contains general purpose utility functions.

Functions
QString	getApplicationName ()
	Return the full name of stellarium, i.e. "stellarium 0.9.0".

QString	getApplicationVersion ()
	Return the version of stellarium, i.e. "0.9.0".

QString	getOperatingSystemInfo ()
	Return the name and the version of operating system, i.e. "Mac OS X 10.7".

QString	getUserAgentString ()
	Return the user agent name, i.e. "Stellarium/0.15.0 (Linux)".

const QString	getEndLineChar ()

double	hmsToHours (const unsigned int h, const unsigned int m, const double s)
	Convert hours, minutes, seconds to decimal hours.

double	hmsToRad (const unsigned int h, const unsigned int m, const double s)
	Convert an angle in hms format to radian. More...

double	dmsToRad (const int d, const unsigned int m, const double s)
	Convert an angle in +-dms format to radian. More...

void	radToHms (double rad, unsigned int &h, unsigned int &m, double &s)
	Convert an angle in radian to hms format. More...

void	radToDms (double rad, bool &sign, unsigned int &d, unsigned int &m, double &s)
	Convert an angle in radian to +-dms format. More...

void	radToDecDeg (double rad, bool &sign, double &deg)
	Convert an angle in radian to decimal degree. More...

QString	radToDecDegStr (const double angle, const int precision=4, const bool useD=false, const bool useC=false)
	Convert an angle in radian to a decimal degree string. More...

QString	radToHmsStrAdapt (const double angle)
	Convert an angle in radian to a hms formatted string. More...

QString	radToHmsStr (const double angle, const bool decimal=false)
	Convert an angle in radian to a hms formatted string. More...

QString	radToDmsStrAdapt (const double angle, const bool useD=false)
	Convert an angle in radian to a dms formatted string. More...

QString	radToDmsStr (const double angle, const bool decimal=false, const bool useD=false)
	Convert an angle in radian to a dms formatted string. More...

QString	radToDmsPStr (const double angle, const int precision=0, const bool useD=false)
	Convert an angle in radian to a dms formatted string. More...

void	decDegToDms (double angle, bool &sign, unsigned int &d, unsigned int &m, double &s)
	Convert an angle in decimal degree to +-dms format. More...

QString	decDegToDmsStr (const double angle)
	Convert an angle in decimal degrees to a dms formatted string. More...

double	dmsStrToRad (const QString &s)
	Convert a dms formatted string to an angle in radian. More...

void	spheToRect (const double lng, const double lat, Vec3d &v)
	Convert from spherical coordinates to Rectangular direction. More...

void	spheToRect (const float lng, const float lat, Vec3f &v)
	Convert from spherical coordinates to Rectangular direction. More...

void	spheToRect (const double lng, const double lat, Vec3f &v)
	Convert from spherical coordinates to Rectangular direction. More...

void	spheToRect (const float lng, const float lat, Vec3d &v)
	Convert from spherical coordinates to Rectangular direction. More...

void	rectToSphe (double lng, double lat, const Vec3d &v)
	Convert from Rectangular direction to spherical coordinate components. More...

void	rectToSphe (float lng, float lat, const Vec3d &v)
	Convert from Rectangular direction to spherical coordinate components. More...

void	rectToSphe (float lng, float lat, const Vec3f &v)
	Convert from Rectangular direction to spherical coordinate components. More...

void	rectToSphe (double lng, double lat, const Vec3f &v)
	Convert from Rectangular direction to spherical coordinate components. More...

void	equToEcl (const double raRad, const double decRad, const double eclRad, double lambdaRad, double betaRad)
	Coordinate Transformation from equatorial to ecliptical.

void	eclToEqu (const double lambdaRad, const double betaRad, const double eclRad, double raRad, double decRad)
	Coordinate Transformation from ecliptical to equatorial.

double	getDecAngle (const QString &str)
	Convert a string longitude, latitude, RA or declination angle to radians. More...

bool	isPowerOfTwo (const int value)
	Check if a number is a power of 2.

int	getBiggerPowerOfTwo (int value)
	Return the first power of two bigger than the given value.

double	asinh (const double z)
	Return the inverse sinus hyperbolic of z.

int	imod (const int a, const int b)
	Integer modulo where the result is always nonnegative.

int	amod (const int a, const int b)
	Integer modulo where the result is always positive.

double	fmodpos (const double a, const double b)
	Double modulo where the result is always nonnegative.

float	fmodpos (const float a, const float b)
	Float modulo where the result is always nonnegative.

long	intFloorDiv (long num, long den)
	Floor integer division provides truncating to the next lower integer, also for negative numerators. More...

void	getDateFromJulianDay (const double julianDay, int year, int month, int *day)
	Make from julianDay a year, month, day for the Julian Date julianDay represents.

void	getTimeFromJulianDay (const double julianDay, int hour, int minute, int second, int millis=Q_NULLPTR)
	Make from julianDay an hour, minute, second.

bool	getDateTimeFromISO8601String (const QString &iso8601Date, int y, int m, int d, int h, int min, float s)
	Parse an ISO8601 date string. More...

QString	julianDayToISO8601String (const double jd, bool addMS=false)
	Format the given Julian Day in (UTC) ISO8601 date string. More...

double	getJulianDayFromISO8601String (const QString &iso8601Date, bool *ok)
	Return the Julian Date matching the ISO8601 date string. More...

QString	localeDateString (const int year, const int month, const int day, const int dayOfWeek, const QString &fmt)
	Format the date and day-of-week per the format in fmt (see QDateTime::toString()). More...

QString	localeDateString (const int year, const int month, const int day, const int dayOfWeek)
	Format the date and day-of-week per the system locale's QLocale::ShortFormat. More...

int	getDayOfWeek (int year, int month, int day)
	Return a day number of week for date. More...

int	getDayOfWeek (double JD)

double	getJDFromSystem ()
	Get the current Julian Date from system time. More...

double	getJDFromBesselianEpoch (const double epoch)
	Get the Julian Day Number (JD) from Besselian epoch. More...

double	qTimeToJDFraction (const QTime &time)
	Convert a time of day to the fraction of a Julian Day. More...

QTime	jdFractionToQTime (const double jd)
	Convert a fraction of a Julian Day to a QTime.

double	qDateTimeToJd (const QDateTime &dateTime)
	Convert a QT QDateTime class to julian day. More...

QDateTime	jdToQDateTime (const double &jd)
	Convert a julian day to a QDateTime. More...

bool	getJDFromDate (double *newjd, const int y, const int m, const int d, const int h, const int min, const float s)
	Compute Julian day number from calendar date. More...

int	numberOfDaysInMonthInYear (const int month, const int year)

bool	isLeapYear (const int year)

int	dayInYear (const int year, const int month, const int day)
	Find day number for date in year. More...

double	yearFraction (const int year, const int month, const double day)
	Return a fractional year like YYYY.ddddd. For negative years, the year number is decreased. E.g. -500.5 occurs in -501.

bool	changeDateTimeForRollover (int oy, int om, int od, int oh, int omin, int os, int ry, int rm, int rd, int rh, int rmin, int rs)

void	debugQVariantMap (const QVariant &m, const QString &indent="", const QString &key="")
	Output a QVariantMap to qDebug(). Formats like a tree where there are nested objects.

float	fastAcos (const float x)
	Compute acos(x) The taylor serie is not accurate around x=1 and x=-1.

float	fastExp (const float x)
	Compute exp(x) for small exponents x.

QString	hoursToHmsStr (const double hours, const bool lowprecision=false)
	Convert decimal hours to hours, minutes, seconds.

QString	hoursToHmsStr (const float hours, const bool lowprecision=false)

double	hmsStrToHours (const QString &s)
	Convert a hms formatted string to decimal hours.

QString	daysFloatToDHMS (float days)
	Convert days (float) to a time string.

double	getDeltaTwithoutCorrection (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByEspenakMeeus (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTBySchoch (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByClemence (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByIAU (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByAstronomicalEphemeris (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByTuckermanGoldstine (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByMullerStephenson (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephenson1978 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephenson1997 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTBySchmadelZech1979 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByMorrisonStephenson1982 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephensonMorrison1984 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephensonMorrison1995 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephensonHoulden (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByEspenak (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByBorkowski (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTBySchmadelZech1988 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByChaprontTouze (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByJPLHorizons (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByMorrisonStephenson2004 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByReijs (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByChaprontMeeus (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByMeeusSimons (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByMontenbruckPfleger (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByReingoldDershowitz (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByBanjevic (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByIslamSadiqQureshi (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByKhalidSultanaZaidi (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getDeltaTByStephensonMorrisonHohenkerk2016 (const double jDay)
	Get Delta-T estimation for a given date. More...

double	getMoonSecularAcceleration (const double jDay, const double ndot, const bool useDE43x)
	Get Secular Acceleration estimation for a given year. More...

double	getDeltaTStandardError (const double jDay)
	Get the standard error (sigma) for the value of DeltaT. More...

double	getMoonFluctuation (const double jDay)
	Get value of the Moon fluctuation Source: The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets Spencer Jones, H. More...

template<typename T >
int	sign (T val)
	Sign function from http://stackoverflow.com/questions/1903954/is-there-a-standard-sign-function-signum-sgn-in-c-c.

float *	ComputeCosSinTheta (const unsigned int slices)
	Compute cosines and sines around a circle which is split in "slices" parts. More...

float *	ComputeCosSinRho (const unsigned int segments)
	Compute cosines and sines around a half-circle which is split in "segments" parts. More...

float *	ComputeCosSinRhoZone (const float dRho, const unsigned int segments, const float minAngle)
	Compute cosines and sines around part of a circle (from top to bottom) which is split in "segments" parts. More...

int	getFixedFromGregorian (const int year, const int month, const int day)
	Calculate fixed days (R.D.) from Gregorian date. More...

int	compareVersions (const QString v1, const QString v2)
	Comparison two string versions and return a result in range -1,0,1. More...

QByteArray	uncompress (const QByteArray &data)
	Uncompress gzip or zlib compressed data.

QByteArray	uncompress (QIODevice &device, qint64 maxBytes=-1)
	Uncompress (gzip/zlib) data from this QIODevice, which must be open and readable. More...

int	gcd (int a, int b)
	Greatest Common Divisor (Euclid's algorithm) More...

int	lcm (int a, int b)
	Least Common Multiple. More...

template<class T >
T	interpolate3 (T n, T y1, T y2, T y3)
	Given regularly spaced steps x1, x2, x3 and curve values y1, y2, y3, calculate an intermediate value of the 3 arguments for the given interpolation point n. More...

template<class T >
T	interpolate5 (T n, T y1, T y2, T y3, T y4, T y5)
	Given regularly spaced steps x1, x2, x3, x4, x5 and curve values y1, y2, y3, y4, y5, calculate an intermediate value of the 5 arguments for the given interpolation point n. More...

template<typename T >
bool	isWithin (const T &value, const T &low, const T &high)
	Interval test. This checks whether. More...

double	trunc (double x)

float	trunc (float x)

Function Documentation

◆ compareVersions()

int StelUtils::compareVersions	(	const QString	v1,
		const QString	v2
	)

Parameters

v1	string for version 1
v2	string for version 2

Returns: result (-1: v1<v2; 0: v1==v2; 1: v1>v2)

◆ ComputeCosSinRho()

float* StelUtils::ComputeCosSinRho ( const unsigned int segments )

Values are stored in the global static array cos_sin_rho. Used for the sin/cos values along a meridian for a spherical mesh.

Parameters

segments number of partitions (elsewhere called "stacks") for the half-circle

◆ ComputeCosSinRhoZone()

float* StelUtils::ComputeCosSinRhoZone	(	const float	dRho,
		const unsigned int	segments,
		const float	minAngle
	)

Values are stored in the global static array cos_sin_rho. Used for the sin/cos values along a meridian. This allows leaving away pole caps. The array now contains values for the region minAngle+segments*phi

Parameters

dRho	a difference angle between the stops
segments	number of segments
minAngle	start angle inside the half-circle. maxAngle=minAngle+segments*phi

◆ ComputeCosSinTheta()

float* StelUtils::ComputeCosSinTheta ( const unsigned int slices )

Values are stored in the global static array cos_sin_theta. Used for the sin/cos values along a latitude circle, equator, etc. for a spherical mesh.

Parameters

slices number of partitions (elsewhere called "segments") for the circle

◆ dayInYear()

int StelUtils::dayInYear	(	const int	year,
		const int	month,
		const int	day
	)

Meeus, Astronomical Algorithms 2nd ed., 1998, ch.7, p.65

◆ decDegToDms()

void StelUtils::decDegToDms	(	double	angle,
		bool &	sign,
		unsigned int &	d,
		unsigned int &	m,
		double &	s
	)

Parameters

angle	input angle in decimal degree
sign	true if positive, false otherwise
d	degree component
m	minute component
s	second component

◆ decDegToDmsStr()

QString StelUtils::decDegToDmsStr ( const double angle )

Parameters

angle input angle in decimal degrees

◆ dmsStrToRad()

double StelUtils::dmsStrToRad ( const QString & s )

Parameters

s	The input string

◆ dmsToRad()

double StelUtils::dmsToRad	(	const int	d,
		const unsigned int	m,
		const double	s
	)

inline

Parameters

d	degree component
m	arcmin component
s	arcsec component

Returns: angle in radian

◆ gcd()

int StelUtils::gcd	(	int	a,
		int	b
	)

Parameters

a	first number
b	second number

Returns: Greatest Common Divisor

◆ getDateTimeFromISO8601String()

bool StelUtils::getDateTimeFromISO8601String	(	const QString &	iso8601Date,
		int *	y,
		int *	m,
		int *	d,
		int *	h,
		int *	min,
		float *	s
	)

Also handles negative and distant years.

◆ getDayOfWeek()

int StelUtils::getDayOfWeek	(	int	year,
		int	month,
		int	day
	)

Returns: number of day: 0 - sunday, 1 - monday,..

◆ getDecAngle()

double StelUtils::getDecAngle ( const QString & str )

Parameters

str the angle in a format according to: angle ::= [sign¹] ( real [degs | mins | secs] | [integer degs] ( [integer mins] real secs | real mins ) ) [cardinal¹] sign ::= + | - digit := 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 integer ::= digit [digits] real ::= integer [. integer] degs ::= d | h² | U+00B0 | U+00BA³ mins ::= m | ' secs ::= s | " cardinal ::= N² | S² | E | W ¹) A cardinal point overrides any sign. N and E result in a positive, W and S in a negative angle. ²) The use of the cardinal points N and S together with the hour sign 'H' or 'h' is forbidden. ³) The MASCULINE ORDINAL INDICATOR U+00BA is accepted, considering Spanish QWERTY keyboards. The string is parsed without regarding to case, except that, after a single real, a solitary 's' indicates seconds whereas an 'S' indicates South. It is highly recommended to use lower case for hdms and upper case for NSEW. Latitude: North is positive, South is negative. Longitude: East is positive, West is negative.

Returns: the angle in radians.

◆ getDeltaTByAstronomicalEphemeris()

double StelUtils::getDeltaTByAstronomicalEphemeris ( const double jDay )

Implementation of algorithm by Astronomical Ephemeris (1960) for DeltaT computation. Sources: Spencer Jones, H., "The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets", Monthly Notices of the Royal Astronomical Society, 99 (1939), 541-558 http://adsabs.harvard.edu/abs/1939MNRAS..99..541S or Explanatory Supplement to the Astr. Ephemeris, 1961, p.87. Also used by Mucke&Meeus, Canon of Solar Eclipses, Vienna 1983.

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByBanjevic()

double StelUtils::getDeltaTByBanjevic ( const double jDay )

Implementation of algorithm by Banjevic (2006) for DeltaT computation. Source: Ancient eclipses and dating the fall of Babylon Banjevic, B. Publications of the Astronomical Observatory of Belgrade, Vol. 80, p. 251-257 (2006) 2006POBeo..80..251B [http://adsabs.harvard.edu/abs/2006POBeo..80..251B]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByBorkowski()

double StelUtils::getDeltaTByBorkowski ( const double jDay )

Implementation of algorithm by Borkowski (1988) for DeltaT computation. Source: ELP 2000-85 and the dynamic time-universal time relation Borkowski, K. M. Astronomy and Astrophysics (ISSN 0004-6361), vol. 205, no. 1-2, Oct. 1988, p. L8-L10. 1988A&A...205L...8B [http://adsabs.harvard.edu/abs/1988A&A...205L...8B]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByChaprontMeeus()

double StelUtils::getDeltaTByChaprontMeeus ( const double jDay )

Implementation of algorithm by Chapront, Chapront-Touze & Francou (1997) & Meeus (1998) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByChaprontTouze()

double StelUtils::getDeltaTByChaprontTouze ( const double jDay )

Implementation of algorithm by Chapront-Touzé & Chapront (1991) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or 0 if year not in -391..1600

◆ getDeltaTByClemence()

double StelUtils::getDeltaTByClemence ( const double jDay )

Implementation of algorithm by Clemence (1948) for DeltaT computation, outdated but may be useful for science-historical purposes. Source: On the system of astronomical constants. Clemence, G. M. Astronomical Journal, Vol. 53, p. 169 1948AJ.....53..169C [http://adsabs.harvard.edu/abs/1948AJ.....53..169C]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByEspenak()

double StelUtils::getDeltaTByEspenak ( const double jDay )

Implementation of algorithm by Espenak (1987, 1989) for DeltaT computation. This relation should not be used before around 1950 or after around 2100 (Espenak, pers. comm.).

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByEspenakMeeus()

double StelUtils::getDeltaTByEspenakMeeus ( const double jDay )

Note that this method is recommended for the year range: -1999 to +3000. It gives details for -500...+2150. Implementation of algorithm by Espenak & Meeus (2006) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByIAU()

double StelUtils::getDeltaTByIAU ( const double jDay )

Implementation of algorithm by IAU (1952) for DeltaT computation, outdated but may be useful for science-historical purposes. Source: Spencer Jones, H., "The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets", Monthly Notices of the Royal Astronomical Society, 99 (1939), 541-558 http://adsabs.harvard.edu/abs/1939MNRAS..99..541S

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByIslamSadiqQureshi()

double StelUtils::getDeltaTByIslamSadiqQureshi ( const double jDay )

Implementation of algorithm by Islam, Sadiq & Qureshi (2008 + revisited 2013) for DeltaT computation. Source: Error Minimization of Polynomial Approximation of DeltaT Islam, S. & Sadiq, M. & Qureshi, M. S. Journal of Astrophysics & Astronomy, Vol. 29, p. 363-366 (2008) http://www.ias.ac.in/jaa/dec2008/JAA610.pdf Note: These polynomials are based on the uncorrected deltaT table from the Astronomical Almanac, thus ndot = -26.0 arcsec/cy^2. Meeus & Simons (2000) corrected the deltaT table for years before 1955.5 using ndot = -25.7376 arcsec/cy^2. Therefore the accuracies stated by Meeus & Simons are correct and cannot be compared with accuracies from Islam & Sadiq & Qureshi.

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByJPLHorizons()

double StelUtils::getDeltaTByJPLHorizons ( const double jDay )

Implementation of the "historical" part of the algorithm by JPL Horizons for DeltaT computation.

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or 0 if year not in -2999..1620 (!)

◆ getDeltaTByKhalidSultanaZaidi()

double StelUtils::getDeltaTByKhalidSultanaZaidi ( const double jDay )

Implementation of polinomial approximation of time period 1620-2013 for DeltaT by M. Khalid, Mariam Sultana and Faheem Zaidi (2014). Source: Delta T: Polynomial Approximation of Time Period 1620-2013 Journal of Astrophysics, Vol. 2014, Article ID 480964 https://doi.org/10.1155/2014/480964

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByMeeusSimons()

double StelUtils::getDeltaTByMeeusSimons ( const double jDay )

Implementation of algorithm by Meeus & Simons (2000) for DeltaT computation. Source: Polynomial approximations to Delta T, 1620-2000 AD Meeus, J.; Simons, L. Journal of the British Astronomical Association, vol.110, no.6, 323 2000JBAA..110..323M [http://adsabs.harvard.edu/abs/2000JBAA..110..323M]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or 0 if year not in 1620..2000

◆ getDeltaTByMontenbruckPfleger()

double StelUtils::getDeltaTByMontenbruckPfleger ( const double jDay )

Implementation of algorithm by Montenbruck & Pfleger (2000) for DeltaT computation, a data fit through the table of values found in Meeus, Astronomical algorithms (1991). Book "Astronomy on the Personal Computer" by O. Montenbruck & T. Pfleger (4th ed., 2000), p.181-182

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or 0 if not 1825<=year<2005

◆ getDeltaTByMorrisonStephenson1982()

double StelUtils::getDeltaTByMorrisonStephenson1982 ( const double jDay )

Implementation of algorithm by Morrison & Stephenson (1982) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByMorrisonStephenson2004()

double StelUtils::getDeltaTByMorrisonStephenson2004 ( const double jDay )

Implementation of algorithm by Morrison & Stephenson (2004, 2005) for DeltaT computation. Sources: Historical values of the Earth's clock error ΔT and the calculation of eclipses Morrison, L. V.; Stephenson, F. R. Journal for the History of Astronomy (ISSN 0021-8286), Vol. 35, Part 3, No. 120, p. 327 - 336 (2004) 2004JHA....35..327M [http://adsabs.harvard.edu/abs/2004JHA....35..327M] Addendum: Historical values of the Earth's clock error Morrison, L. V.; Stephenson, F. R. Journal for the History of Astronomy (ISSN 0021-8286), Vol. 36, Part 3, No. 124, p. 339 (2005) 2005JHA....36..339M [http://adsabs.harvard.edu/abs/2005JHA....36..339M]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByMullerStephenson()

double StelUtils::getDeltaTByMullerStephenson ( const double jDay )

Implementation of algorithm by Muller & Stephenson (1975) for DeltaT computation. Source: The accelerations of the earth and moon from early astronomical observations Muller, P. M.; Stephenson, F. R. Growth rhythms and the history of the earth's rotation; Proceedings of the Interdisciplinary Winter Conference on Biological Clocks and Changes in the Earth's Rotation: Geophysical and Astronomical Consequences, Newcastle-upon-Tyne, England, January 8-10, 1974. (A76-18126 06-46) London, Wiley-Interscience, 1975, p. 459-533; Discussion, p. 534. 1975grhe.conf..459M [http://adsabs.harvard.edu/abs/1975grhe.conf..459M]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByReijs()

double StelUtils::getDeltaTByReijs ( const double jDay )

Implementation of algorithm by Reijs (2006) for DeltaT computation Details: http://www.iol.ie/~geniet/eng/DeltaTeval.htm

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByReingoldDershowitz()

double StelUtils::getDeltaTByReingoldDershowitz ( const double jDay )

Implementation of algorithm by Reingold & Dershowitz (1997, 2001, 2002, 2007, 2018) for DeltaT computation. This is again mostly a data fit based on the table in Meeus, Astronomical Algorithms (1991). This is the version given in the 4rd edition ("the ultimate edition"; 2018) which added the fit for -500..1699 and 2006..2150 omitted from previous editions. Calendrical Calculations: The Ultimate Edition / Edward M. Reingold, Nachum Dershowitz - 4th Edition, Cambridge University Press, 2018. - 660p. ISBN: 9781107057623, DOI: 10.1017/9781107415058

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTBySchmadelZech1979()

double StelUtils::getDeltaTBySchmadelZech1979 ( const double jDay )

Implementation of algorithm by Schmadel & Zech (1979) for DeltaT computation. Outdated, but may be useful for science-historical purposes. Source: Polynomial approximations for the correction delta T E.T.-U.T. in the period 1800-1975 Schmadel, L. D.; Zech, G. Acta Astronomica, vol. 29, no. 1, 1979, p. 101-104. 1979AcA....29..101S [http://adsabs.harvard.edu/abs/1979AcA....29..101S]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

Note: The polynome is strictly applicable 1800...1975 only! Delivers values for the nearer edge (1800/1989) if jDay is outside.

◆ getDeltaTBySchmadelZech1988()

double StelUtils::getDeltaTBySchmadelZech1988 ( const double jDay )

Implementation of algorithm by Schmadel & Zech (1988) for DeltaT computation. Source: Empirical Transformations from U.T. to E.T. for the Period 1800-1988 Schmadel, L. D.; Zech, G. Astronomische Nachrichten 309, 219-221 1988AN....309..219S [http://adsabs.harvard.edu/abs/1988AN....309..219S]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

Note: The polynome is strictly applicable 1800...1988 only! Delivers values for the nearer edge (1800/1989) if jDay is outside.

◆ getDeltaTBySchoch()

double StelUtils::getDeltaTBySchoch ( const double jDay )

Implementation of algorithm by Schoch (1931) for DeltaT computation, outdated but may be useful for science-historical purposes. Source: Schoch, C. (1931). Die sekulare Accelaration des Mondes und der Sonne. Astronomische Abhandlungen, Ergnzungshefte zu den Astronomischen Nachrichten, Band 8, B2. Kiel.

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByStephenson1978()

double StelUtils::getDeltaTByStephenson1978 ( const double jDay )

Implementation of algorithm by Stephenson (1978) for DeltaT computation. Source: Pre-Telescopic Astronomical Observations Stephenson, F. R. Tidal Friction and the Earth's Rotation, Proceedings of a Workshop, held in Bielefeld, September 26-30, 1977, Edited by P. Brosche, and J. Sundermann. Berlin: Springer-Verlag, 1978, p.5 1978tfer.conf....5S [http://adsabs.harvard.edu/abs/1978tfer.conf....5S]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByStephenson1997()

double StelUtils::getDeltaTByStephenson1997 ( const double jDay )

Implementation of algorithm by Stephenson (1997) for DeltaT computation. Source: Book "Historical Eclipses and Earth's Rotation" by F. R. Stephenson (1997) http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511525186

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByStephensonHoulden()

double StelUtils::getDeltaTByStephensonHoulden ( const double jDay )

Implementation of algorithm by Stephenson & Houlden (1986) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or 0 if year > 1600

◆ getDeltaTByStephensonMorrison1984()

double StelUtils::getDeltaTByStephensonMorrison1984 ( const double jDay )

Implementation of algorithm by Stephenson & Morrison (1984) for DeltaT computation Source: Long-term changes in the rotation of the earth - 700 B.C. to A.D. 1980. Stephenson, F. R.; Morrison, L. V. Philosophical Transactions, Series A (ISSN 0080-4614), vol. 313, no. 1524, Nov. 27, 1984, p. 47-70. 1984RSPTA.313...47S [http://adsabs.harvard.edu/abs/1984RSPTA.313...47S]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds or Zero if date outside years -391..1600

◆ getDeltaTByStephensonMorrison1995()

double StelUtils::getDeltaTByStephensonMorrison1995 ( const double jDay )

Implementation of algorithm by Stephenson & Morrison (1995) for DeltaT computation Source: Long-Term Fluctuations in the Earth's Rotation: 700 BC to AD 1990. Stephenson, F. R.; Morrison, L. V. Philosophical Transactions: Physical Sciences and Engineering, Volume 351, Issue 1695, pp. 165-202 1995RSPTA.351..165S [http://adsabs.harvard.edu/abs/1995RSPTA.351..165S]

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTByStephensonMorrisonHohenkerk2016()

double StelUtils::getDeltaTByStephensonMorrisonHohenkerk2016 ( const double jDay )

Implementation of a spline approximation for time period -720-2016.0 for DeltaT by Stephenson, Morrison and Hohenkerk (2016). Source: Measurement of the Earth’s rotation: 720 BC to AD 2015 Proc. R. Soc. A 472: 20160404. https://doi.org/10.1098/rspa.2016.0404

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds. For times outside the limits, return result from the fitting parabola.

◆ getDeltaTByTuckermanGoldstine()

double StelUtils::getDeltaTByTuckermanGoldstine ( const double jDay )

Implementation of algorithm by Tuckerman (1962, 1964) & Goldstine (1973) for DeltaT computation

Parameters

jDay	the date and time expressed as a Julian day

Returns: Delta-T in seconds

◆ getDeltaTStandardError()

double StelUtils::getDeltaTStandardError ( const double jDay )

Parameters

jDay the JD

Returns: sigma in seconds

◆ getDeltaTwithoutCorrection()

double StelUtils::getDeltaTwithoutCorrection ( const double jDay )

This is just an "empty" correction function, returning 0.

◆ getFixedFromGregorian()

int StelUtils::getFixedFromGregorian	(	const int	year,
		const int	month,
		const int	day
	)

Parameters

year
month
day

Returns: days from Rata Die

◆ getJDFromBesselianEpoch()

double StelUtils::getJDFromBesselianEpoch ( const double epoch )

Parameters

epoch Besselian epoch, expressed as year

Returns: Julian Day number (JD) for B<Year>

◆ getJDFromDate()

bool StelUtils::getJDFromDate	(	double *	newjd,
		const int	y,
		const int	m,
		const int	d,
		const int	h,
		const int	min,
		const float	s
	)

Uses QDate functionality if possible, but also works for negative JD. Dates before 1582-10-15 are in the Julian Calendar.

Parameters

newjd	pointer to JD
y	Calendar year.
m	month, 1=January ... 12=December
d	day
h	hour
min	minute
s	second

Returns: true in all conceivable cases.

◆ getJDFromSystem()

double StelUtils::getJDFromSystem ( )

Returns: the current Julian Date

◆ getJulianDayFromISO8601String()

double StelUtils::getJulianDayFromISO8601String	(	const QString &	iso8601Date,
		bool *	ok
	)

Also handles negative and distant years.

◆ getMoonFluctuation()

double StelUtils::getMoonFluctuation ( const double jDay )

Monthly Notices of the Royal Astronomical Society, 99 (1939), 541-558 1939MNRAS..99..541S [http://adsabs.harvard.edu/abs/1939MNRAS..99..541S]

Parameters

jDay the JD

Returns: fluctuation in seconds

◆ getMoonSecularAcceleration()

double StelUtils::getMoonSecularAcceleration	(	const double	jDay,
		const double	ndot,
		const bool	useDE43x
	)

Method described is here: http://eclipse.gsfc.nasa.gov/SEcat5/secular.html For adapting from -26 to -25.858, use -0.91072 * (-25.858 + 26.0) = -0.12932224 For adapting from -26 to -23.895, use -0.91072 * (-23.895 + 26.0) = -1.9170656

Parameters

jDay	the JD
ndot	value of n-dot (secular acceleration of the Moon) which should be used in the lunar ephemeris instead of the default values.
useDE43x	true if function should adapt calculation of the secular acceleration of the Moon to the DE43x ephemeris

Returns: SecularAcceleration in seconds

Note: n-dot for secular acceleration of the Moon in ELP2000-82B is -23.8946 "/cy/cy and for DE43x is -25.8 "/cy/cy

◆ hmsToRad()

double StelUtils::hmsToRad	(	const unsigned int	h,
		const unsigned int	m,
		const double	s
	)

inline

Parameters

h	hour component
m	minute component
s	second component

Returns: angle in radian

◆ interpolate3()

template<class T >

T StelUtils::interpolate3	(	T	n,
		T	y1,
		T	y2,
		T	y3
	)

Parameters

n	Interpolation factor: steps from x2
y1	Argument 1
y2	Argument 2
y3	Argument 3

Returns: interpolation value

◆ interpolate5()

template<class T >

T StelUtils::interpolate5	(	T	n,
		T	y1,
		T	y2,
		T	y3,
		T	y4,
		T	y5
	)

Parameters

n	Interpolation factor: steps from x3
y1	Argument 1
y2	Argument 2
y3	Argument 3
y3	Argument 4
y3	Argument 5

Returns: interpolation value

◆ intFloorDiv()

long StelUtils::intFloorDiv	(	long	num,
		long	den
	)

inline

https://stackoverflow.com/questions/2622441/c-integer-floor-function

Returns: floor(num/den)

◆ isLeapYear()

bool StelUtils::isLeapYear ( const int year )

Returns: true if year is a leap year. Observes 1582 switch from Julian to Gregorian Calendar.

◆ isWithin()

template<typename T >

bool StelUtils::isWithin	(	const T &	value,
		const T &	low,
		const T &	high
	)

Parameters

value	is within [
low

◆ jdToQDateTime()

QDateTime StelUtils::jdToQDateTime ( const double & jd )

Parameters

jd	to convert

Returns: the matching UTC QDateTime

◆ julianDayToISO8601String()

QString StelUtils::julianDayToISO8601String	(	const double	jd,
		bool	addMS = `false`
	)

Also handles negative and distant years.

◆ lcm()

int StelUtils::lcm	(	int	a,
		int	b
	)

Parameters

a	first number
b	second number

Returns: Least Common Multiple

◆ localeDateString() [1/2]

QString StelUtils::localeDateString	(	const int	year,
		const int	month,
		const int	day,
		const int	dayOfWeek,
		const QString &	fmt
	)

Uses the system locale, not the one set in Stellarium.

Returns: QString representing the formatted date

◆ localeDateString() [2/2]

QString StelUtils::localeDateString	(	const int	year,
		const int	month,
		const int	day,
		const int	dayOfWeek
	)

Returns: QString representing the formatted date

◆ qDateTimeToJd()

double StelUtils::qDateTimeToJd ( const QDateTime & dateTime )

inline

Parameters

dateTime the UTC QDateTime to convert

Returns: the matching decimal Julian Day

◆ qTimeToJDFraction()

double StelUtils::qTimeToJDFraction ( const QTime & time )

Note that a Julian Day starts at 12:00, not 0:00, and so 12:00 == 0.0 and 0:00 == 0.5

◆ radToDecDeg()

void StelUtils::radToDecDeg	(	double	rad,
		bool &	sign,
		double &	deg
	)

Parameters

rad	input angle in radian
sign	true if positive, false otherwise
deg	decimal degree

◆ radToDecDegStr()

QString StelUtils::radToDecDegStr	(	const double	angle,
		const int	precision = `4`,
		const bool	useD = `false`,
		const bool	useC = `false`
	)

Parameters

angle	input angle in radian
precision
useD	Define if letter "d" must be used instead of deg sign
useC	Define if function should use 0-360 degrees

◆ radToDms()

void StelUtils::radToDms	(	double	rad,
		bool &	sign,
		unsigned int &	d,
		unsigned int &	m,
		double &	s
	)

Parameters

rad	input angle in radian
sign	true if positive, false otherwise
d	degree component
m	minute component
s	second component

◆ radToDmsPStr()

QString StelUtils::radToDmsPStr	(	const double	angle,
		const int	precision = `0`,
		const bool	useD = `false`
	)

Parameters

angle	input angle in radian
precision
useD	Define if letter "d" must be used instead of deg sign

◆ radToDmsStr()

QString StelUtils::radToDmsStr	(	const double	angle,
		const bool	decimal = `false`,
		const bool	useD = `false`
	)

Parameters

angle	input angle in radian
decimal	output second value with decimal fraction
useD	Define if letter "d" must be used instead of deg sign

◆ radToDmsStrAdapt()

QString StelUtils::radToDmsStrAdapt	(	const double	angle,
		const bool	useD = `false`
	)

If the second, minute part is == 0, it is not output

Parameters

angle	input angle in radian
useD	Define if letter "d" must be used instead of deg sign

◆ radToHms()

void StelUtils::radToHms	(	double	rad,
		unsigned int &	h,
		unsigned int &	m,
		double &	s
	)

Parameters

rad	input angle in radian
h	hour component
m	minute component
s	second component

◆ radToHmsStr()

QString StelUtils::radToHmsStr	(	const double	angle,
		const bool	decimal = `false`
	)

Parameters

angle	input angle in radian
decimal	output decimal second value

◆ radToHmsStrAdapt()

QString StelUtils::radToHmsStrAdapt ( const double angle )

If the second, minute part is == 0, it is not output

Parameters

angle input angle in radian

◆ rectToSphe() [1/4]

void StelUtils::rectToSphe	(	double *	lng,
		double *	lat,
		const Vec3d &	v
	)

inline

Parameters

lng	double* to store longitude in radian
lat	double* to store latitude in radian
v	the input 3D vector

◆ rectToSphe() [2/4]

void StelUtils::rectToSphe	(	float *	lng,
		float *	lat,
		const Vec3d &	v
	)

inline

Parameters

lng	float* to store longitude in radian
lat	float* to store latitude in radian
v	the input 3D vector

◆ rectToSphe() [3/4]

void StelUtils::rectToSphe	(	float *	lng,
		float *	lat,
		const Vec3f &	v
	)

inline

Parameters

lng	float* to store longitude in radian
lat	float* to store latitude in radian
v	the input 3D vector

◆ rectToSphe() [4/4]

void StelUtils::rectToSphe	(	double *	lng,
		double *	lat,
		const Vec3f &	v
	)

inline

Parameters

lng	double* to store longitude in radian
lat	double* to store latitude in radian
v	the input 3D vector

◆ spheToRect() [1/4]

void StelUtils::spheToRect	(	const double	lng,
		const double	lat,
		Vec3d &	v
	)

inline

Parameters

lng	longitude in radian
lat	latitude in radian
v	the resulting 3D unit vector

◆ spheToRect() [2/4]

void StelUtils::spheToRect	(	const float	lng,
		const float	lat,
		Vec3f &	v
	)

inline

Parameters

lng	longitude in radian
lat	latitude in radian
v	the resulting 3D unit vector

◆ spheToRect() [3/4]

void StelUtils::spheToRect	(	const double	lng,
		const double	lat,
		Vec3f &	v
	)

inline

Parameters

lng	longitude in radian
lat	latitude in radian
v	the resulting 3D unit vector

◆ spheToRect() [4/4]

void StelUtils::spheToRect	(	const float	lng,
		const float	lat,
		Vec3d &	v
	)

inline

Parameters

lng	longitude in radian
lat	latitude in radian
v	the resulting 3D unit vector

◆ uncompress()

QByteArray StelUtils::uncompress	(	QIODevice &	device,
		qint64	maxBytes = `-1`
	)

Parameters

device	The device to read from, must already be opened with an OpenMode supporting reading
maxBytes	The max. amount of bytes to read from the device, or -1 to read until EOF. Note that it always stops when inflate() returns Z_STREAM_END. Positive values can be used for interleaving compressed data with other data.

Functions

Function Documentation

◆ compareVersions()

◆ ComputeCosSinRho()

◆ ComputeCosSinRhoZone()

◆ ComputeCosSinTheta()

◆ dayInYear()

◆ decDegToDms()

◆ decDegToDmsStr()

◆ dmsStrToRad()

◆ dmsToRad()

◆ gcd()

◆ getDateTimeFromISO8601String()

◆ getDayOfWeek()

◆ getDecAngle()

◆ getDeltaTByAstronomicalEphemeris()

◆ getDeltaTByBanjevic()

◆ getDeltaTByBorkowski()

◆ getDeltaTByChaprontMeeus()

◆ getDeltaTByChaprontTouze()

◆ getDeltaTByClemence()

◆ getDeltaTByEspenak()

◆ getDeltaTByEspenakMeeus()

◆ getDeltaTByIAU()

◆ getDeltaTByIslamSadiqQureshi()

◆ getDeltaTByJPLHorizons()

◆ getDeltaTByKhalidSultanaZaidi()

◆ getDeltaTByMeeusSimons()

◆ getDeltaTByMontenbruckPfleger()

◆ getDeltaTByMorrisonStephenson1982()

◆ getDeltaTByMorrisonStephenson2004()

◆ getDeltaTByMullerStephenson()

◆ getDeltaTByReijs()

◆ getDeltaTByReingoldDershowitz()

◆ getDeltaTBySchmadelZech1979()

◆ getDeltaTBySchmadelZech1988()

◆ getDeltaTBySchoch()

◆ getDeltaTByStephenson1978()

◆ getDeltaTByStephenson1997()

◆ getDeltaTByStephensonHoulden()

◆ getDeltaTByStephensonMorrison1984()

◆ getDeltaTByStephensonMorrison1995()

◆ getDeltaTByStephensonMorrisonHohenkerk2016()

◆ getDeltaTByTuckermanGoldstine()

◆ getDeltaTStandardError()

◆ getDeltaTwithoutCorrection()

◆ getFixedFromGregorian()

◆ getJDFromBesselianEpoch()

◆ getJDFromDate()

◆ getJDFromSystem()

◆ getJulianDayFromISO8601String()

◆ getMoonFluctuation()

◆ getMoonSecularAcceleration()

◆ hmsToRad()

◆ interpolate3()

◆ interpolate5()

◆ intFloorDiv()

◆ isLeapYear()

◆ isWithin()

◆ jdToQDateTime()

◆ julianDayToISO8601String()

◆ lcm()

◆ localeDateString() [1/2]

◆ localeDateString() [2/2]

◆ qDateTimeToJd()

◆ qTimeToJDFraction()

◆ radToDecDeg()

◆ radToDecDegStr()

◆ radToDms()

◆ radToDmsPStr()

◆ radToDmsStr()

◆ radToDmsStrAdapt()

◆ radToHms()

◆ radToHmsStr()

◆ radToHmsStrAdapt()

◆ rectToSphe() [1/4]

◆ rectToSphe() [2/4]

◆ rectToSphe() [3/4]

◆ rectToSphe() [4/4]

◆ spheToRect() [1/4]