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/* Astronomy Engine for C/C++. https://github.com/cosinekitty/astronomy MIT License Copyright (c) 2019-2020 Don Cross <cosinekitty@gmail.com> Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #include <stdio.h> #include <stdlib.h> #include <string.h> #include <time.h> #include <math.h> #include "astronomy.h" #ifdef __cplusplus extern "C" { #endif /** @cond DOXYGEN_SKIP */ #define PI 3.14159265358979323846 typedef struct { double x; double y; double z; } terse_vector_t; static const terse_vector_t VecZero; static terse_vector_t VecAdd(terse_vector_t a, terse_vector_t b) { terse_vector_t c; c.x = a.x + b.x; c.y = a.y + b.y; c.z = a.z + b.z; return c; } static terse_vector_t VecSub(terse_vector_t a, terse_vector_t b) { terse_vector_t c; c.x = a.x - b.x; c.y = a.y - b.y; c.z = a.z - b.z; return c; } static void VecIncr(terse_vector_t *target, terse_vector_t source) { target->x += source.x; target->y += source.y; target->z += source.z; } static void VecDecr(terse_vector_t *target, terse_vector_t source) { target->x -= source.x; target->y -= source.y; target->z -= source.z; } static terse_vector_t VecMul(double s, terse_vector_t v) { terse_vector_t p; p.x = s * v.x; p.y = s * v.y; p.z = s * v.z; return p; } static void VecScale(terse_vector_t *target, double scalar) { target->x *= scalar; target->y *= scalar; target->z *= scalar; } static terse_vector_t VecRamp(terse_vector_t a, terse_vector_t b, double ramp) { terse_vector_t c; c.x = (1-ramp)*a.x + ramp*b.x; c.y = (1-ramp)*a.y + ramp*b.y; c.z = (1-ramp)*a.z + ramp*b.z; return c; } static terse_vector_t VecMean(terse_vector_t a, terse_vector_t b) { terse_vector_t c; c.x = (a.x + b.x) / 2; c.y = (a.y + b.y) / 2; c.z = (a.z + b.z) / 2; return c; } static astro_vector_t PublicVec(astro_time_t time, terse_vector_t terse) { astro_vector_t vector; vector.status = ASTRO_SUCCESS; vector.t = time; vector.x = terse.x; vector.y = terse.y; vector.z = terse.z; return vector; } typedef struct { double tt; /* Terrestrial Time in J2000 days */ terse_vector_t r; /* position [au] */ terse_vector_t v; /* velocity [au/day] */ } body_state_t; /** @endcond */ static const double DAYS_PER_TROPICAL_YEAR = 365.24217; static const double DEG2RAD = 0.017453292519943296; static const double RAD2DEG = 57.295779513082321; static const double ASEC360 = 1296000.0; static const double ASEC2RAD = 4.848136811095359935899141e-6; static const double PI2 = 2.0 * PI; static const double ARC = 3600.0 * 180.0 / PI; /* arcseconds per radian */ static const double C_AUDAY = 173.1446326846693; /* speed of light in AU/day */ static const double KM_PER_AU = 1.4959787069098932e+8; static const double SECONDS_PER_DAY = 24.0 * 3600.0; static const double SOLAR_DAYS_PER_SIDEREAL_DAY = 0.9972695717592592; static const double MEAN_SYNODIC_MONTH = 29.530588; /* average number of days for Moon to return to the same phase */ static const double EARTH_ORBITAL_PERIOD = 365.256; static const double NEPTUNE_ORBITAL_PERIOD = 60189.0; static const double REFRACTION_NEAR_HORIZON = 34.0 / 60.0; /* degrees of refractive "lift" seen for objects near horizon */ static const double SUN_RADIUS_KM = 695700.0; #define SUN_RADIUS_AU (SUN_RADIUS_KM / KM_PER_AU) #define EARTH_FLATTENING 0.996647180302104 #define EARTH_EQUATORIAL_RADIUS_KM 6378.1366 #define EARTH_EQUATORIAL_RADIUS_AU (EARTH_EQUATORIAL_RADIUS_KM / KM_PER_AU) #define EARTH_MEAN_RADIUS_KM 6371.0 /* mean radius of the Earth's geoid, without atmosphere */ #define EARTH_ATMOSPHERE_KM 88.0 /* effective atmosphere thickness for lunar eclipses */ #define EARTH_ECLIPSE_RADIUS_KM (EARTH_MEAN_RADIUS_KM + EARTH_ATMOSPHERE_KM) /* Note: if we ever need Earth's polar radius, it is (EARTH_FLATTENING * EARTH_EQUATORIAL_RADIUS_KM) */ #define MOON_EQUATORIAL_RADIUS_KM 1738.1 #define MOON_MEAN_RADIUS_KM 1737.4 #define MOON_POLAR_RADIUS_KM 1736.0 #define MOON_EQUATORIAL_RADIUS_AU (MOON_EQUATORIAL_RADIUS_KM / KM_PER_AU) static const double ASEC180 = 180.0 * 60.0 * 60.0; /* arcseconds per 180 degrees (or pi radians) */ static const double EARTH_MOON_MASS_RATIO = 81.30056; /* Masses of the Sun and outer planets, used for: (1) Calculating the Solar System Barycenter (2) Integrating the movement of Pluto https://web.archive.org/web/20120220062549/http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdf Page 10 in the above document describes the constants used in the DE405 ephemeris. The following are G*M values (gravity constant * mass) in [au^3 / day^2]. This side-steps issues of not knowing the exact values of G and masses M[i]; the products GM[i] are known extremely accurately. */ static const double SUN_GM = 0.2959122082855911e-03; static const double JUPITER_GM = 0.2825345909524226e-06; static const double SATURN_GM = 0.8459715185680659e-07; static const double URANUS_GM = 0.1292024916781969e-07; static const double NEPTUNE_GM = 0.1524358900784276e-07; /** @cond DOXYGEN_SKIP */ #define ARRAYSIZE(x) (sizeof(x) / sizeof(x[0])) #define AU_PER_PARSEC (ASEC180 / PI) /* exact definition of how many AU = one parsec */ #define Y2000_IN_MJD (T0 - MJD_BASIS) /** @endcond */ static astro_ecliptic_t RotateEquatorialToEcliptic(const double pos[3], double obliq_radians); static int QuadInterp( double tm, double dt, double fa, double fm, double fb, double *x, double *t, double *df_dt); static double LongitudeOffset(double diff) { double offset = diff; while (offset <= -180.0) offset += 360.0; while (offset > 180.0) offset -= 360.0; return offset; } static double NormalizeLongitude(double lon) { while (lon < 0.0) lon += 360.0; while (lon >= 360.0) lon -= 360.0; return lon; } /** * @brief Calculates the length of the given vector. * * Calculates the non-negative length of the given vector. * The length is expressed in the same units as the vector's components, * usually astronomical units (AU). * * @param vector The vector whose length is to be calculated. * @return The length of the vector. */ double Astronomy_VectorLength(astro_vector_t vector) { return sqrt(vector.x*vector.x + vector.y*vector.y + vector.z*vector.z); } /** * @brief Finds the name of a celestial body. * @param body The celestial body whose name is to be found. * @return The English-language name of the celestial body, or "" if the body is not valid. */ const char *Astronomy_BodyName(astro_body_t body) { switch (body) { case BODY_MERCURY: return "Mercury"; case BODY_VENUS: return "Venus"; case BODY_EARTH: return "Earth"; case B