LAL  7.1.7.1-37cf38b
Header LALConstants.h

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
#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...
 

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_SI   3.986004418e+14
 Geocentric gravitational constant, m^3 s^-2 (TCB) More...
 
#define LAL_RSUN_SI   6.96342e+8
 Solar equatorial radius, m. More...
 
#define LAL_LSUN_SI   3.846e+26
 Solar luminosity, W. More...
 
#define LAL_GMSUN_SI   1.32712442099e+20
 Solar mass parameter, m^3 s^-2 (TCB) 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   5.972168494074284943739418365970963247e24
 Earth mass, kg. More...
 
#define LAL_MSUN_SI   1.988409902147041637325262574352366540e30
 Solar mass, kg. More...
 
#define LAL_MRSUN_SI   1.476625061404649406193430731479084713e3
 Geometrized solar mass, m. More...
 
#define LAL_MTSUN_SI   4.925491025543575903411922162094833998e-6
 Geometrized solar mass, s. 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 384 of file LALConstants.h.

◆ LAL_DAYJUL_SI

#define LAL_DAYJUL_SI   86400e0

Julian day, s.

Definition at line 385 of file LALConstants.h.

◆ LAL_YRJUL_SI

#define LAL_YRJUL_SI   31557600e0

Julian year, s.

Definition at line 386 of file LALConstants.h.

◆ LAL_LYR_SI

#define LAL_LYR_SI   9460730472580800e0

(Julian) Lightyear, m

Definition at line 387 of file LALConstants.h.

◆ LAL_AU_SI

#define LAL_AU_SI   149597870700e0

Astronomical unit, m.

Definition at line 388 of file LALConstants.h.

◆ LAL_PC_SI

#define LAL_PC_SI   3.085677581491367278913937957796471611e16

Parsec, m.

Definition at line 389 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 404 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 410 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 424 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 433 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 439 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 457 of file LALConstants.h.

◆ LAL_GMEARTH_SI

#define LAL_GMEARTH_SI   3.986004418e+14

Geocentric gravitational constant, m^3 s^-2 (TCB)

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

Definition at line 463 of file LALConstants.h.

◆ LAL_RSUN_SI

#define LAL_RSUN_SI   6.96342e+8

Solar equatorial radius, m.

See also
http://dx.doi.org/10.1088/0004-637X/750/2/135

Definition at line 469 of file LALConstants.h.

◆ LAL_LSUN_SI

#define LAL_LSUN_SI   3.846e+26

Solar luminosity, W.

See also
http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html

Definition at line 475 of file LALConstants.h.

◆ LAL_GMSUN_SI

#define LAL_GMSUN_SI   1.32712442099e+20

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

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

Definition at line 481 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 487 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 493 of file LALConstants.h.

◆ LAL_COSIEARTH

#define LAL_COSIEARTH   0.917482143065241841533315838574859003

Cosine of Earth inclination (2000)

LAL_COSIEARTH = cos(LAL_IEARTH)

Definition at line 511 of file LALConstants.h.

◆ LAL_SINIEARTH

#define LAL_SINIEARTH   0.397776969112605992551264763661918798

Sine of Earth inclination (2000)

LAL_SINIEARTH = sin(LAL_IEARTH)

Definition at line 518 of file LALConstants.h.

◆ LAL_MEARTH_SI

#define LAL_MEARTH_SI   5.972168494074284943739418365970963247e24

Earth mass, kg.

LAL_MEARTH_SI = LAL_GMEARTH_SI / LAL_G_SI

Definition at line 525 of file LALConstants.h.

◆ LAL_MSUN_SI

#define LAL_MSUN_SI   1.988409902147041637325262574352366540e30

Solar mass, kg.

LAL_MSUN_SI = LAL_GMSUN_SI / LAL_G_SI

Definition at line 532 of file LALConstants.h.

◆ LAL_MRSUN_SI

#define LAL_MRSUN_SI   1.476625061404649406193430731479084713e3

Geometrized solar mass, m.

LAL_MRSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI)

Definition at line 539 of file LALConstants.h.

◆ LAL_MTSUN_SI

#define LAL_MTSUN_SI   4.925491025543575903411922162094833998e-6

Geometrized solar mass, s.

LAL_MTSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI * LAL_C_SI)

Definition at line 546 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 555 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 564 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 591 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 602 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 609 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 620 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 626 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 634 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 644 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 651 of file LALConstants.h.