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// Copyright 2022 Benjamin Barenblat
//
// Licensed under the Apache License, Version 2.0 (the "License"); you may not
// use this file except in compliance with the License. You may obtain a copy of
// the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
// License for the specific language governing permissions and limitations under
// the License.
#include "src/astro.h"
#include <math.h>
#include <chrono>
#include <utility>
#include "third_party/date/include/date/tz.h"
namespace glplanet {
namespace {
// The J2000 epoch--January 1, 2000, at 12:00:00 Terrestrial Time. This is
// January 1, 2000, at 11:59:27.816 TAI (because TAI lags TT(TAI) by 32.184 s),
// or January 1, 2000, at 11:58:55.816 UTC (because TAI-UTC was 32 seconds on
// January 1, 2000).
constexpr auto kJ2000Epoch =
std::chrono::time_point<date::tai_clock, std::chrono::milliseconds>() +
std::chrono::days(42 * 365 + 10 /* leap days */) + std::chrono::hours(11) +
std::chrono::minutes(59) + std::chrono::milliseconds(27'816);
constexpr double kMillisecondsPerEphemerisCentury =
uint64_t{36'525} * 24 * 60 * 60 * 1'000;
constexpr double kRadiansPerDegree = M_PI / 180.0;
struct CommonValues {
// The time, measured in ephemeris centuries from the J2000 epoch.
double t;
double sun_mean_longitude_degrees;
double omega;
double ecliptic_obliquity;
};
CommonValues ComputeCommonValues(
std::chrono::time_point<date::tai_clock, std::chrono::milliseconds>
now) noexcept {
const double t =
static_cast<double>(std::chrono::duration_cast<std::chrono::milliseconds>(
now - kJ2000Epoch)
.count()) /
kMillisecondsPerEphemerisCentury;
// Digit groupings in these magic constants match those in Meeus for easy
// auditing.
const double mean_longitude_degrees =
(0.000'3032 * t + 36'000.769'83) * t + 280.46646;
const double omega =
(((2.222222222222222e-6 * t + 0.002'0708) * t + -1934.136'261) * t +
125.04452) *
kRadiansPerDegree;
// From Meeus (22.2) and (25.8).
const double ecliptic_obliquity_degrees =
((5.036111111111111e-7 * t + -1.6388888888888888e-7) * t +
-1.3004166666666667e-2) *
t +
0.00256 * cos(omega) + // (25.8)
23.43929111111111;
return {
.t = t,
.sun_mean_longitude_degrees = mean_longitude_degrees,
.omega = omega,
.ecliptic_obliquity = ecliptic_obliquity_degrees * kRadiansPerDegree,
};
}
std::pair<double, double> SunEquatorialPositionWithCommonValues(
const CommonValues& common) noexcept {
// Reference: Jean Meeus, _Astronomical Algorithms_, 2nd edition,
// Willmann-Bell, 1998 (ISBN 0-943396-61-1), chapter 25.
const auto& [t, mean_longitude_degrees, omega, ecliptic_obliquity] = common;
// Again, digit groupings match Meeus.
const double mean_anomaly_degrees =
(0.000'1537 * t + 35'999.050'29) * t + 357.52911;
const double equation_of_center_degrees =
0.000'289 * sin(mean_anomaly_degrees * (M_PI / 60.0)) +
(-0.000'101 * t + 0.019'993) * sin(mean_anomaly_degrees * (M_PI / 90.0)) +
((-0.000'014 * t - 0.004'817) * t + 1.914'602) *
sin(mean_anomaly_degrees * (M_PI / 180.0));
const double apparent_longitude_degrees = -0.00478 * sin(omega) - 0.00569 +
equation_of_center_degrees +
mean_longitude_degrees;
const double apparent_longitude =
apparent_longitude_degrees * kRadiansPerDegree;
// Per Meeus, latitude never exceeds 1.2 arcseconds = 0.0003 degrees,
// within margin of error. We therefore have:
const double right_ascension_radians =
atan2(cos(ecliptic_obliquity) * sin(apparent_longitude),
cos(apparent_longitude));
const double declination_radians =
asin(sin(ecliptic_obliquity) * sin(apparent_longitude));
return {right_ascension_radians, declination_radians};
}
double ApparentSiderealTimeAtGreenwichWithCommonValues(
const CommonValues& common) noexcept {
// Reference: Meeus, page 88.
const auto& [t, mean_longitude_degrees, omega, ecliptic_obliquity] = common;
const double moon_mean_longitude_degrees = 481'267.8831 * t + 218.3165;
const double longitude_nutation_degrees =
5.833333333333333e-5 * sin(2 * omega) +
-6.38888888888888e-5 * sin(moon_mean_longitude_degrees * M_PI / 90.0) +
-3.6666666666666666e-4 * sin(mean_longitude_degrees * M_PI / 90.0) +
-4.7777777777777777e-3 * sin(omega);
double greenwich_apparent_sidereal_time_degrees =
((-2.5833118057349522e-8 * t + 0.000'387'933) * t + 13185000.770053742) *
t +
longitude_nutation_degrees * cos(ecliptic_obliquity) +
280.460'618'37; // (12.4)
greenwich_apparent_sidereal_time_degrees =
fmod(greenwich_apparent_sidereal_time_degrees, 360.0);
if (greenwich_apparent_sidereal_time_degrees < -180.0) {
greenwich_apparent_sidereal_time_degrees += 360.0;
}
return greenwich_apparent_sidereal_time_degrees * kRadiansPerDegree;
}
} // namespace
std::pair<double, double> SunEquatorialPosition(
const std::chrono::time_point<date::tai_clock, std::chrono::milliseconds>
now) noexcept {
return SunEquatorialPositionWithCommonValues(ComputeCommonValues(now));
}
double ApparentSiderealTimeAtGreenwich(
std::chrono::time_point<date::tai_clock, std::chrono::milliseconds>
now) noexcept {
return ApparentSiderealTimeAtGreenwichWithCommonValues(
ComputeCommonValues(now));
}
std::pair<double, double> HighNoonLocation(
std::chrono::time_point<date::tai_clock, std::chrono::milliseconds>
now) noexcept {
CommonValues common = ComputeCommonValues(now);
const auto& [right_ascension, declination] =
SunEquatorialPositionWithCommonValues(common);
double greenwich_apparent_sidereal_time =
ApparentSiderealTimeAtGreenwichWithCommonValues(common);
// The declination is the latitude.
const double latitude = declination;
// Computing the longitude is only a bit more complex. We're sitting right
// under the sun, so our local hour angle is 0, giving
//
// east longitude = right ascension - apparent sidereal time at Greenwich
//
// (cf. Meeus, page 92).
const double longitude = right_ascension - greenwich_apparent_sidereal_time;
return {longitude, latitude};
}
} // namespace glplanet
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