).unwrap();
assert_eq!(lat, location.latitude());
assert_eq!(long, location.longitude());
lat += 1.0;
}
long += 1.0;
}
}
#[test]
fn check_location_errors() {
let lat_too_small = Location::try_new(-90.1, 15.0, 1000.0, 0.0).unwrap_err();
assert_eq!(lat_too_small, LocationOutOfBoundsError::Latitude(-90.1));
let lat_too_large = Location::try_new(90.1, -15.0, 1000.0, 0.0).unwrap_err();
assert_eq!(lat_too_large, LocationOutOfBoundsError::Latitude(90.1));
let long_too_small = Location::try_new(15.0, 180.1, 1000.0, 0.0).unwrap_err();
assert_eq!(long_too_small, LocationOutOfBoundsError::Longitude(180.1));
let long_too_large = Location::try_new(-15.0, -180.1, 1000.0, 0.0).unwrap_err();
assert_eq!(long_too_large, LocationOutOfBoundsError::Longitude(-180.1));
}
#[test]
fn check_obliquity() {
let rd_vals = [
-214193, -61387, 25469, 49217, 171307, 210155, 253427, 369740, 400085, 434355, 452605,
470160, 473837, 507850, 524156, 544676, 567118, 569477, 601716, 613424, 626596, 645554,
664224, 671401, 694799, 704424, 708842, 709409, 709580, 727274, 728714, 744313, 764652,
];
let expected_obliquity_val = [
23.766686762858193,
23.715893268155952,
23.68649428364133,
23.678396646319815,
23.636406172247575,
23.622930685681105,
23.607863050353394,
23.567099369895143,
23.556410268115442,
23.544315732982724,
23.5378658942414,
23.531656189162007,
23.53035487913322,
23.518307553466993,
23.512526100422757,
23.50524564635773,
23.49727762748816,
23.49643975090472,
23.48498365949255,
23.48082101433542,
23.476136639530452,
23.469392588649566,
23.46274905945532,
23.460194773340504,
23.451866181318085,
23.44843969966849,
23.44686683973517,
23.446664978744177,
23.44660409993624,
23.440304562352033,
23.43979187336218,
23.434238093381342,
23.426996977623215,
];
for (rd, expected_obl_val) in rd_vals.iter().zip(expected_obliquity_val.iter()) {
let moment = Moment::new(*rd as f64);
let obl_val = Astronomical::obliquity(moment);
let expected_val = *expected_obl_val;
assert_eq_f64!(expected_val, obl_val, moment)
}
}
}