305 lines
11 KiB
C
305 lines
11 KiB
C
// Compute times of moonrise and moonset at a specified latitude and longitude.
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//
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// This software minimizes computational work by performing the full calculation
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// of the lunar position three times, at the beginning, middle, and end of the
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// period of interest. Three point interpolation is used to predict the
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// position for each hour, and the arithmetic mean is used to predict the
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// half-hour positions.
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//
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// The full computational burden is negligible on modern computers, but the
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// algorithm is effective and still useful for small embedded systems.
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//
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// This software was originally adapted to javascript by Stephen R. Schmitt
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// from a BASIC program from the 'Astronomical Computing' column of Sky &
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// Telescope, April 1989, page 78.
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//
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// Subsequently adapted from Stephen R. Schmitt's javascript to c++ for the
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// Arduino by Cyrus Rahman.
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//
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// Subsequently adapted from Cyrus Rahman's Arduino C++ to C for the Sensor
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// Watch by hueso, this work is subject to Stephen Schmitt's copyright:
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//
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// Copyright 2007 Stephen R. Schmitt
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// Subsequent work Copyright 2020 Cyrus Rahman
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// You may use or modify this source code in any way you find useful, provided
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// that you agree that the author(s) have no warranty, obligations or liability.
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// You must determine the suitability of this source code for your use.
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//
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// Redistributions of this source code must retain this copyright notice.
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#include "moonrise.h"
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#include <math.h>
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#define K1 15 * (M_PI / 180) * 1.0027379
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// Determine the nearest moon rise or set event previous, and the nearest
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// moon rise or set event subsequent, to the specified time in seconds since the
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// Unix epoch (January 1, 1970) and at the specified latitude and longitude in
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// degrees.
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//
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// We look for events from MR_WINDOW/2 hours in the past to MR_WINDOW/2 hours
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// in the future.
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MoonRise MoonRise_calculate(double latitude, double longitude, uint32_t t) {
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MoonRise self = {};
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skyCoordinates moonPosition[3];
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double offsetDays;
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self.queryTime = t;
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offsetDays = julianDate(t) - 2451545L; // Days since Jan 1, 2000, 1200UTC.
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// Begin testing (MR_WINDOW / 2) hours before requested time.
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// offsetDays -= (double)MR_WINDOW / (2 * 24) ;
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// Calculate coordinates at start, middle, and end of search period.
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for (int i = 0; i < 3; i++) {
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moonPosition[i] = moon(offsetDays + i * (double)MR_WINDOW / (2 * 24));
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}
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// If the RA wraps around during this period, unwrap it to keep the
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// sequence smooth for interpolation.
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if (moonPosition[1].RA <= moonPosition[0].RA)
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moonPosition[1].RA += 2 * M_PI;
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if (moonPosition[2].RA <= moonPosition[1].RA)
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moonPosition[2].RA += 2 * M_PI;
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// Initialize interpolation array.
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skyCoordinates mpWindow[3];
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mpWindow[0].RA = moonPosition[0].RA;
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mpWindow[0].declination = moonPosition[0].declination;
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mpWindow[0].distance = moonPosition[0].distance;
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for (int k = 0; k < MR_WINDOW; k++) { // Check each interval of search period
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float ph = (float)(k + 1) / MR_WINDOW;
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mpWindow[2].RA = interpolate(moonPosition[0].RA, moonPosition[1].RA,
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moonPosition[2].RA, ph);
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mpWindow[2].declination =
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interpolate(moonPosition[0].declination, moonPosition[1].declination,
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moonPosition[2].declination, ph);
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mpWindow[2].distance = moonPosition[2].distance;
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// Look for moonrise/set events during this interval.
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{
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double ha[3], VHz[3];
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double lSideTime;
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// Get (local_sidereal_time - MR_WINDOW / 2) hours in radians.
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lSideTime = localSiderealTime(offsetDays, longitude) * 2 * M_PI / 360;
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// Calculate Hour Angle.
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ha[0] = lSideTime - mpWindow[0].RA + k * K1;
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ha[2] = lSideTime - mpWindow[2].RA + k * K1 + K1;
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// Hour Angle and declination at half hour.
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ha[1] = (ha[2] + ha[0]) / 2;
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mpWindow[1].declination =
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(mpWindow[2].declination + mpWindow[0].declination) / 2;
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double s = sin(M_PI / 180 * latitude);
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double c = cos(M_PI / 180 * latitude);
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// refraction + semidiameter at horizon + distance correction
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double z = cos(M_PI / 180 * (90.567 - 41.685 / mpWindow[0].distance));
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VHz[0] = s * sin(mpWindow[0].declination) +
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c * cos(mpWindow[0].declination) * cos(ha[0]) - z;
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VHz[2] = s * sin(mpWindow[2].declination) +
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c * cos(mpWindow[2].declination) * cos(ha[2]) - z;
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if (signbit(VHz[0]) == signbit(VHz[2]))
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goto noevent; // No event this hour.
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VHz[1] = s * sin(mpWindow[1].declination) +
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c * cos(mpWindow[1].declination) * cos(ha[1]) - z;
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double a, b, d, e, time;
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a = 2 * VHz[2] - 4 * VHz[1] + 2 * VHz[0];
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b = 4 * VHz[1] - 3 * VHz[0] - VHz[2];
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d = b * b - 4 * a * VHz[0];
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if (d < 0)
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goto noevent; // No event this hour.
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d = sqrt(d);
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e = (-b + d) / (2 * a);
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if ((e < 0) || (e > 1))
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e = (-b - d) / (2 * a);
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time = k + e + 1 / 120; // Time since k=0 of event (in hours).
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// The time we started searching + the time from the start of the search
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// to the event is the time of the event.
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uint32_t eventTime;
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eventTime = self.queryTime + (time) * 60 * 60;
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double hz, nz, dz, az;
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hz = ha[0] + e * (ha[2] - ha[0]); // Azimuth of the moon at the event.
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nz = -cos(mpWindow[1].declination) * sin(hz);
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dz = c * sin(mpWindow[1].declination) -
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s * cos(mpWindow[1].declination) * cos(hz);
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az = atan2(nz, dz) / (M_PI / 180);
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if (az < 0)
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az += 360;
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// If there is no previously recorded event of this type, save this event.
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//
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// If this event is previous to queryTime, and is the nearest event to
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// queryTime of events of its type previous to queryType, save this event,
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// replacing the previously recorded event of its type. Events subsequent
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// to queryTime are treated similarly, although since events are tested in
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// chronological order no replacements will occur as successive events
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// will be further from queryTime.
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//
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// If this event is subsequent to queryTime and there is an event of its
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// type previous to queryTime, then there is an event of the other type
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// between the two events of this event's type. If the event of the other
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// type is previous to queryTime, then it is the nearest event to
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// queryTime that is previous to queryTime. In this case save the current
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// event, replacing the previously recorded event of its type. Otherwise
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// discard the current event.
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//
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if ((VHz[0] < 0) && (VHz[2] > 0)) {
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if (!self.hasRise ||
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((self.riseTime < self.queryTime) == (eventTime < self.queryTime) &&
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(self.riseTime - self.queryTime) > (eventTime - self.queryTime)) ||
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((self.riseTime < self.queryTime) != (eventTime < self.queryTime) &&
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(self.hasSet && (self.riseTime < self.queryTime) ==
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(self.setTime < self.queryTime)))) {
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self.riseTime = eventTime;
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self.riseAz = az;
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self.hasRise = true;
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}
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}
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if ((VHz[0] > 0) && (VHz[2] < 0)) {
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if (!self.hasSet ||
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((self.setTime < self.queryTime) == (eventTime < self.queryTime) &&
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(self.setTime - self.queryTime) > (eventTime - self.queryTime)) ||
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((self.setTime < self.queryTime) != (eventTime < self.queryTime) &&
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(self.hasRise && (self.setTime < self.queryTime) ==
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(self.riseTime < self.queryTime)))) {
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self.setTime = eventTime;
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self.setAz = az;
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self.hasSet = true;
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}
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}
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noevent:
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// There are obscure cases in the polar regions that require extra logic.
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if (!self.hasRise && !self.hasSet)
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self.isVisible = !signbit(VHz[2]);
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else if (self.hasRise && !self.hasSet)
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self.isVisible = (self.queryTime > self.riseTime);
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else if (!self.hasRise && self.hasSet)
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self.isVisible = (self.queryTime < self.setTime);
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else
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self.isVisible =
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((self.riseTime < self.setTime && self.riseTime < self.queryTime &&
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self.setTime > self.queryTime) ||
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(self.riseTime > self.setTime && (self.riseTime < self.queryTime ||
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self.setTime > self.queryTime)));
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}
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if (self.hasSet && self.hasRise)
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break;
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mpWindow[0] = mpWindow[2]; // Advance to next interval.
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}
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return self;
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}
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// Moon position using fundamental arguments
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// (Van Flandern & Pulkkinen, 1979)
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skyCoordinates moon(double dayOffset) {
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double l = 0.606434 + 0.03660110129 * dayOffset;
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double m = 0.374897 + 0.03629164709 * dayOffset;
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double f = 0.259091 + 0.03674819520 * dayOffset;
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double d = 0.827362 + 0.03386319198 * dayOffset;
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double n = 0.347343 - 0.00014709391 * dayOffset;
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double g = 0.993126 + 0.00273777850 * dayOffset;
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l = 2 * M_PI * (l - floor(l));
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m = 2 * M_PI * (m - floor(m));
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f = 2 * M_PI * (f - floor(f));
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d = 2 * M_PI * (d - floor(d));
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n = 2 * M_PI * (n - floor(n));
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g = 2 * M_PI * (g - floor(g));
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double v, u, w;
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v = 0.39558 * sin(f + n)
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+ 0.08200 * sin(f)
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+ 0.03257 * sin(m - f - n)
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+ 0.01092 * sin(m + f + n)
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+ 0.00666 * sin(m - f)
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- 0.00644 * sin(m + f - 2*d + n)
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- 0.00331 * sin(f - 2*d + n)
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- 0.00304 * sin(f - 2*d)
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- 0.00240 * sin(m - f - 2*d - n)
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+ 0.00226 * sin(m + f)
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- 0.00108 * sin(m + f - 2*d)
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- 0.00079 * sin(f - n)
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+ 0.00078 * sin(f + 2*d + n);
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u = 1
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- 0.10828 * cos(m)
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- 0.01880 * cos(m - 2*d)
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- 0.01479 * cos(2*d)
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+ 0.00181 * cos(2*m - 2*d)
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- 0.00147 * cos(2*m)
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- 0.00105 * cos(2*d - g)
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- 0.00075 * cos(m - 2*d + g);
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w = 0.10478 * sin(m)
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- 0.04105 * sin(2*f + 2*n)
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- 0.02130 * sin(m - 2*d)
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- 0.01779 * sin(2*f + n)
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+ 0.01774 * sin(n)
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+ 0.00987 * sin(2*d)
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- 0.00338 * sin(m - 2*f - 2*n)
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- 0.00309 * sin(g)
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- 0.00190 * sin(2*f)
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- 0.00144 * sin(m + n)
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- 0.00144 * sin(m - 2*f - n)
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- 0.00113 * sin(m + 2*f + 2*n)
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- 0.00094 * sin(m - 2*d + g)
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- 0.00092 * sin(2*m - 2*d);
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double s;
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skyCoordinates sc;
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s = w / sqrt(u - v*v);
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sc.RA = l + atan(s / sqrt(1 - s*s)); // Right ascension
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s = v / sqrt(u);
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sc.declination = atan(s / sqrt(1 - s*s)); // Declination
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sc.distance = 60.40974 * sqrt(u); // Distance
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return(sc);
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}
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// 3-point interpolation
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double interpolate(double f0, double f1, double f2, double p) {
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double a = f1 - f0;
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double b = f2 - f1 - a;
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return(f0 + p * (2*a + b * (2*p - 1)));
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}
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// Determine Julian date from Unix time.
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// Provides marginally accurate results with Arduino 4-byte double.
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double julianDate(uint32_t t) {
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return (t / 86400.0L + 2440587.5);
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}
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// Local Sidereal Time
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// Provides local sidereal time in degrees, requires longitude in degrees
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// and time in fractional Julian days since Jan 1, 2000, 1200UTC (e.g. the
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// Julian date - 2451545).
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// cf. USNO Astronomical Almanac and
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// https://astronomy.stackexchange.com/questions/24859/local-sidereal-time
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double localSiderealTime(double offsetDays, double longitude) {
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double lSideTime = (15.0L * (6.697374558L + 0.06570982441908L * offsetDays +
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remainder(offsetDays, 1) * 24 + 12 +
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0.000026 * (offsetDays / 36525) * (offsetDays / 36525))
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+ longitude) / 360;
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lSideTime -= floor(lSideTime);
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lSideTime *= 360; // Convert to degrees.
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return(lSideTime);
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}
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