CalendarAstronomer is a class that can perform the calculations to
* determine the positions of the sun and moon, the time of sunrise and
* sunset, and other astronomy-related data. The calculations it performs
* are in some cases quite complicated, and this utility class saves you
* the trouble of worrying about them.
*
* The measurement of time is a very important part of astronomy. Because
* astronomical bodies are constantly in motion, observations are only valid
* at a given moment in time. Accordingly, each CalendarAstronomer
* object has a time property that determines the date
* and time for which its calculations are performed. You can set and
* retrieve this property with {@link #setDate setDate}, {@link #getDate getDate}
* and related methods.
*
* Almost all of the calculations performed by this class, or by any * astronomer, are approximations to various degrees of accuracy. The * calculations in this class are mostly modelled after those described * in the book * * Practical Astronomy With Your Calculator, by Peter J. * Duffett-Smith, Cambridge University Press, 1990. This is an excellent * book, and if you want a greater understanding of how these calculations * are performed it a very good, readable starting point. *
* WARNING: This class is very early in its development, and
* it is highly likely that its API will change to some degree in the future.
* At the moment, it basically does just enough to support {@link android.icu.util.IslamicCalendar}
* and {@link android.icu.util.ChineseCalendar}.
*
* @author Laura Werner
* @author Alan Liu
* @hide Only a subset of ICU is exposed in Android
* @hide draft / provisional / internal are hidden on Android
*/
public class CalendarAstronomer {
//-------------------------------------------------------------------------
// Astronomical constants
//-------------------------------------------------------------------------
/**
* The number of standard hours in one sidereal day.
* Approximately 24.93.
* @hide draft / provisional / internal are hidden on Android
*/
public static final double SIDEREAL_DAY = 23.93446960027;
/**
* The number of sidereal hours in one mean solar day.
* Approximately 24.07.
* @hide draft / provisional / internal are hidden on Android
*/
public static final double SOLAR_DAY = 24.065709816;
/**
* The average number of solar days from one new moon to the next. This is the time
* it takes for the moon to return the same ecliptic longitude as the sun.
* It is longer than the sidereal month because the sun's longitude increases
* during the year due to the revolution of the earth around the sun.
* Approximately 29.53.
*
* @see #SIDEREAL_MONTH
* @hide draft / provisional / internal are hidden on Android
*/
public static final double SYNODIC_MONTH = 29.530588853;
/**
* The average number of days it takes
* for the moon to return to the same ecliptic longitude relative to the
* stellar background. This is referred to as the sidereal month.
* It is shorter than the synodic month due to
* the revolution of the earth around the sun.
* Approximately 27.32.
*
* @see #SYNODIC_MONTH
* @hide draft / provisional / internal are hidden on Android
*/
public static final double SIDEREAL_MONTH = 27.32166;
/**
* The average number number of days between successive vernal equinoxes.
* Due to the precession of the earth's
* axis, this is not precisely the same as the sidereal year.
* Approximately 365.24
*
* @see #SIDEREAL_YEAR
* @hide draft / provisional / internal are hidden on Android
*/
public static final double TROPICAL_YEAR = 365.242191;
/**
* The average number of days it takes
* for the sun to return to the same position against the fixed stellar
* background. This is the duration of one orbit of the earth about the sun
* as it would appear to an outside observer.
* Due to the precession of the earth's
* axis, this is not precisely the same as the tropical year.
* Approximately 365.25.
*
* @see #TROPICAL_YEAR
* @hide draft / provisional / internal are hidden on Android
*/
public static final double SIDEREAL_YEAR = 365.25636;
//-------------------------------------------------------------------------
// Time-related constants
//-------------------------------------------------------------------------
/**
* The number of milliseconds in one second.
* @hide draft / provisional / internal are hidden on Android
*/
public static final int SECOND_MS = 1000;
/**
* The number of milliseconds in one minute.
* @hide draft / provisional / internal are hidden on Android
*/
public static final int MINUTE_MS = 60*SECOND_MS;
/**
* The number of milliseconds in one hour.
* @hide draft / provisional / internal are hidden on Android
*/
public static final int HOUR_MS = 60*MINUTE_MS;
/**
* The number of milliseconds in one day.
* @hide draft / provisional / internal are hidden on Android
*/
public static final long DAY_MS = 24*HOUR_MS;
/**
* The start of the julian day numbering scheme used by astronomers, which
* is 1/1/4713 BC (Julian), 12:00 GMT. This is given as the number of milliseconds
* since 1/1/1970 AD (Gregorian), a negative number.
* Note that julian day numbers and
* the Julian calendar are not the same thing. Also note that
* julian days start at noon, not midnight.
* @hide draft / provisional / internal are hidden on Android
*/
public static final long JULIAN_EPOCH_MS = -210866760000000L;
// static {
// Calendar cal = new GregorianCalendar(TimeZone.getTimeZone("GMT"));
// cal.clear();
// cal.set(cal.ERA, 0);
// cal.set(cal.YEAR, 4713);
// cal.set(cal.MONTH, cal.JANUARY);
// cal.set(cal.DATE, 1);
// cal.set(cal.HOUR_OF_DAY, 12);
// System.out.println("1.5 Jan 4713 BC = " + cal.getTime().getTime());
// cal.clear();
// cal.set(cal.YEAR, 2000);
// cal.set(cal.MONTH, cal.JANUARY);
// cal.set(cal.DATE, 1);
// cal.add(cal.DATE, -1);
// System.out.println("0.0 Jan 2000 = " + cal.getTime().getTime());
// }
/**
* Milliseconds value for 0.0 January 2000 AD.
*/
static final long EPOCH_2000_MS = 946598400000L;
//-------------------------------------------------------------------------
// Assorted private data used for conversions
//-------------------------------------------------------------------------
// My own copies of these so compilers are more likely to optimize them away
static private final double PI = 3.14159265358979323846;
static private final double PI2 = PI * 2.0;
static private final double RAD_HOUR = 12 / PI; // radians -> hours
static private final double DEG_RAD = PI / 180; // degrees -> radians
static private final double RAD_DEG = 180 / PI; // radians -> degrees
//-------------------------------------------------------------------------
// Constructors
//-------------------------------------------------------------------------
/**
* Construct a new CalendarAstronomer object that is initialized to
* the current date and time.
* @hide draft / provisional / internal are hidden on Android
*/
public CalendarAstronomer() {
this(System.currentTimeMillis());
}
/**
* Construct a new CalendarAstronomer object that is initialized to
* the specified date and time.
* @hide draft / provisional / internal are hidden on Android
*/
public CalendarAstronomer(Date d) {
this(d.getTime());
}
/**
* Construct a new CalendarAstronomer object that is initialized to
* the specified time. The time is expressed as a number of milliseconds since
* January 1, 1970 AD (Gregorian).
*
* @see java.util.Date#getTime()
* @hide draft / provisional / internal are hidden on Android
*/
public CalendarAstronomer(long aTime) {
time = aTime;
}
/**
* Construct a new CalendarAstronomer object with the given
* latitude and longitude. The object's time is set to the current
* date and time.
*
* @param longitude The desired longitude, in degrees east of
* the Greenwich meridian.
*
* @param latitude The desired latitude, in degrees. Positive
* values signify North, negative South.
*
* @see java.util.Date#getTime()
* @hide draft / provisional / internal are hidden on Android
*/
public CalendarAstronomer(double longitude, double latitude) {
this();
fLongitude = normPI(longitude * DEG_RAD);
fLatitude = normPI(latitude * DEG_RAD);
fGmtOffset = (long)(fLongitude * 24 * HOUR_MS / PI2);
}
//-------------------------------------------------------------------------
// Time and date getters and setters
//-------------------------------------------------------------------------
/**
* Set the current date and time of this CalendarAstronomer object. All
* astronomical calculations are performed based on this time setting.
*
* @param aTime the date and time, expressed as the number of milliseconds since
* 1/1/1970 0:00 GMT (Gregorian).
*
* @see #setDate
* @see #getTime
* @hide draft / provisional / internal are hidden on Android
*/
public void setTime(long aTime) {
time = aTime;
clearCache();
}
/**
* Set the current date and time of this CalendarAstronomer object. All
* astronomical calculations are performed based on this time setting.
*
* @param date the time and date, expressed as a Date object.
*
* @see #setTime
* @see #getDate
* @hide draft / provisional / internal are hidden on Android
*/
public void setDate(Date date) {
setTime(date.getTime());
}
/**
* Set the current date and time of this CalendarAstronomer object. All
* astronomical calculations are performed based on this time setting.
*
* @param jdn the desired time, expressed as a "julian day number",
* which is the number of elapsed days since
* 1/1/4713 BC (Julian), 12:00 GMT. Note that julian day
* numbers start at noon. To get the jdn for
* the corresponding midnight, subtract 0.5.
*
* @see #getJulianDay
* @see #JULIAN_EPOCH_MS
* @hide draft / provisional / internal are hidden on Android
*/
public void setJulianDay(double jdn) {
time = (long)(jdn * DAY_MS) + JULIAN_EPOCH_MS;
clearCache();
julianDay = jdn;
}
/**
* Get the current time of this CalendarAstronomer object,
* represented as the number of milliseconds since
* 1/1/1970 AD 0:00 GMT (Gregorian).
*
* @see #setTime
* @see #getDate
* @hide draft / provisional / internal are hidden on Android
*/
public long getTime() {
return time;
}
/**
* Get the current time of this CalendarAstronomer object,
* represented as a Date object.
*
* @see #setDate
* @see #getTime
* @hide draft / provisional / internal are hidden on Android
*/
public Date getDate() {
return new Date(time);
}
/**
* Get the current time of this CalendarAstronomer object,
* expressed as a "julian day number", which is the number of elapsed
* days since 1/1/4713 BC (Julian), 12:00 GMT.
*
* @see #setJulianDay
* @see #JULIAN_EPOCH_MS
* @hide draft / provisional / internal are hidden on Android
*/
public double getJulianDay() {
if (julianDay == INVALID) {
julianDay = (double)(time - JULIAN_EPOCH_MS) / (double)DAY_MS;
}
return julianDay;
}
/**
* Return this object's time expressed in julian centuries:
* the number of centuries after 1/1/1900 AD, 12:00 GMT
*
* @see #getJulianDay
* @hide draft / provisional / internal are hidden on Android
*/
public double getJulianCentury() {
if (julianCentury == INVALID) {
julianCentury = (getJulianDay() - 2415020.0) / 36525;
}
return julianCentury;
}
/**
* Returns the current Greenwich sidereal time, measured in hours
* @hide draft / provisional / internal are hidden on Android
*/
public double getGreenwichSidereal() {
if (siderealTime == INVALID) {
// See page 86 of "Practical Astronomy with your Calculator",
// by Peter Duffet-Smith, for details on the algorithm.
double UT = normalize((double)time/HOUR_MS, 24);
siderealTime = normalize(getSiderealOffset() + UT*1.002737909, 24);
}
return siderealTime;
}
private double getSiderealOffset() {
if (siderealT0 == INVALID) {
double JD = Math.floor(getJulianDay() - 0.5) + 0.5;
double S = JD - 2451545.0;
double T = S / 36525.0;
siderealT0 = normalize(6.697374558 + 2400.051336*T + 0.000025862*T*T, 24);
}
return siderealT0;
}
/**
* Returns the current local sidereal time, measured in hours
* @hide draft / provisional / internal are hidden on Android
*/
public double getLocalSidereal() {
return normalize(getGreenwichSidereal() + (double)fGmtOffset/HOUR_MS, 24);
}
/**
* Converts local sidereal time to Universal Time.
*
* @param lst The Local Sidereal Time, in hours since sidereal midnight
* on this object's current date.
*
* @return The corresponding Universal Time, in milliseconds since
* 1 Jan 1970, GMT.
*/
private long lstToUT(double lst) {
// Convert to local mean time
double lt = normalize((lst - getSiderealOffset()) * 0.9972695663, 24);
// Then find local midnight on this day
long base = DAY_MS * ((time + fGmtOffset)/DAY_MS) - fGmtOffset;
//out(" lt =" + lt + " hours");
//out(" base=" + new Date(base));
return base + (long)(lt * HOUR_MS);
}
//-------------------------------------------------------------------------
// Coordinate transformations, all based on the current time of this object
//-------------------------------------------------------------------------
/**
* Convert from ecliptic to equatorial coordinates.
*
* @param ecliptic A point in the sky in ecliptic coordinates.
* @return The corresponding point in equatorial coordinates.
* @hide draft / provisional / internal are hidden on Android
*/
public final Equatorial eclipticToEquatorial(Ecliptic ecliptic)
{
return eclipticToEquatorial(ecliptic.longitude, ecliptic.latitude);
}
/**
* Convert from ecliptic to equatorial coordinates.
*
* @param eclipLong The ecliptic longitude
* @param eclipLat The ecliptic latitude
*
* @return The corresponding point in equatorial coordinates.
* @hide draft / provisional / internal are hidden on Android
*/
public final Equatorial eclipticToEquatorial(double eclipLong, double eclipLat)
{
// See page 42 of "Practical Astronomy with your Calculator",
// by Peter Duffet-Smith, for details on the algorithm.
double obliq = eclipticObliquity();
double sinE = Math.sin(obliq);
double cosE = Math.cos(obliq);
double sinL = Math.sin(eclipLong);
double cosL = Math.cos(eclipLong);
double sinB = Math.sin(eclipLat);
double cosB = Math.cos(eclipLat);
double tanB = Math.tan(eclipLat);
return new Equatorial(Math.atan2(sinL*cosE - tanB*sinE, cosL),
Math.asin(sinB*cosE + cosB*sinE*sinL) );
}
/**
* Convert from ecliptic longitude to equatorial coordinates.
*
* @param eclipLong The ecliptic longitude
*
* @return The corresponding point in equatorial coordinates.
* @hide draft / provisional / internal are hidden on Android
*/
public final Equatorial eclipticToEquatorial(double eclipLong)
{
return eclipticToEquatorial(eclipLong, 0); // TODO: optimize
}
/**
* @hide draft / provisional / internal are hidden on Android
*/
public Horizon eclipticToHorizon(double eclipLong)
{
Equatorial equatorial = eclipticToEquatorial(eclipLong);
double H = getLocalSidereal()*PI/12 - equatorial.ascension; // Hour-angle
double sinH = Math.sin(H);
double cosH = Math.cos(H);
double sinD = Math.sin(equatorial.declination);
double cosD = Math.cos(equatorial.declination);
double sinL = Math.sin(fLatitude);
double cosL = Math.cos(fLatitude);
double altitude = Math.asin(sinD*sinL + cosD*cosL*cosH);
double azimuth = Math.atan2(-cosD*cosL*sinH, sinD - sinL * Math.sin(altitude));
return new Horizon(azimuth, altitude);
}
//-------------------------------------------------------------------------
// The Sun
//-------------------------------------------------------------------------
//
// Parameters of the Sun's orbit as of the epoch Jan 0.0 1990
// Angles are in radians (after multiplying by PI/180)
//
static final double JD_EPOCH = 2447891.5; // Julian day of epoch
static final double SUN_ETA_G = 279.403303 * PI/180; // Ecliptic longitude at epoch
static final double SUN_OMEGA_G = 282.768422 * PI/180; // Ecliptic longitude of perigee
static final double SUN_E = 0.016713; // Eccentricity of orbit
//double sunR0 = 1.495585e8; // Semi-major axis in KM
//double sunTheta0 = 0.533128 * PI/180; // Angular diameter at R0
// The following three methods, which compute the sun parameters
// given above for an arbitrary epoch (whatever time the object is
// set to), make only a small difference as compared to using the
// above constants. E.g., Sunset times might differ by ~12
// seconds. Furthermore, the eta-g computation is befuddled by
// Duffet-Smith's incorrect coefficients (p.86). I've corrected
// the first-order coefficient but the others may be off too - no
// way of knowing without consulting another source.
// /**
// * Return the sun's ecliptic longitude at perigee for the current time.
// * See Duffett-Smith, p. 86.
// * @return radians
// */
// private double getSunOmegaG() {
// double T = getJulianCentury();
// return (281.2208444 + (1.719175 + 0.000452778*T)*T) * DEG_RAD;
// }
// /**
// * Return the sun's ecliptic longitude for the current time.
// * See Duffett-Smith, p. 86.
// * @return radians
// */
// private double getSunEtaG() {
// double T = getJulianCentury();
// //return (279.6966778 + (36000.76892 + 0.0003025*T)*T) * DEG_RAD;
// //
// // The above line is from Duffett-Smith, and yields manifestly wrong
// // results. The below constant is derived empirically to match the
// // constant he gives for the 1990 EPOCH.
// //
// return (279.6966778 + (-0.3262541582718024 + 0.0003025*T)*T) * DEG_RAD;
// }
// /**
// * Return the sun's eccentricity of orbit for the current time.
// * See Duffett-Smith, p. 86.
// * @return double
// */
// private double getSunE() {
// double T = getJulianCentury();
// return 0.01675104 - (0.0000418 + 0.000000126*T)*T;
// }
/**
* The longitude of the sun at the time specified by this object.
* The longitude is measured in radians along the ecliptic
* from the "first point of Aries," the point at which the ecliptic
* crosses the earth's equatorial plane at the vernal equinox.
*
* Currently, this method uses an approximation of the two-body Kepler's
* equation for the earth and the sun. It does not take into account the
* perturbations caused by the other planets, the moon, etc.
* @hide draft / provisional / internal are hidden on Android
*/
public double getSunLongitude()
{
// See page 86 of "Practical Astronomy with your Calculator",
// by Peter Duffet-Smith, for details on the algorithm.
if (sunLongitude == INVALID) {
double[] result = getSunLongitude(getJulianDay());
sunLongitude = result[0];
meanAnomalySun = result[1];
}
return sunLongitude;
}
/**
* TODO Make this public when the entire class is package-private.
*/
/*public*/ double[] getSunLongitude(double julian)
{
// See page 86 of "Practical Astronomy with your Calculator",
// by Peter Duffet-Smith, for details on the algorithm.
double day = julian - JD_EPOCH; // Days since epoch
// Find the angular distance the sun in a fictitious
// circular orbit has travelled since the epoch.
double epochAngle = norm2PI(PI2/TROPICAL_YEAR*day);
// The epoch wasn't at the sun's perigee; find the angular distance
// since perigee, which is called the "mean anomaly"
double meanAnomaly = norm2PI(epochAngle + SUN_ETA_G - SUN_OMEGA_G);
// Now find the "true anomaly", e.g. the real solar longitude
// by solving Kepler's equation for an elliptical orbit
// NOTE: The 3rd ed. of the book lists omega_g and eta_g in different
// equations; omega_g is to be correct.
return new double[] {
norm2PI(trueAnomaly(meanAnomaly, SUN_E) + SUN_OMEGA_G),
meanAnomaly
};
}
/**
* The position of the sun at this object's current date and time,
* in equatorial coordinates.
* @hide draft / provisional / internal are hidden on Android
*/
public Equatorial getSunPosition() {
return eclipticToEquatorial(getSunLongitude(), 0);
}
private static class SolarLongitude {
double value;
SolarLongitude(double val) { value = val; }
}
/**
* Constant representing the vernal equinox.
* For use with {@link #getSunTime(SolarLongitude, boolean) getSunTime}.
* Note: In this case, "vernal" refers to the northern hemisphere's seasons.
* @hide draft / provisional / internal are hidden on Android
*/
public static final SolarLongitude VERNAL_EQUINOX = new SolarLongitude(0);
/**
* Constant representing the summer solstice.
* For use with {@link #getSunTime(SolarLongitude, boolean) getSunTime}.
* Note: In this case, "summer" refers to the northern hemisphere's seasons.
* @hide draft / provisional / internal are hidden on Android
*/
public static final SolarLongitude SUMMER_SOLSTICE = new SolarLongitude(PI/2);
/**
* Constant representing the autumnal equinox.
* For use with {@link #getSunTime(SolarLongitude, boolean) getSunTime}.
* Note: In this case, "autumn" refers to the northern hemisphere's seasons.
* @hide draft / provisional / internal are hidden on Android
*/
public static final SolarLongitude AUTUMN_EQUINOX = new SolarLongitude(PI);
/**
* Constant representing the winter solstice.
* For use with {@link #getSunTime(SolarLongitude, boolean) getSunTime}.
* Note: In this case, "winter" refers to the northern hemisphere's seasons.
* @hide draft / provisional / internal are hidden on Android
*/
public static final SolarLongitude WINTER_SOLSTICE = new SolarLongitude((PI*3)/2);
/**
* Find the next time at which the sun's ecliptic longitude will have
* the desired value.
* @hide draft / provisional / internal are hidden on Android
*/
public long getSunTime(double desired, boolean next)
{
return timeOfAngle( new AngleFunc() { @Override
public double eval() { return getSunLongitude(); } },
desired,
TROPICAL_YEAR,
MINUTE_MS,
next);
}
/**
* Find the next time at which the sun's ecliptic longitude will have
* the desired value.
* @hide draft / provisional / internal are hidden on Android
*/
public long getSunTime(SolarLongitude desired, boolean next) {
return getSunTime(desired.value, next);
}
/**
* Returns the time (GMT) of sunrise or sunset on the local date to which
* this calendar is currently set.
*
* NOTE: This method only works well if this object is set to a
* time near local noon. Because of variations between the local
* official time zone and the geographic longitude, the
* computation can flop over into an adjacent day if this object
* is set to a time near local midnight.
*
* @hide draft / provisional / internal are hidden on Android
*/
public long getSunRiseSet(boolean rise) {
long t0 = time;
// Make a rough guess: 6am or 6pm local time on the current day
long noon = ((time + fGmtOffset)/DAY_MS)*DAY_MS - fGmtOffset + 12*HOUR_MS;
setTime(noon + (rise ? -6L : 6L) * HOUR_MS);
long t = riseOrSet(new CoordFunc() {
@Override
public Equatorial eval() { return getSunPosition(); }
},
rise,
.533 * DEG_RAD, // Angular Diameter
34 /60.0 * DEG_RAD, // Refraction correction
MINUTE_MS / 12); // Desired accuracy
setTime(t0);
return t;
}
// Commented out - currently unused. ICU 2.6, Alan
// //-------------------------------------------------------------------------
// // Alternate Sun Rise/Set
// // See Duffett-Smith p.93
// //-------------------------------------------------------------------------
//
// // This yields worse results (as compared to USNO data) than getSunRiseSet().
// /**
// * TODO Make this public when the entire class is package-private.
// */
// /*public*/ long getSunRiseSet2(boolean rise) {
// // 1. Calculate coordinates of the sun's center for midnight
// double jd = Math.floor(getJulianDay() - 0.5) + 0.5;
// double[] sl = getSunLongitude(jd);
// double lambda1 = sl[0];
// Equatorial pos1 = eclipticToEquatorial(lambda1, 0);
//
// // 2. Add ... to lambda to get position 24 hours later
// double lambda2 = lambda1 + 0.985647*DEG_RAD;
// Equatorial pos2 = eclipticToEquatorial(lambda2, 0);
//
// // 3. Calculate LSTs of rising and setting for these two positions
// double tanL = Math.tan(fLatitude);
// double H = Math.acos(-tanL * Math.tan(pos1.declination));
// double lst1r = (PI2 + pos1.ascension - H) * 24 / PI2;
// double lst1s = (pos1.ascension + H) * 24 / PI2;
// H = Math.acos(-tanL * Math.tan(pos2.declination));
// double lst2r = (PI2-H + pos2.ascension ) * 24 / PI2;
// double lst2s = (H + pos2.ascension ) * 24 / PI2;
// if (lst1r > 24) lst1r -= 24;
// if (lst1s > 24) lst1s -= 24;
// if (lst2r > 24) lst2r -= 24;
// if (lst2s > 24) lst2s -= 24;
//
// // 4. Convert LSTs to GSTs. If GST1 > GST2, add 24 to GST2.
// double gst1r = lstToGst(lst1r);
// double gst1s = lstToGst(lst1s);
// double gst2r = lstToGst(lst2r);
// double gst2s = lstToGst(lst2s);
// if (gst1r > gst2r) gst2r += 24;
// if (gst1s > gst2s) gst2s += 24;
//
// // 5. Calculate GST at 0h UT of this date
// double t00 = utToGst(0);
//
// // 6. Calculate GST at 0h on the observer's longitude
// double offset = Math.round(fLongitude*12/PI); // p.95 step 6; he _rounds_ to nearest 15 deg.
// double t00p = t00 - offset*1.002737909;
// if (t00p < 0) t00p += 24; // do NOT normalize
//
// // 7. Adjust
// if (gst1r < t00p) {
// gst1r += 24;
// gst2r += 24;
// }
// if (gst1s < t00p) {
// gst1s += 24;
// gst2s += 24;
// }
//
// // 8.
// double gstr = (24.07*gst1r-t00*(gst2r-gst1r))/(24.07+gst1r-gst2r);
// double gsts = (24.07*gst1s-t00*(gst2s-gst1s))/(24.07+gst1s-gst2s);
//
// // 9. Correct for parallax, refraction, and sun's diameter
// double dec = (pos1.declination + pos2.declination) / 2;
// double psi = Math.acos(Math.sin(fLatitude) / Math.cos(dec));
// double x = 0.830725 * DEG_RAD; // parallax+refraction+diameter
// double y = Math.asin(Math.sin(x) / Math.sin(psi)) * RAD_DEG;
// double delta_t = 240 * y / Math.cos(dec) / 3600; // hours
//
// // 10. Add correction to GSTs, subtract from GSTr
// gstr -= delta_t;
// gsts += delta_t;
//
// // 11. Convert GST to UT and then to local civil time
// double ut = gstToUt(rise ? gstr : gsts);
// //System.out.println((rise?"rise=":"set=") + ut + ", delta_t=" + delta_t);
// long midnight = DAY_MS * (time / DAY_MS); // Find UT midnight on this day
// return midnight + (long) (ut * 3600000);
// }
// Commented out - currently unused. ICU 2.6, Alan
// /**
// * Convert local sidereal time to Greenwich sidereal time.
// * Section 15. Duffett-Smith p.21
// * @param lst in hours (0..24)
// * @return GST in hours (0..24)
// */
// double lstToGst(double lst) {
// double delta = fLongitude * 24 / PI2;
// return normalize(lst - delta, 24);
// }
// Commented out - currently unused. ICU 2.6, Alan
// /**
// * Convert UT to GST on this date.
// * Section 12. Duffett-Smith p.17
// * @param ut in hours
// * @return GST in hours
// */
// double utToGst(double ut) {
// return normalize(getT0() + ut*1.002737909, 24);
// }
// Commented out - currently unused. ICU 2.6, Alan
// /**
// * Convert GST to UT on this date.
// * Section 13. Duffett-Smith p.18
// * @param gst in hours
// * @return UT in hours
// */
// double gstToUt(double gst) {
// return normalize(gst - getT0(), 24) * 0.9972695663;
// }
// Commented out - currently unused. ICU 2.6, Alan
// double getT0() {
// // Common computation for UT <=> GST
//
// // Find JD for 0h UT
// double jd = Math.floor(getJulianDay() - 0.5) + 0.5;
//
// double s = jd - 2451545.0;
// double t = s / 36525.0;
// double t0 = 6.697374558 + (2400.051336 + 0.000025862*t)*t;
// return t0;
// }
// Commented out - currently unused. ICU 2.6, Alan
// //-------------------------------------------------------------------------
// // Alternate Sun Rise/Set
// // See sci.astro FAQ
// // http://www.faqs.org/faqs/astronomy/faq/part3/section-5.html
// //-------------------------------------------------------------------------
//
// // Note: This method appears to produce inferior accuracy as
// // compared to getSunRiseSet().
//
// /**
// * TODO Make this public when the entire class is package-private.
// */
// /*public*/ long getSunRiseSet3(boolean rise) {
//
// // Compute day number for 0.0 Jan 2000 epoch
// double d = (double)(time - EPOCH_2000_MS) / DAY_MS;
//
// // Now compute the Local Sidereal Time, LST:
// //
// double LST = 98.9818 + 0.985647352 * d + /*UT*15 + long*/
// fLongitude*RAD_DEG;
// //
// // (east long. positive). Note that LST is here expressed in degrees,
// // where 15 degrees corresponds to one hour. Since LST really is an angle,
// // it's convenient to use one unit---degrees---throughout.
//
// // COMPUTING THE SUN'S POSITION
// // ----------------------------
// //
// // To be able to compute the Sun's rise/set times, you need to be able to
// // compute the Sun's position at any time. First compute the "day
// // number" d as outlined above, for the desired moment. Next compute:
// //
// double oblecl = 23.4393 - 3.563E-7 * d;
// //
// double w = 282.9404 + 4.70935E-5 * d;
// double M = 356.0470 + 0.9856002585 * d;
// double e = 0.016709 - 1.151E-9 * d;
// //
// // This is the obliquity of the ecliptic, plus some of the elements of
// // the Sun's apparent orbit (i.e., really the Earth's orbit): w =
// // argument of perihelion, M = mean anomaly, e = eccentricity.
// // Semi-major axis is here assumed to be exactly 1.0 (while not strictly
// // true, this is still an accurate approximation). Next compute E, the
// // eccentric anomaly:
// //
// double E = M + e*(180/PI) * Math.sin(M*DEG_RAD) * ( 1.0 + e*Math.cos(M*DEG_RAD) );
// //
// // where E and M are in degrees. This is it---no further iterations are
// // needed because we know e has a sufficiently small value. Next compute
// // the true anomaly, v, and the distance, r:
// //
// /* r * cos(v) = */ double A = Math.cos(E*DEG_RAD) - e;
// /* r * sin(v) = */ double B = Math.sqrt(1 - e*e) * Math.sin(E*DEG_RAD);
// //
// // and
// //
// // r = sqrt( A*A + B*B )
// double v = Math.atan2( B, A )*RAD_DEG;
// //
// // The Sun's true longitude, slon, can now be computed:
// //
// double slon = v + w;
// //
// // Since the Sun is always at the ecliptic (or at least very very close to
// // it), we can use simplified formulae to convert slon (the Sun's ecliptic
// // longitude) to sRA and sDec (the Sun's RA and Dec):
// //
// // sin(slon) * cos(oblecl)
// // tan(sRA) = -------------------------
// // cos(slon)
// //
// // sin(sDec) = sin(oblecl) * sin(slon)
// //
// // As was the case when computing az, the Azimuth, if possible use an
// // atan2() function to compute sRA.
//
// double sRA = Math.atan2(Math.sin(slon*DEG_RAD) * Math.cos(oblecl*DEG_RAD), Math.cos(slon*DEG_RAD))*RAD_DEG;
//
// double sin_sDec = Math.sin(oblecl*DEG_RAD) * Math.sin(slon*DEG_RAD);
// double sDec = Math.asin(sin_sDec)*RAD_DEG;
//
// // COMPUTING RISE AND SET TIMES
// // ----------------------------
// //
// // To compute when an object rises or sets, you must compute when it
// // passes the meridian and the HA of rise/set. Then the rise time is
// // the meridian time minus HA for rise/set, and the set time is the
// // meridian time plus the HA for rise/set.
// //
// // To find the meridian time, compute the Local Sidereal Time at 0h local
// // time (or 0h UT if you prefer to work in UT) as outlined above---name
// // that quantity LST0. The Meridian Time, MT, will now be:
// //
// // MT = RA - LST0
// double MT = normalize(sRA - LST, 360);
// //
// // where "RA" is the object's Right Ascension (in degrees!). If negative,
// // add 360 deg to MT. If the object is the Sun, leave the time as it is,
// // but if it's stellar, multiply MT by 365.2422/366.2422, to convert from
// // sidereal to solar time. Now, compute HA for rise/set, name that
// // quantity HA0:
// //
// // sin(h0) - sin(lat) * sin(Dec)
// // cos(HA0) = ---------------------------------
// // cos(lat) * cos(Dec)
// //
// // where h0 is the altitude selected to represent rise/set. For a purely
// // mathematical horizon, set h0 = 0 and simplify to:
// //
// // cos(HA0) = - tan(lat) * tan(Dec)
// //
// // If you want to account for refraction on the atmosphere, set h0 = -35/60
// // degrees (-35 arc minutes), and if you want to compute the rise/set times
// // for the Sun's upper limb, set h0 = -50/60 (-50 arc minutes).
// //
// double h0 = -50/60 * DEG_RAD;
//
// double HA0 = Math.acos(
// (Math.sin(h0) - Math.sin(fLatitude) * sin_sDec) /
// (Math.cos(fLatitude) * Math.cos(sDec*DEG_RAD)))*RAD_DEG;
//
// // When HA0 has been computed, leave it as it is for the Sun but multiply
// // by 365.2422/366.2422 for stellar objects, to convert from sidereal to
// // solar time. Finally compute:
// //
// // Rise time = MT - HA0
// // Set time = MT + HA0
// //
// // convert the times from degrees to hours by dividing by 15.
// //
// // If you'd like to check that your calculations are accurate or just
// // need a quick result, check the USNO's Sun or Moon Rise/Set Table,
// //
* @param desired The desired longitude.
* @param next true if the next occurrance of the phase
* is desired, false for the previous occurrance.
* @hide draft / provisional / internal are hidden on Android
*/
public long getMoonTime(double desired, boolean next)
{
return timeOfAngle( new AngleFunc() {
@Override
public double eval() { return getMoonAge(); } },
desired,
SYNODIC_MONTH,
MINUTE_MS,
next);
}
/**
* Find the next or previous time at which the moon will be in the
* desired phase.
*
* @param desired The desired phase of the moon.
* @param next true if the next occurrance of the phase
* is desired, false for the previous occurrance.
* @hide draft / provisional / internal are hidden on Android
*/
public long getMoonTime(MoonAge desired, boolean next) {
return getMoonTime(desired.value, next);
}
/**
* Returns the time (GMT) of sunrise or sunset on the local date to which
* this calendar is currently set.
* @hide draft / provisional / internal are hidden on Android
*/
public long getMoonRiseSet(boolean rise)
{
return riseOrSet(new CoordFunc() {
@Override
public Equatorial eval() { return getMoonPosition(); }
},
rise,
.533 * DEG_RAD, // Angular Diameter
34 /60.0 * DEG_RAD, // Refraction correction
MINUTE_MS); // Desired accuracy
}
//-------------------------------------------------------------------------
// Interpolation methods for finding the time at which a given event occurs
//-------------------------------------------------------------------------
private interface AngleFunc {
public double eval();
}
private long timeOfAngle(AngleFunc func, double desired,
double periodDays, long epsilon, boolean next)
{
// Find the value of the function at the current time
double lastAngle = func.eval();
// Find out how far we are from the desired angle
double deltaAngle = norm2PI(desired - lastAngle) ;
// Using the average period, estimate the next (or previous) time at
// which the desired angle occurs.
double deltaT = (deltaAngle + (next ? 0 : -PI2)) * (periodDays*DAY_MS) / PI2;
double lastDeltaT = deltaT; // Liu
long startTime = time; // Liu
setTime(time + (long)deltaT);
// Now iterate until we get the error below epsilon. Throughout
// this loop we use normPI to get values in the range -Pi to Pi,
// since we're using them as correction factors rather than absolute angles.
do {
// Evaluate the function at the time we've estimated
double angle = func.eval();
// Find the # of milliseconds per radian at this point on the curve
double factor = Math.abs(deltaT / normPI(angle-lastAngle));
// Correct the time estimate based on how far off the angle is
deltaT = normPI(desired - angle) * factor;
// HACK:
//
// If abs(deltaT) begins to diverge we need to quit this loop.
// This only appears to happen when attempting to locate, for
// example, a new moon on the day of the new moon. E.g.:
//
// This result is correct:
// newMoon(7508(Mon Jul 23 00:00:00 CST 1990,false))=
// Sun Jul 22 10:57:41 CST 1990
//
// But attempting to make the same call a day earlier causes deltaT
// to diverge:
// CalendarAstronomer.timeOfAngle() diverging: 1.348508727575625E9 ->
// 1.3649828540224032E9
// newMoon(7507(Sun Jul 22 00:00:00 CST 1990,false))=
// Sun Jul 08 13:56:15 CST 1990
//
// As a temporary solution, we catch this specific condition and
// adjust our start time by one eighth period days (either forward
// or backward) and try again.
// Liu 11/9/00
if (Math.abs(deltaT) > Math.abs(lastDeltaT)) {
long delta = (long) (periodDays * DAY_MS / 8);
setTime(startTime + (next ? delta : -delta));
return timeOfAngle(func, desired, periodDays, epsilon, next);
}
lastDeltaT = deltaT;
lastAngle = angle;
setTime(time + (long)deltaT);
}
while (Math.abs(deltaT) > epsilon);
return time;
}
private interface CoordFunc {
public Equatorial eval();
}
private long riseOrSet(CoordFunc func, boolean rise,
double diameter, double refraction,
long epsilon)
{
Equatorial pos = null;
double tanL = Math.tan(fLatitude);
long deltaT = Long.MAX_VALUE;
int count = 0;
//
// Calculate the object's position at the current time, then use that
// position to calculate the time of rising or setting. The position
// will be different at that time, so iterate until the error is allowable.
//
do {
// See "Practical Astronomy With Your Calculator, section 33.
pos = func.eval();
double angle = Math.acos(-tanL * Math.tan(pos.declination));
double lst = ((rise ? PI2-angle : angle) + pos.ascension ) * 24 / PI2;
// Convert from LST to Universal Time.
long newTime = lstToUT( lst );
deltaT = newTime - time;
setTime(newTime);
}
while (++ count < 5 && Math.abs(deltaT) > epsilon);
// Calculate the correction due to refraction and the object's angular diameter
double cosD = Math.cos(pos.declination);
double psi = Math.acos(Math.sin(fLatitude) / cosD);
double x = diameter / 2 + refraction;
double y = Math.asin(Math.sin(x) / Math.sin(psi));
long delta = (long)((240 * y * RAD_DEG / cosD)*SECOND_MS);
return time + (rise ? -delta : delta);
}
//-------------------------------------------------------------------------
// Other utility methods
//-------------------------------------------------------------------------
/***
* Given 'value', add or subtract 'range' until 0 <= 'value' < range.
* The modulus operator.
*/
private static final double normalize(double value, double range) {
return value - range * Math.floor(value / range);
}
/**
* Normalize an angle so that it's in the range 0 - 2pi.
* For positive angles this is just (angle % 2pi), but the Java
* mod operator doesn't work that way for negative numbers....
*/
private static final double norm2PI(double angle) {
return normalize(angle, PI2);
}
/**
* Normalize an angle into the range -PI - PI
*/
private static final double normPI(double angle) {
return normalize(angle + PI, PI2) - PI;
}
/**
* Find the "true anomaly" (longitude) of an object from
* its mean anomaly and the eccentricity of its orbit. This uses
* an iterative solution to Kepler's equation.
*
* @param meanAnomaly The object's longitude calculated as if it were in
* a regular, circular orbit, measured in radians
* from the point of perigee.
*
* @param eccentricity The eccentricity of the orbit
*
* @return The true anomaly (longitude) measured in radians
*/
private double trueAnomaly(double meanAnomaly, double eccentricity)
{
// First, solve Kepler's equation iteratively
// Duffett-Smith, p.90
double delta;
double E = meanAnomaly;
do {
delta = E - eccentricity * Math.sin(E) - meanAnomaly;
E = E - delta / (1 - eccentricity * Math.cos(E));
}
while (Math.abs(delta) > 1e-5); // epsilon = 1e-5 rad
return 2.0 * Math.atan( Math.tan(E/2) * Math.sqrt( (1+eccentricity)
/(1-eccentricity) ) );
}
/**
* Return the obliquity of the ecliptic (the angle between the ecliptic
* and the earth's equator) at the current time. This varies due to
* the precession of the earth's axis.
*
* @return the obliquity of the ecliptic relative to the equator,
* measured in radians.
*/
private double eclipticObliquity() {
if (eclipObliquity == INVALID) {
final double epoch = 2451545.0; // 2000 AD, January 1.5
double T = (getJulianDay() - epoch) / 36525;
eclipObliquity = 23.439292
- 46.815/3600 * T
- 0.0006/3600 * T*T
+ 0.00181/3600 * T*T*T;
eclipObliquity *= DEG_RAD;
}
return eclipObliquity;
}
//-------------------------------------------------------------------------
// Private data
//-------------------------------------------------------------------------
/**
* Current time in milliseconds since 1/1/1970 AD
* @see java.util.Date#getTime
*/
private long time;
/* These aren't used yet, but they'll be needed for sunset calculations
* and equatorial to horizon coordinate conversions
*/
private double fLongitude = 0.0;
private double fLatitude = 0.0;
private long fGmtOffset = 0;
//
// The following fields are used to cache calculated results for improved
// performance. These values all depend on the current time setting
// of this object, so the clearCache method is provided.
//
static final private double INVALID = Double.MIN_VALUE;
private transient double julianDay = INVALID;
private transient double julianCentury = INVALID;
private transient double sunLongitude = INVALID;
private transient double meanAnomalySun = INVALID;
private transient double moonLongitude = INVALID;
private transient double moonEclipLong = INVALID;
//private transient double meanAnomalyMoon = INVALID;
private transient double eclipObliquity = INVALID;
private transient double siderealT0 = INVALID;
private transient double siderealTime = INVALID;
private transient Equatorial moonPosition = null;
private void clearCache() {
julianDay = INVALID;
julianCentury = INVALID;
sunLongitude = INVALID;
meanAnomalySun = INVALID;
moonLongitude = INVALID;
moonEclipLong = INVALID;
//meanAnomalyMoon = INVALID;
eclipObliquity = INVALID;
siderealTime = INVALID;
siderealT0 = INVALID;
moonPosition = null;
}
//private static void out(String s) {
// System.out.println(s);
//}
//private static String deg(double rad) {
// return Double.toString(rad * RAD_DEG);
//}
//private static String hours(long ms) {
// return Double.toString((double)ms / HOUR_MS) + " hours";
//}
/**
* @hide draft / provisional / internal are hidden on Android
*/
public String local(long localMillis) {
return new Date(localMillis - TimeZone.getDefault().getRawOffset()).toString();
}
/**
* Represents the position of an object in the sky relative to the ecliptic,
* the plane of the earth's orbit around the Sun.
* This is a spherical coordinate system in which the latitude
* specifies the position north or south of the plane of the ecliptic.
* The longitude specifies the position along the ecliptic plane
* relative to the "First Point of Aries", which is the Sun's position in the sky
* at the Vernal Equinox.
*
* Note that Ecliptic objects are immutable and cannot be modified
* once they are constructed. This allows them to be passed and returned by
* value without worrying about whether other code will modify them.
*
* @see CalendarAstronomer.Equatorial
* @see CalendarAstronomer.Horizon
* @hide Only a subset of ICU is exposed in Android
* @hide draft / provisional / internal are hidden on Android
*/
public static final class Ecliptic {
/**
* Constructs an Ecliptic coordinate object.
*
* @param lat The ecliptic latitude, measured in radians.
* @param lon The ecliptic longitude, measured in radians.
* @hide draft / provisional / internal are hidden on Android
*/
public Ecliptic(double lat, double lon) {
latitude = lat;
longitude = lon;
}
/**
* Return a string representation of this object
* @hide draft / provisional / internal are hidden on Android
*/
@Override
public String toString() {
return Double.toString(longitude*RAD_DEG) + "," + (latitude*RAD_DEG);
}
/**
* The ecliptic latitude, in radians. This specifies an object's
* position north or south of the plane of the ecliptic,
* with positive angles representing north.
* @hide draft / provisional / internal are hidden on Android
*/
public final double latitude;
/**
* The ecliptic longitude, in radians.
* This specifies an object's position along the ecliptic plane
* relative to the "First Point of Aries", which is the Sun's position
* in the sky at the Vernal Equinox,
* with positive angles representing east.
*
* A bit of trivia: the first point of Aries is currently in the
* constellation Pisces, due to the precession of the earth's axis.
* @hide draft / provisional / internal are hidden on Android
*/
public final double longitude;
}
/**
* Represents the position of an
* object in the sky relative to the plane of the earth's equator.
* The Right Ascension specifies the position east or west
* along the equator, relative to the sun's position at the vernal
* equinox. The Declination is the position north or south
* of the equatorial plane.
*
* Note that Equatorial objects are immutable and cannot be modified
* once they are constructed. This allows them to be passed and returned by
* value without worrying about whether other code will modify them.
*
* @see CalendarAstronomer.Ecliptic
* @see CalendarAstronomer.Horizon
* @hide Only a subset of ICU is exposed in Android
* @hide draft / provisional / internal are hidden on Android
*/
public static final class Equatorial {
/**
* Constructs an Equatorial coordinate object.
*
* @param asc The right ascension, measured in radians.
* @param dec The declination, measured in radians.
* @hide draft / provisional / internal are hidden on Android
*/
public Equatorial(double asc, double dec) {
ascension = asc;
declination = dec;
}
/**
* Return a string representation of this object, with the
* angles measured in degrees.
* @hide draft / provisional / internal are hidden on Android
*/
@Override
public String toString() {
return Double.toString(ascension*RAD_DEG) + "," + (declination*RAD_DEG);
}
/**
* Return a string representation of this object with the right ascension
* measured in hours, minutes, and seconds.
* @hide draft / provisional / internal are hidden on Android
*/
public String toHmsString() {
return radToHms(ascension) + "," + radToDms(declination);
}
/**
* The right ascension, in radians.
* This is the position east or west along the equator
* relative to the sun's position at the vernal equinox,
* with positive angles representing East.
* @hide draft / provisional / internal are hidden on Android
*/
public final double ascension;
/**
* The declination, in radians.
* This is the position north or south of the equatorial plane,
* with positive angles representing north.
* @hide draft / provisional / internal are hidden on Android
*/
public final double declination;
}
/**
* Represents the position of an object in the sky relative to
* the local horizon.
* The Altitude represents the object's elevation above the horizon,
* with objects below the horizon having a negative altitude.
* The Azimuth is the geographic direction of the object from the
* observer's position, with 0 representing north. The azimuth increases
* clockwise from north.
*
* Note that Horizon objects are immutable and cannot be modified
* once they are constructed. This allows them to be passed and returned by
* value without worrying about whether other code will modify them.
*
* @see CalendarAstronomer.Ecliptic
* @see CalendarAstronomer.Equatorial
* @hide Only a subset of ICU is exposed in Android
* @hide draft / provisional / internal are hidden on Android
*/
public static final class Horizon {
/**
* Constructs a Horizon coordinate object.
*
* @param alt The altitude, measured in radians above the horizon.
* @param azim The azimuth, measured in radians clockwise from north.
* @hide draft / provisional / internal are hidden on Android
*/
public Horizon(double alt, double azim) {
altitude = alt;
azimuth = azim;
}
/**
* Return a string representation of this object, with the
* angles measured in degrees.
* @hide draft / provisional / internal are hidden on Android
*/
@Override
public String toString() {
return Double.toString(altitude*RAD_DEG) + "," + (azimuth*RAD_DEG);
}
/**
* The object's altitude above the horizon, in radians.
* @hide draft / provisional / internal are hidden on Android
*/
public final double altitude;
/**
* The object's direction, in radians clockwise from north.
* @hide draft / provisional / internal are hidden on Android
*/
public final double azimuth;
}
static private String radToHms(double angle) {
int hrs = (int) (angle*RAD_HOUR);
int min = (int)((angle*RAD_HOUR - hrs) * 60);
int sec = (int)((angle*RAD_HOUR - hrs - min/60.0) * 3600);
return Integer.toString(hrs) + "h" + min + "m" + sec + "s";
}
static private String radToDms(double angle) {
int deg = (int) (angle*RAD_DEG);
int min = (int)((angle*RAD_DEG - deg) * 60);
int sec = (int)((angle*RAD_DEG - deg - min/60.0) * 3600);
return Integer.toString(deg) + "\u00b0" + min + "'" + sec + "\"";
}
}
double in the range
* 0 <= phase < 1, interpreted as follows:
*
*
*
* @see #getMoonAge
* @hide draft / provisional / internal are hidden on Android
*/
public double getMoonPhase() {
// See page 147 of "Practical Astronomy with your Calculator",
// by Peter Duffet-Smith, for details on the algorithm.
return 0.5 * (1 - Math.cos(getMoonAge()));
}
private static class MoonAge {
double value;
MoonAge(double val) { value = val; }
}
/**
* Constant representing a new moon.
* For use with {@link #getMoonTime(MoonAge, boolean) getMoonTime}
* @hide draft / provisional / internal are hidden on Android
*/
public static final MoonAge NEW_MOON = new MoonAge(0);
/**
* Constant representing the moon's first quarter.
* For use with {@link #getMoonTime(MoonAge, boolean) getMoonTime}
* @hide draft / provisional / internal are hidden on Android
*/
public static final MoonAge FIRST_QUARTER = new MoonAge(PI/2);
/**
* Constant representing a full moon.
* For use with {@link #getMoonTime(MoonAge, boolean) getMoonTime}
* @hide draft / provisional / internal are hidden on Android
*/
public static final MoonAge FULL_MOON = new MoonAge(PI);
/**
* Constant representing the moon's last quarter.
* For use with {@link #getMoonTime(MoonAge, boolean) getMoonTime}
* @hide draft / provisional / internal are hidden on Android
*/
public static final MoonAge LAST_QUARTER = new MoonAge((PI*3)/2);
/**
* Find the next or previous time at which the Moon's ecliptic
* longitude will have the desired value.
*