Detailed Description

Provides standard numerical constants for LAL.

Author: Creighton, T. D.

This header defines a number of useful numerical constants for use in LAL routines. These constants come in three basic flavours: arithmetic and mathematical constants, fundamental (or defined) physical constants, and measured astrophysical and cosmological parameters.

Note that this header is not included automatically by the header LALStdlib.h. Include it explicitly if you need any of these constants.

Floating-point constants
The following constants define the precision and range of floating-point arithmetic in LAL. They are taken from the IEEE standard 754 for binary arithmetic. All numbers are dimensionless. See also http://dx.doi.org/10.1109/IEEESTD.2008.4610935
#define	LAL_REAL4_MANT 24
	Bits of precision in the mantissa of a REAL4. More...

#define	LAL_REAL4_MAX 0x1.fffffe0000000p+127
	Largest normalized REAL4 number (2-2^-23)*2^127. More...

#define	LAL_REAL4_MIN 0x1.0000000000000p-126
	Smallest normalized REAL4 number 2^-126. More...

#define	LAL_REAL4_EPS 0x1.0000000000000p-23
	Difference between 1 and the next resolvable REAL4 2^-23. More...

#define	LAL_REAL8_MANT 53
	Bits of precision in the mantissa of a REAL8. More...

#define	LAL_REAL8_MAX 0x1.fffffffffffffp+1023
	Largest normalized REAL8 number (2-2^-52)*2^1023. More...

#define	LAL_REAL8_MIN 0x1.0000000000000p-1022
	Smallest normalized REAL8 number 2^-1022. More...

#define	LAL_REAL8_EPS 0x1.0000000000000p-52
	Difference between 1 and the next resolvable REAL8 2^-52. More...

Integer constants
Extremal integer values, all expressed as unsigned long long.
#define	LAL_UINT8_MAX LAL_UINT8_C(18446744073709551615)

#define	LAL_UINT4_MAX LAL_UINT8_C(4294967295)

#define	LAL_UINT2_MAX LAL_UINT8_C(65535)

#define	LAL_INT8_MAX LAL_UINT8_C(9223372036854775807)

#define	LAL_INT4_MAX LAL_UINT8_C(2147483647)

#define	LAL_INT2_MAX LAL_UINT8_C(32767)

Mathematical constants
All are dimensionless.
#define	LAL_E 2.718281828459045235360287471352662498
	Euler's constant, e. More...

#define	LAL_LOG2E 1.442695040888963407359924681001892137
	base-2 logarithm of e, log_2(e) More...

#define	LAL_LOG10E 0.434294481903251827651128918916605082
	common logarithm of e, log_10(e) More...

#define	LAL_LN2 0.693147180559945309417232121458176568
	natural log of 2, ln(2) More...

#define	LAL_LN10 2.302585092994045684017991454684364208
	natural log of 10, ln(10) More...

#define	LAL_SQRT2 1.414213562373095048801688724209698079
	Pythagoras's constant, sqrt(2) More...

#define	LAL_SQRT1_2 0.707106781186547524400844362104849039
	1/sqrt(2) More...

#define	LAL_GAMMA 0.577215664901532860606512090082402431
	Euler-Mascheroni constant, gamma. More...

#define	LAL_EXPGAMMA 1.781072417990197985236504103107179549
	exp(gamma) More...

#define	LAL_PI 3.141592653589793238462643383279502884
	Archimedes's constant, pi. More...

#define	LAL_TWOPI 6.283185307179586476925286766559005768
	2*pi is circumference of a circle divided by its radius More...

#define	LAL_PI_2 1.570796326794896619231321691639751442
	pi/2 More...

#define	LAL_PI_4 0.785398163397448309615660845819875721
	pi/4 is the least positive solution to sin(x) = cos(x) More...

#define	LAL_1_PI 0.318309886183790671537767526745028724
	1/pi is the ratio of the volume of a regular octahedron to the volume of the circumscribed sphere More...

#define	LAL_2_PI 0.636619772367581343075535053490057448
	2/pi is Buffon's constant More...

#define	LAL_2_SQRTPI 1.128379167095512573896158903121545172
	2/sqrt(pi) More...

#define	LAL_PI_180 1.745329251994329576923690768488612713e-2
	180/pi is the number of degrees in one radian More...

#define	LAL_180_PI 57.295779513082320876798154814105170332
	pi/180 is the number of radians in one degree More...

#define	LAL_LNPI 1.144729885849400174143427351353058712
	natural log of pi, ln(pi) More...

Exact physical constants
The following physical constants are defined to have exact values. The dimensions in SI units are as shown. See also 2018 CODATA adjustment: http://physics.nist.gov/constants
#define	LAL_C_SI 299792458e0
	Speed of light in vacuum, m s^-1. More...

#define	LAL_H_SI 6.62607015e-34
	Planck constant, J s. More...

#define	LAL_QE_SI 1.602176634e-19
	Electron charge, C. More...

#define	LAL_MOL 6.02214076e+23
	Avogadro constant, dimensionless. More...

#define	LAL_K_SI 1.380649e-23
	Boltzmann constant, J K^-1. More...

#define	LAL_GEARTH_SI 9.80665
	Standard gravity, m s^-2. More...

#define	LAL_PATM_SI 101325e0
	Standard atmosphere, Pa. More...

#define	LAL_HBAR_SI 1.054571817646156391262428003302280745e-34
	Reduced Planck constant, J s. More...

#define	LAL_R_SI 8.31446261815324
	Molar gas constant, J mol^-1 K^-1. More...

#define	LAL_SIGMA_SI 5.670374419184429453970996731889230876e-8
	Stefan-Boltzmann constant, W m^-2 K^-4. More...

#define	LAL_C2RAD_SI 1.438776877503933802146671601543911595e-2
	Second radiation constant, m K. More...

#define	LAL_BWIEN_SI 2.897771955185172661478605448092884727e-3
	Wien displacement law constant, m K. More...

Primary physical constants
These physical constants are given to the precision to which they are known. Other physical constants derived from these are given in the next section. See also 2018 CODATA adjustment: http://physics.nist.gov/constants
#define	LAL_ALPHA 0.0072973525693
	Fine structure constant, dimensionless. More...

#define	LAL_RYD_SI 10973731.568160
	Rydberg constant, m^-1. More...

#define	LAL_MP_ME 1836.15267343
	Proton-electron mass ratio, dimensionless. More...

#define	LAL_ME_AMU 0.000548579909065
	Electron mass, atomic mass units. More...

#define	LAL_G_SI 6.67430e-11
	Gravitational constant, N m^2 kg^-2. More...

Derived physical constants
The following constants are derived from the primary physical constants. When not dimensionless, they are given in the SI units shown. Precision beyond the accuracy is retained for these constants in order that equivalent combinations yield the same value.
#define	LAL_MU0_SI 1.256637062123837330602573817851770477e-6
	Permeability of free space, N A^-2. More...

#define	LAL_EPSILON0_SI 8.854187812773347391812964575762341677e-12
	Permittivity of free space, C^2 N^-1 m^-2. More...

#define	LAL_MPL_SI 2.176434342717898213927914919024147041e-8
	Planck mass, kg. More...

#define	LAL_LPL_SI 1.616255024423705286500047697249314157e-35
	Planck length, m. More...

#define	LAL_TPL_SI 5.391246448313603961644851309932934193e-44
	Planck time, s. More...

#define	LAL_LUMPL_SI 3.628254904411280064474144638555430509e52
	Planck luminosity, J s^-1. More...

#define	LAL_MP_AMU 1.00727646661968604164295
	Proton mass, atomic mass units. More...

#define	LAL_ME_SI 9.109383701517728819842163772087735080e-31
	Electron mass, kg. More...

#define	LAL_MP_SI 1.672621923684144692109494784075478798e-27
	Proton mass, kg. More...

#define	LAL_AMU_SI 1.660539066595378801332508797951914123e-27
	Atomic mass unit, kg. More...

#define	LAL_AB_SI 5.291772109034624983506063293620795401e-11
	Bohr radius, m. More...

#define	LAL_LAMBDAE_SI 2.426310238678370231942278247906312873e-12
	Electron Compton wavelength, m. More...

#define	LAL_RE_SI 2.817940326207927528347087481623789683e-15
	Classical electron radius, m. More...

#define	LAL_MUB_SI 9.274010078344114556082608495144137435e-24
	Bohr magneton, J T^-1. More...

#define	LAL_MUN_SI 5.050783746114056140501321131006282803e-27
	Nuclear magneton, J T^-1. More...

Exact astrophysical parameters
The following astrophysical constants are defined to have exact values. The dimensions in SI units are as shown. See also http://asa.hmnao.com/SecK/Constants.html https://doi.org/10.3847/0004-6256/152/2/41
#define	LAL_ROT_DAY 1.00273781191135448
	Number of Earth rotations in one UT1 day, dimensionless. More...

#define	LAL_DAYJUL_SI 86400e0
	Julian day, s. More...

#define	LAL_YRJUL_SI 31557600e0
	Julian year, s. More...

#define	LAL_LYR_SI 9460730472580800e0
	(Julian) Lightyear, m More...

#define	LAL_AU_SI 149597870700e0
	Astronomical unit, m. More...

#define	LAL_PC_SI 3.085677581491367278913937957796471611e16
	Parsec, m. More...

#define	LAL_GMEARTH_SI 3.986004e+14
	Nominal Earth mass parameter, m^3 s^-2. More...

#define	LAL_REEARTH_SI 6.3781e+6
	Nominal Earth equatorial radius, m. More...

#define	LAL_RPEARTH_SI 6.3568e+6
	Nominal Earth polar radius, m. More...

#define	LAL_GMJUP_SI 1.2668653e+17
	Nominal Jupiter mass parameter, m^3 s^-2. More...

#define	LAL_REJUP_SI 7.1492e+7
	Nominal Jupiter equatorial radius, m. More...

#define	LAL_RPJUP_SI 6.6854e+7
	Nominal Jupiter polar radius, m. More...

#define	LAL_GMSUN_SI 1.3271244e+20
	Nominal solar mass parameter, m^3 s^-2. More...

#define	LAL_RSUN_SI 6.957e+8
	Nominal solar radius, m. More...

#define	LAL_SSUN_SI 1361e0
	Nominal total solar irradiance, W m^-2. More...

#define	LAL_LSUN_SI 3.828e+26
	Nominal solar luminosity, W. More...

#define	LAL_TSUN_SI 5772e0
	Nominal solar effective temperature, K. More...

Primary astrophysical parameters
These astrophysical constants are given to the precision to which they are known. Other physical constants derived from these are given in the next section.
#define	LAL_REARTH_SI 6378136.6
	Earth equatorial radius, m. More...

#define	LAL_AWGS84_SI 6378137e0
	Semimajor axis of WGS-84 Reference Ellipsoid, m. More...

#define	LAL_BWGS84_SI 6356752.314
	Semiminor axis of WGS-84 Reference Ellipsoid, m. More...

#define	LAL_IEARTH 0.409092600600582871467239393761915655
	Earth inclination (2000), radians. More...

#define	LAL_EEARTH 0.0167
	Earth orbital eccentricity, dimensionless. More...

#define	LAL_EPREC_SI 1.127703867758020059420250393792953007e-12
	Rate of Earth precession (2000), Hz. More...

#define	LAL_GMEARTH_TCB_SI 3.986004418e+14
	Earth mass parameter, m^3 s^-2 (TCB) More...

#define	LAL_GMEARTH_TDB_SI 3.986004356e+14
	Earth mass parameter, m^3 s^-2 (TDB) More...

#define	LAL_GMEARTH_TT_SI 3.986004415e+14
	Earth mass parameter, m^3 s^-2 (TT) More...

#define	LAL_GMSUN_TCB_SI 1.32712442099e+20
	Solar mass parameter, m^3 s^-2 (TCB) More...

#define	LAL_GMSUN_TDB_SI 1.32712440041e+20
	Solar mass parameter, m^3 s^-2 (TDB) More...

#define	LAL_YRTROP_SI 31556925.1874707200
	Tropical year (2000), s. More...

#define	LAL_YRSID_SI 31558149.763545600
	Sidereal year (2000), s. More...

Derived astrophysical parameters
The following constants are derived from the primary astrophysical constants. When not dimensionless, they are given in the SI units shown. Precision beyond the accuracy is retained for these constants in order that equivalent combinations yield the same value.
#define	LAL_COSIEARTH 0.917482143065241841533315838574859003
	Cosine of Earth inclination (2000) More...

#define	LAL_SINIEARTH 0.397776969112605992551264763661918798
	Sine of Earth inclination (2000) More...

#define	LAL_MEARTH_SI 5.972167867791378871192484605127129437e24
	Nominal Earth mass, kg. More...

#define	LAL_MEARTH_TCB_SI 5.972168494074284943739418365970963247e24
	Earth mass, kg (TCB) More...

#define	LAL_MEARTH_TDB_SI 5.972168401180648157859251157424748663e24
	Earth mass, kg (TDB) More...

#define	LAL_MEARTH_TT_SI 5.972168489579431550874248984912275445e24
	Earth mass, kg (TT) More...

#define	LAL_MJUP_SI 1.898124597336050222495242946825884362e27
	Nominal Jupiter mass, kg. More...

#define	LAL_MSUN_SI 1.988409870698050731911960804878414216e30
	Nominal solar mass, kg. More...

#define	LAL_MRSUN_SI 1.476625038050124729627979840144936351e3
	Geometrized nominal solar mass, m. More...

#define	LAL_MTSUN_SI 4.925490947641266978197229498498379006e-6
	Geometrized nominal solar mass, s. More...

#define	LAL_MSUN_TCB_SI 1.988409902147041637325262574352366540e30
	Solar mass, kg (TCB) More...

#define	LAL_MSUN_TDB_SI 1.988409871312347362270200620289768215e30
	Solar mass, kg (TDB) More...

#define	LAL_SOL_SID 1.002737909344968654292933133909634024
	Ratio of mean solar day to sidereal day, dimensionless. More...

#define	LAL_DAYSID_SI 86164.090531333536768710524462700317733190
	Mean sidereal day, s. More...

Cosmological parameters
The following cosmological parameters are derived from measurements of the Hubble expansion rate and of the cosmic microwave background radiation. In what follows, the normalized Hubble constant \(h_0\) is equal to the actual Hubble constant \(H_0\) divided by \(\langle H \rangle=100\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}\). Thus the Hubble constant can be written as: \(H_0 = \langle H \rangle * h_0\). Similarly, the critical energy density \(\rho_c\) required for spatial flatness is given by: \(\rho_c = \langle\rho\rangle h_0^2\). Current estimates give \(h_0\) a value of around 0.69 which is what is assumed below. All values are in the SI units shown. See also http://arxiv.org/abs/1303.5062 http://dx.doi.org/10.1088/0067-0049/208/2/20
#define	LAL_H0FAC_SI 3.240779289444365023237687716352957261e-18
	Hubble constant prefactor, s^-1. More...

#define	LAL_H0_SI (0.69 * LAL_H0FAC_SI)
	Approximate Hubble constant, s^-1. More...

#define	LAL_RHOCFAC_SI 1.688169255655572064052978218230767915e-9
	Critical energy density prefactor, J m^-3. More...

#define	LAL_RHOC_SI (0.69 * 0.69 * LAL_RHOCFAC_SI)
	Approximate critical energy density, J m^-3. More...

#define	LAL_TCMB_SI 2.72548
	Cosmic microwave background radiation temperature, K. More...

#define	LAL_VCMB_SI 369883.9346804
	Solar velocity with respect to the cosmic microwave background radiation, m s^-1. More...

#define	LAL_NCMB_SI 4.107178061233267795913602167900672966e8
	Number density of cosmic microwave background radiation photons, m^-3. More...

#define	LAL_SCMB_SI 2.042296344521760298284258925842980552e-14
	Entropy density of cosmic microwave background radiation, J K^-1 m^-3. More...

Macro Definition Documentation

◆ LAL_REAL4_MANT

#define LAL_REAL4_MANT 24

Bits of precision in the mantissa of a REAL4.

Definition at line 54 of file LALConstants.h.

◆ LAL_REAL4_MAX

#define LAL_REAL4_MAX 0x1.fffffe0000000p+127

Largest normalized REAL4 number (2-2^-23)*2^127.

Definition at line 55 of file LALConstants.h.

◆ LAL_REAL4_MIN

#define LAL_REAL4_MIN 0x1.0000000000000p-126

Smallest normalized REAL4 number 2^-126.

Definition at line 56 of file LALConstants.h.

◆ LAL_REAL4_EPS

#define LAL_REAL4_EPS 0x1.0000000000000p-23

Difference between 1 and the next resolvable REAL4 2^-23.

Definition at line 57 of file LALConstants.h.

◆ LAL_REAL8_MANT

#define LAL_REAL8_MANT 53

Bits of precision in the mantissa of a REAL8.

Definition at line 58 of file LALConstants.h.

◆ LAL_REAL8_MAX

#define LAL_REAL8_MAX 0x1.fffffffffffffp+1023

Largest normalized REAL8 number (2-2^-52)*2^1023.

Definition at line 59 of file LALConstants.h.

◆ LAL_REAL8_MIN

#define LAL_REAL8_MIN 0x1.0000000000000p-1022

Smallest normalized REAL8 number 2^-1022.

Definition at line 60 of file LALConstants.h.

◆ LAL_REAL8_EPS

#define LAL_REAL8_EPS 0x1.0000000000000p-52

Difference between 1 and the next resolvable REAL8 2^-52.

Definition at line 61 of file LALConstants.h.

◆ LAL_UINT8_MAX

#define LAL_UINT8_MAX LAL_UINT8_C(18446744073709551615)

Definition at line 79 of file LALConstants.h.

◆ LAL_UINT4_MAX

#define LAL_UINT4_MAX LAL_UINT8_C(4294967295)

Definition at line 80 of file LALConstants.h.

◆ LAL_UINT2_MAX

#define LAL_UINT2_MAX LAL_UINT8_C(65535)

Definition at line 81 of file LALConstants.h.

◆ LAL_INT8_MAX

#define LAL_INT8_MAX LAL_UINT8_C(9223372036854775807)

Definition at line 82 of file LALConstants.h.

◆ LAL_INT4_MAX

#define LAL_INT4_MAX LAL_UINT8_C(2147483647)

Definition at line 83 of file LALConstants.h.

◆ LAL_INT2_MAX

#define LAL_INT2_MAX LAL_UINT8_C(32767)

Definition at line 84 of file LALConstants.h.

◆ LAL_E

#define LAL_E 2.718281828459045235360287471352662498

Euler's constant, e.

See also: https://oeis.org/A001113

Definition at line 169 of file LALConstants.h.

◆ LAL_LOG2E

#define LAL_LOG2E 1.442695040888963407359924681001892137

base-2 logarithm of e, log_2(e)

See also: http://oeis.org/A007525

Definition at line 170 of file LALConstants.h.

◆ LAL_LOG10E

#define LAL_LOG10E 0.434294481903251827651128918916605082

common logarithm of e, log_10(e)

See also: http://oeis.org/A002285

Definition at line 171 of file LALConstants.h.

◆ LAL_LN2

#define LAL_LN2 0.693147180559945309417232121458176568

natural log of 2, ln(2)

See also: http://oeis.org/A002162

Definition at line 172 of file LALConstants.h.

◆ LAL_LN10

#define LAL_LN10 2.302585092994045684017991454684364208

natural log of 10, ln(10)

See also: http://oeis.org/A002392

Definition at line 173 of file LALConstants.h.

◆ LAL_SQRT2

#define LAL_SQRT2 1.414213562373095048801688724209698079

Pythagoras's constant, sqrt(2)

See also: https://oeis.org/A002193

Definition at line 174 of file LALConstants.h.

◆ LAL_SQRT1_2

#define LAL_SQRT1_2 0.707106781186547524400844362104849039

1/sqrt(2)

See also: https://oeis.org/A010503

Definition at line 175 of file LALConstants.h.

◆ LAL_GAMMA

#define LAL_GAMMA 0.577215664901532860606512090082402431

Euler-Mascheroni constant, gamma.

See also: https://oeis.org/A001620

Definition at line 176 of file LALConstants.h.

◆ LAL_EXPGAMMA

#define LAL_EXPGAMMA 1.781072417990197985236504103107179549

exp(gamma)

See also: https://oeis.org/A073004

Definition at line 177 of file LALConstants.h.

◆ LAL_PI

#define LAL_PI 3.141592653589793238462643383279502884

Archimedes's constant, pi.

See also: https://oeis.org/A000796

Definition at line 179 of file LALConstants.h.

◆ LAL_TWOPI

#define LAL_TWOPI 6.283185307179586476925286766559005768

2*pi is circumference of a circle divided by its radius

See also: https://oeis.org/A019692

Definition at line 180 of file LALConstants.h.

◆ LAL_PI_2

#define LAL_PI_2 1.570796326794896619231321691639751442

pi/2

See also: http://oeis.org/A019669

Definition at line 181 of file LALConstants.h.

◆ LAL_PI_4

#define LAL_PI_4 0.785398163397448309615660845819875721

pi/4 is the least positive solution to sin(x) = cos(x)

See also: http://oeis.org/A003881

Definition at line 182 of file LALConstants.h.

◆ LAL_1_PI

#define LAL_1_PI 0.318309886183790671537767526745028724

1/pi is the ratio of the volume of a regular octahedron to the volume of the circumscribed sphere

See also: http://oeis.org/A049541

Definition at line 183 of file LALConstants.h.

◆ LAL_2_PI

#define LAL_2_PI 0.636619772367581343075535053490057448

2/pi is Buffon's constant

See also: http://oeis.org/A060294

Definition at line 184 of file LALConstants.h.

◆ LAL_2_SQRTPI

#define LAL_2_SQRTPI 1.128379167095512573896158903121545172

2/sqrt(pi)

See also: http://oeis.org/A190732

Definition at line 185 of file LALConstants.h.

◆ LAL_PI_180

#define LAL_PI_180 1.745329251994329576923690768488612713e-2

180/pi is the number of degrees in one radian

See also: http://oeis.org/A072097

Definition at line 186 of file LALConstants.h.

◆ LAL_180_PI

#define LAL_180_PI 57.295779513082320876798154814105170332

pi/180 is the number of radians in one degree

See also: http://oeis.org/A019685

Definition at line 187 of file LALConstants.h.

◆ LAL_LNPI

#define LAL_LNPI 1.144729885849400174143427351353058712

natural log of pi, ln(pi)

See also: http://oeis.org/A053510

Definition at line 188 of file LALConstants.h.

◆ LAL_C_SI

#define LAL_C_SI 299792458e0

Speed of light in vacuum, m s^-1.

Definition at line 198 of file LALConstants.h.

◆ LAL_H_SI

#define LAL_H_SI 6.62607015e-34

Planck constant, J s.

Definition at line 199 of file LALConstants.h.

◆ LAL_QE_SI

#define LAL_QE_SI 1.602176634e-19

Electron charge, C.

Definition at line 200 of file LALConstants.h.

◆ LAL_MOL

#define LAL_MOL 6.02214076e+23

Avogadro constant, dimensionless.

Definition at line 201 of file LALConstants.h.

◆ LAL_K_SI

#define LAL_K_SI 1.380649e-23

Boltzmann constant, J K^-1.

Definition at line 202 of file LALConstants.h.

◆ LAL_GEARTH_SI

#define LAL_GEARTH_SI 9.80665

Standard gravity, m s^-2.

Definition at line 203 of file LALConstants.h.

◆ LAL_PATM_SI

#define LAL_PATM_SI 101325e0

Standard atmosphere, Pa.

Definition at line 204 of file LALConstants.h.

◆ LAL_HBAR_SI

#define LAL_HBAR_SI 1.054571817646156391262428003302280745e-34

Reduced Planck constant, J s.

LAL_HBAR_SI = LAL_H_SI / (2 * LAL_PI)

Definition at line 211 of file LALConstants.h.

◆ LAL_R_SI

#define LAL_R_SI 8.31446261815324

Molar gas constant, J mol^-1 K^-1.

LAL_R_SI = LAL_MOL * LAL_K_SI

Definition at line 218 of file LALConstants.h.

◆ LAL_SIGMA_SI

#define LAL_SIGMA_SI 5.670374419184429453970996731889230876e-8

Stefan-Boltzmann constant, W m^-2 K^-4.

LAL_SIGMA_SI = ((LAL_PI * LAL_PI * LAL_K_SI * LAL_K_SI * LAL_K_SI * LAL_K_SI) / (60 * LAL_HBAR_SI * LAL_HBAR_SI * LAL_HBAR_SI * LAL_C_SI * LAL_C_SI))

Definition at line 225 of file LALConstants.h.

◆ LAL_C2RAD_SI

#define LAL_C2RAD_SI 1.438776877503933802146671601543911595e-2

Second radiation constant, m K.

LAL_C2RAD_SI = (LAL_H_SI * LAL_C_SI / LAL_K_SI)

Definition at line 232 of file LALConstants.h.

◆ LAL_BWIEN_SI

#define LAL_BWIEN_SI 2.897771955185172661478605448092884727e-3

Wien displacement law constant, m K.

LAL_BWIEN_SI = (LAL_C2RAD_SI / X)

where the factor X satisfies

X * exp(X) = 5 * (exp(X) - 1)

Definition at line 243 of file LALConstants.h.

◆ LAL_ALPHA

#define LAL_ALPHA 0.0072973525693

Fine structure constant, dimensionless.

Definition at line 254 of file LALConstants.h.

◆ LAL_RYD_SI

#define LAL_RYD_SI 10973731.568160

Rydberg constant, m^-1.

Definition at line 255 of file LALConstants.h.

◆ LAL_MP_ME

#define LAL_MP_ME 1836.15267343

Proton-electron mass ratio, dimensionless.

Definition at line 256 of file LALConstants.h.

◆ LAL_ME_AMU

#define LAL_ME_AMU 0.000548579909065

Electron mass, atomic mass units.

Definition at line 257 of file LALConstants.h.

◆ LAL_G_SI

#define LAL_G_SI 6.67430e-11

Gravitational constant, N m^2 kg^-2.

Definition at line 258 of file LALConstants.h.

◆ LAL_MU0_SI

#define LAL_MU0_SI 1.256637062123837330602573817851770477e-6

Permeability of free space, N A^-2.

LAL_MU0_SI = 4 * LAL_PI * LAL_ALPHA * LAL_HBAR_SI / (LAL_QE_SI * LAL_QE_SI * LAL_C_SI)

Definition at line 276 of file LALConstants.h.

◆ LAL_EPSILON0_SI

#define LAL_EPSILON0_SI 8.854187812773347391812964575762341677e-12

Permittivity of free space, C^2 N^-1 m^-2.

LAL_EPSILON0_SI = 1 / (LAL_MU0_SI * LAL_C_SI * LAL_C_SI)

Definition at line 283 of file LALConstants.h.

◆ LAL_MPL_SI

#define LAL_MPL_SI 2.176434342717898213927914919024147041e-8

Planck mass, kg.

LAL_MPL_SI = sqrt(LAL_HBAR_SI * LAL_C_SI / LAL_G_SI)

Definition at line 290 of file LALConstants.h.

◆ LAL_LPL_SI

#define LAL_LPL_SI 1.616255024423705286500047697249314157e-35

Planck length, m.

LAL_LPL_SI = (LAL_HBAR_SI / (LAL_MPL_SI * LAL_C_SI))

Definition at line 297 of file LALConstants.h.

◆ LAL_TPL_SI

#define LAL_TPL_SI 5.391246448313603961644851309932934193e-44

Planck time, s.

LAL_TPL_SI = (LAL_LPL_SI / LAL_C_SI)

Definition at line 304 of file LALConstants.h.

◆ LAL_LUMPL_SI

#define LAL_LUMPL_SI 3.628254904411280064474144638555430509e52

Planck luminosity, J s^-1.

LAL_LUMPL_SI = (LAL_C_SI * LAL_C_SI * LAL_C_SI * LAL_C_SI * LAL_C_SI) / (LAL_G_SI)

Definition at line 311 of file LALConstants.h.

◆ LAL_MP_AMU

#define LAL_MP_AMU 1.00727646661968604164295

Proton mass, atomic mass units.

LAL_MP_AMU = (LAL_ME_AMU * LAL_MP_ME)

Definition at line 318 of file LALConstants.h.

◆ LAL_ME_SI

#define LAL_ME_SI 9.109383701517728819842163772087735080e-31

Electron mass, kg.

LAL_ME_SI = ((2 * LAL_RYD_SI * LAL_H_SI) / (LAL_C_SI * LAL_ALPHA * LAL_ALPHA))

Definition at line 325 of file LALConstants.h.

◆ LAL_MP_SI

#define LAL_MP_SI 1.672621923684144692109494784075478798e-27

Proton mass, kg.

LAL_MP_SI = (LAL_ME_SI * LAL_MP_ME)

Definition at line 332 of file LALConstants.h.

◆ LAL_AMU_SI

#define LAL_AMU_SI 1.660539066595378801332508797951914123e-27

Atomic mass unit, kg.

LAL_AMU_SI = (LAL_ME_SI / LAL_ME_AMU)

Definition at line 339 of file LALConstants.h.

◆ LAL_AB_SI

#define LAL_AB_SI 5.291772109034624983506063293620795401e-11

Bohr radius, m.

LAL_AB_SI = (LAL_ALPHA / (4 * LAL_PI * LAL_RYD_SI))

Definition at line 346 of file LALConstants.h.

◆ LAL_LAMBDAE_SI

#define LAL_LAMBDAE_SI 2.426310238678370231942278247906312873e-12

Electron Compton wavelength, m.

LAL_LAMBDAE_SI = (2 * LAL_PI * LAL_ALPHA * LAL_AB_SI)

Definition at line 353 of file LALConstants.h.

◆ LAL_RE_SI

#define LAL_RE_SI 2.817940326207927528347087481623789683e-15

Classical electron radius, m.

LAL_RE_SI = (LAL_ALPHA * LAL_ALPHA * LAL_AB_SI)

Definition at line 360 of file LALConstants.h.

◆ LAL_MUB_SI

#define LAL_MUB_SI 9.274010078344114556082608495144137435e-24

Bohr magneton, J T^-1.

LAL_MUB_SI = (LAL_LAMBDAE_SI * LAL_C_SI * LAL_QE_SI / (4 * LAL_PI))

Definition at line 367 of file LALConstants.h.

◆ LAL_MUN_SI

#define LAL_MUN_SI 5.050783746114056140501321131006282803e-27

Nuclear magneton, J T^-1.

LAL_MUN_SI = (LAL_MUB_SI / LAL_MP_ME)

Definition at line 374 of file LALConstants.h.

◆ LAL_ROT_DAY

#define LAL_ROT_DAY 1.00273781191135448

Number of Earth rotations in one UT1 day, dimensionless.

Definition at line 385 of file LALConstants.h.

◆ LAL_DAYJUL_SI

#define LAL_DAYJUL_SI 86400e0

Julian day, s.

Definition at line 386 of file LALConstants.h.

◆ LAL_YRJUL_SI

#define LAL_YRJUL_SI 31557600e0

Julian year, s.

Definition at line 387 of file LALConstants.h.

◆ LAL_LYR_SI

#define LAL_LYR_SI 9460730472580800e0

(Julian) Lightyear, m

Definition at line 388 of file LALConstants.h.

◆ LAL_AU_SI

#define LAL_AU_SI 149597870700e0

Astronomical unit, m.

Definition at line 389 of file LALConstants.h.

◆ LAL_PC_SI

#define LAL_PC_SI 3.085677581491367278913937957796471611e16

Parsec, m.

Definition at line 390 of file LALConstants.h.

◆ LAL_GMEARTH_SI

#define LAL_GMEARTH_SI 3.986004e+14

Nominal Earth mass parameter, m^3 s^-2.

Definition at line 391 of file LALConstants.h.

◆ LAL_REEARTH_SI

#define LAL_REEARTH_SI 6.3781e+6

Nominal Earth equatorial radius, m.

Definition at line 392 of file LALConstants.h.

◆ LAL_RPEARTH_SI

#define LAL_RPEARTH_SI 6.3568e+6

Nominal Earth polar radius, m.

Definition at line 393 of file LALConstants.h.

◆ LAL_GMJUP_SI

#define LAL_GMJUP_SI 1.2668653e+17

Nominal Jupiter mass parameter, m^3 s^-2.

Definition at line 394 of file LALConstants.h.

◆ LAL_REJUP_SI

#define LAL_REJUP_SI 7.1492e+7

Nominal Jupiter equatorial radius, m.

Definition at line 395 of file LALConstants.h.

◆ LAL_RPJUP_SI

#define LAL_RPJUP_SI 6.6854e+7

Nominal Jupiter polar radius, m.

Definition at line 396 of file LALConstants.h.

◆ LAL_GMSUN_SI

#define LAL_GMSUN_SI 1.3271244e+20

Nominal solar mass parameter, m^3 s^-2.

Definition at line 397 of file LALConstants.h.

◆ LAL_RSUN_SI

#define LAL_RSUN_SI 6.957e+8

Nominal solar radius, m.

Definition at line 398 of file LALConstants.h.

◆ LAL_SSUN_SI

#define LAL_SSUN_SI 1361e0

Nominal total solar irradiance, W m^-2.

Definition at line 399 of file LALConstants.h.

◆ LAL_LSUN_SI

#define LAL_LSUN_SI 3.828e+26

Nominal solar luminosity, W.

Definition at line 400 of file LALConstants.h.

◆ LAL_TSUN_SI

#define LAL_TSUN_SI 5772e0

Nominal solar effective temperature, K.

Definition at line 401 of file LALConstants.h.

◆ LAL_REARTH_SI

#define LAL_REARTH_SI 6378136.6

Earth equatorial radius, m.

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 416 of file LALConstants.h.

◆ LAL_AWGS84_SI

#define LAL_AWGS84_SI 6378137e0

Semimajor axis of WGS-84 Reference Ellipsoid, m.

See also: Department of Defense World Geodedic System 1984 http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf

Definition at line 422 of file LALConstants.h.

◆ LAL_BWGS84_SI

#define LAL_BWGS84_SI 6356752.314

Semiminor axis of WGS-84 Reference Ellipsoid, m.

LAL_BWGS84_SI = LAL_AWGS84_SI * (1 - f)

where f is the flattening

1/f = 298.257223563

Note: This constant is not given to full precision for compatibility.

See also: Department of Defense World Geodedic System 1984 http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf

Definition at line 436 of file LALConstants.h.

◆ LAL_IEARTH

#define LAL_IEARTH 0.409092600600582871467239393761915655

Earth inclination (2000), radians.

This is the measured value of the mean obliquity of the ecliptic, 84381.406 arcseconds, converted to radians.

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 445 of file LALConstants.h.

◆ LAL_EEARTH

#define LAL_EEARTH 0.0167

Earth orbital eccentricity, dimensionless.

See also: E. Myles Standish and James G. Williams, Orbital Ephemerides of the Sun, Moon, and Planets ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/ExplSupplChap8.pdf

Definition at line 451 of file LALConstants.h.

◆ LAL_EPREC_SI

#define LAL_EPREC_SI 1.127703867758020059420250393792953007e-12

Rate of Earth precession (2000), Hz.

This is the rate of precession of the Earth, 4612.156534 arcseconds per Julian century, converted to cycles per second, at the epoch J2000.0 (=2000-01-01T12:00:00Z):

LAL_EPREC_SI = 4612.156534 / 36525 / 15 / 86400 / LAL_DAYJUL_SI

See also: Linear (in t) term in Eq. (42) of N. Capitaine, P. T. Wallace and J. Chapront "Expressions for IAU 2000 precession quantities", Astronomy & Astrophysics 412 567 (2003) https://doi.org/10.1051/0004-6361:20031539

Definition at line 469 of file LALConstants.h.

◆ LAL_GMEARTH_TCB_SI

#define LAL_GMEARTH_TCB_SI 3.986004418e+14

Earth mass parameter, m^3 s^-2 (TCB)

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 475 of file LALConstants.h.

◆ LAL_GMEARTH_TDB_SI

#define LAL_GMEARTH_TDB_SI 3.986004356e+14

Earth mass parameter, m^3 s^-2 (TDB)

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 481 of file LALConstants.h.

◆ LAL_GMEARTH_TT_SI

#define LAL_GMEARTH_TT_SI 3.986004415e+14

Earth mass parameter, m^3 s^-2 (TT)

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 487 of file LALConstants.h.

◆ LAL_GMSUN_TCB_SI

#define LAL_GMSUN_TCB_SI 1.32712442099e+20

Solar mass parameter, m^3 s^-2 (TCB)

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 493 of file LALConstants.h.

◆ LAL_GMSUN_TDB_SI

#define LAL_GMSUN_TDB_SI 1.32712440041e+20

Solar mass parameter, m^3 s^-2 (TDB)

See also: http://asa.hmnao.com/SecK/Constants.html

Definition at line 499 of file LALConstants.h.

◆ LAL_YRTROP_SI

#define LAL_YRTROP_SI 31556925.1874707200

Tropical year (2000), s.

See also: Borkowski, K. M., The Tropical Year and Solar Calendar, Journal of the Royal Astronomical Society of Canada, Vol. 85, NO. 3/JUN, P.121, 1991 http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1991JRASC..85..121B&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

Definition at line 505 of file LALConstants.h.

◆ LAL_YRSID_SI

#define LAL_YRSID_SI 31558149.763545600

Sidereal year (2000), s.

See also: http://hpiers.obspm.fr/eop-pc/models/constants.html

Definition at line 511 of file LALConstants.h.

◆ LAL_COSIEARTH

#define LAL_COSIEARTH 0.917482143065241841533315838574859003

Cosine of Earth inclination (2000)

LAL_COSIEARTH = cos(LAL_IEARTH)

Definition at line 529 of file LALConstants.h.

◆ LAL_SINIEARTH

#define LAL_SINIEARTH 0.397776969112605992551264763661918798

Sine of Earth inclination (2000)

LAL_SINIEARTH = sin(LAL_IEARTH)

Definition at line 536 of file LALConstants.h.

◆ LAL_MEARTH_SI

#define LAL_MEARTH_SI 5.972167867791378871192484605127129437e24

Nominal Earth mass, kg.

LAL_MEARTH_SI = LAL_GMEARTH_SI / LAL_G_SI

Definition at line 543 of file LALConstants.h.

◆ LAL_MEARTH_TCB_SI

#define LAL_MEARTH_TCB_SI 5.972168494074284943739418365970963247e24

Earth mass, kg (TCB)

LAL_MEARTH_TCB_SI = LAL_GMEARTH_TCB_SI / LAL_G_SI

Definition at line 550 of file LALConstants.h.

◆ LAL_MEARTH_TDB_SI

#define LAL_MEARTH_TDB_SI 5.972168401180648157859251157424748663e24

Earth mass, kg (TDB)

LAL_MEARTH_TDB_SI = LAL_GMEARTH_TDB_SI / LAL_G_SI

Definition at line 557 of file LALConstants.h.

◆ LAL_MEARTH_TT_SI

#define LAL_MEARTH_TT_SI 5.972168489579431550874248984912275445e24

Earth mass, kg (TT)

LAL_MEARTH_TT_SI = LAL_GMEARTH_TT_SI / LAL_G_SI

Definition at line 564 of file LALConstants.h.

◆ LAL_MJUP_SI

#define LAL_MJUP_SI 1.898124597336050222495242946825884362e27

Nominal Jupiter mass, kg.

LAL_MJUP_SI = LAL_GMJUP_SI / LAL_G_SI

Definition at line 571 of file LALConstants.h.

◆ LAL_MSUN_SI

#define LAL_MSUN_SI 1.988409870698050731911960804878414216e30

Nominal solar mass, kg.

LAL_MSUN_SI = LAL_GMSUN_SI / LAL_G_SI

Definition at line 578 of file LALConstants.h.

◆ LAL_MRSUN_SI

#define LAL_MRSUN_SI 1.476625038050124729627979840144936351e3

Geometrized nominal solar mass, m.

LAL_MRSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI)

Definition at line 585 of file LALConstants.h.

◆ LAL_MTSUN_SI

#define LAL_MTSUN_SI 4.925490947641266978197229498498379006e-6

Geometrized nominal solar mass, s.

LAL_MTSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI * LAL_C_SI)

Definition at line 592 of file LALConstants.h.

◆ LAL_MSUN_TCB_SI

#define LAL_MSUN_TCB_SI 1.988409902147041637325262574352366540e30

Solar mass, kg (TCB)

LAL_MSUN_TCB_SI = LAL_GMSUN_TCB_SI / LAL_G_SI

Definition at line 599 of file LALConstants.h.

◆ LAL_MSUN_TDB_SI

#define LAL_MSUN_TDB_SI 1.988409871312347362270200620289768215e30

Solar mass, kg (TDB)

LAL_MSUN_TDB_SI = LAL_GMSUN_TDB_SI / LAL_G_SI

Definition at line 606 of file LALConstants.h.

◆ LAL_SOL_SID

#define LAL_SOL_SID 1.002737909344968654292933133909634024

Ratio of mean solar day to sidereal day, dimensionless.

This quantity is evaluated at the epoch J2000.0 (=2000-01-01T12:00:00Z) as:

LAL_SOL_SID = LAL_ROT_DAY + LAL_DAYJUL_SI * LAL_EPREC_SI

Definition at line 615 of file LALConstants.h.

◆ LAL_DAYSID_SI

#define LAL_DAYSID_SI 86164.090531333536768710524462700317733190

Mean sidereal day, s.

This quantity is evaluated at the epoch J2000.0 (=2000-01-01T12:00:00Z) as:

LAL_DAYSID_SI = LAL_DAYJUL_SI / LAL_SOL_SID

Definition at line 624 of file LALConstants.h.

◆ LAL_H0FAC_SI

#define LAL_H0FAC_SI 3.240779289444365023237687716352957261e-18

Hubble constant prefactor, s^-1.

LAL_H0FAC_SI = 100 km s^-1 Mpc^-1

Definition at line 651 of file LALConstants.h.

◆ LAL_H0_SI

#define LAL_H0_SI (0.69 * LAL_H0FAC_SI)

Approximate Hubble constant, s^-1.

LAL_H0_SI = h0 * LAL_H0FAC_SI

where h0 is approximately 0.69 (the value adopted here).

See also: http://arxiv.org/abs/1303.5062; http://dx.doi.org/10.1088/0067-0049/208/2/20

Definition at line 662 of file LALConstants.h.

◆ LAL_RHOCFAC_SI

#define LAL_RHOCFAC_SI 1.688169255655572064052978218230767915e-9

Critical energy density prefactor, J m^-3.

LAL_RHOCFAC_SI = 3 * (LAL_H0FAC_SI * LAL_C_SI)^2 / (8 * LAL_PI * LAL_G_SI)

Definition at line 669 of file LALConstants.h.

◆ LAL_RHOC_SI

#define LAL_RHOC_SI (0.69 * 0.69 * LAL_RHOCFAC_SI)

Approximate critical energy density, J m^-3.

LAL_RHOC_SI = h0^2 * LAL_RHOCFAC_SI

where h0 is approximately 0.69 (the value adopted here).

See also: http://arxiv.org/abs/1303.5062; http://dx.doi.org/10.1088/0067-0049/208/2/20

Definition at line 680 of file LALConstants.h.

◆ LAL_TCMB_SI

#define LAL_TCMB_SI 2.72548

Cosmic microwave background radiation temperature, K.

See also: http://dx.doi.org/10.1088/0004-637X/707/2/916

Definition at line 686 of file LALConstants.h.

◆ LAL_VCMB_SI

#define LAL_VCMB_SI 369883.9346804

Solar velocity with respect to the cosmic microwave background radiation, m s^-1.

Adopted value is v/c = 0.0012338

See also: http://dx.doi.org/10.1088/0004-637X/707/2/916

Definition at line 694 of file LALConstants.h.

◆ LAL_NCMB_SI

#define LAL_NCMB_SI 4.107178061233267795913602167900672966e8

Number density of cosmic microwave background radiation photons, m^-3.

LAL_NCMB_SI = 16 * zeta(3) * LAL_PI * (LAL_K_SI * LAL_TCMB_SI / (LAL_C_SI * LAL_H_SI))^3

where zeta is the Riemann zeta function and zeta(3) is Apery's constant.

See also: http://oeis.org/A002117

Definition at line 704 of file LALConstants.h.

◆ LAL_SCMB_SI

#define LAL_SCMB_SI 2.042296344521760298284258925842980552e-14

Entropy density of cosmic microwave background radiation, J K^-1 m^-3.

LAL_SCMB_SI = 4 * LAL_PI^2 * LAL_K_SI * (LAL_K_SI * LAL_TCMB_SI / (LAL_C_SI * LAL_HBAR_SI))^3 / 45

Definition at line 711 of file LALConstants.h.