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Defines |
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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.
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| #define | LAL_REAL4_MANT 24 |
| | Bits of precision in the mantissa of a REAL4.
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| #define | LAL_REAL4_MAX 3.40282347e+38 |
| | Largest REAL4.
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| #define | LAL_REAL4_MIN 1.17549435e-38 |
| | Smallest nonzero REAL4.
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| #define | LAL_REAL4_EPS 1.19209290e-07 |
| | 0.5^(LAL_REAL4_MANT-1), i.e.
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| #define | LAL_REAL8_MANT 53 |
| | Bits of precision in the mantissa of a REAL8.
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| #define | LAL_REAL8_MAX 1.7976931348623157e+308 |
| | Largest REAL8.
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| #define | LAL_REAL8_MIN 2.2250738585072014e-308 |
| | Smallest nonzero REAL8.
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| #define | LAL_REAL8_EPS 2.2204460492503131e-16 |
| | 0.5^(LAL_REAL8_MANT-1), i.e.
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The following are fundamental mathematical constants.
They are mostly taken from the GNU C math.h header (with the exception of LAL_TWOPI, which was computed using Maple). All numbers are dimensionless.
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| #define | LAL_E 2.7182818284590452353602874713526625 |
| | e
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| #define | LAL_LOG2E 1.4426950408889634073599246810018922 |
| | log_2 e
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| #define | LAL_LOG10E 0.4342944819032518276511289189166051 |
| | log_10 e
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| #define | LAL_LN2 0.6931471805599453094172321214581766 |
| | log_e 2
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| #define | LAL_LN10 2.3025850929940456840179914546843642 |
| | log_e 10
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| #define | LAL_SQRT2 1.4142135623730950488016887242096981 |
| | sqrt(2)
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| #define | LAL_SQRT1_2 0.7071067811865475244008443621048490 |
| | 1/sqrt(2)
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| #define | LAL_GAMMA 0.5772156649015328606065120900824024 |
| | gamma
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| #define | LAL_PI 3.1415926535897932384626433832795029 |
| | pi
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| #define | LAL_TWOPI 6.2831853071795864769252867665590058 |
| | 2*pi
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| #define | LAL_PI_2 1.5707963267948966192313216916397514 |
| | pi/2
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| #define | LAL_PI_4 0.7853981633974483096156608458198757 |
| | pi/4
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| #define | LAL_1_PI 0.3183098861837906715377675267450287 |
| | 1/pi
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| #define | LAL_2_PI 0.6366197723675813430755350534900574 |
| | 2/pi
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| #define | LAL_2_SQRTPI 1.1283791670955125738961589031215452 |
| | 2/sqrt(pi)
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| #define | LAL_PI_180 1.7453292519943295769236907684886127e-2 |
| | pi/180
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| #define | LAL_180_PI 57.295779513082320876798154814105170 |
| | 180/pi
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| #define | LAL_C_SI 299792458 |
| | Speed of light in vacuo, m s^-1.
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| #define | LAL_EPSILON0_SI 8.8541878176203898505365630317107503e-12 |
| | Permittivity of free space, C^2 N^-1 m^-2.
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| #define | LAL_MU0_SI 1.2566370614359172953850573533118012e-6 |
| | Permeability of free space, N A^-2.
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| #define | LAL_GEARTH_SI 9.80665 |
| | Standard gravity, m s^-2.
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| #define | LAL_PATM_SI 101325 |
| | Standard atmosphere, Pa.
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The following are measured fundamental physical constants, with values given in Barnet (1996).
When not dimensionless, they are given in the SI units shown.
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| #define | LAL_G_SI 6.67259e-11 |
| | Gravitational constant, N m^2 kg^-2.
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| #define | LAL_H_SI 6.6260755e-34 |
| | Planck constant, J s.
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| #define | LAL_HBAR_SI 1.05457266e-34 |
| | Reduced Planck constant, J s.
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| #define | LAL_MPL_SI 2.17671e-8 |
| | Planck mass, kg.
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| #define | LAL_LPL_SI 1.61605e-35 |
| | Planck length, m.
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| #define | LAL_TPL_SI 5.39056e-44 |
| | Planck time, s.
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| #define | LAL_K_SI 1.380658e-23 |
| | Boltzmann constant, J K^-1.
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| #define | LAL_R_SI 8.314511 |
| | Ideal gas constant, J K^-1.
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| #define | LAL_MOL 6.0221367e23 |
| | Avogadro constant, dimensionless.
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| #define | LAL_BWIEN_SI 2.897756e-3 |
| | Wien displacement law constant, m K.
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| #define | LAL_SIGMA_SI 5.67051e-8 |
| | Stefan-Boltzmann constant, W m^-2 K^-4.
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| #define | LAL_AMU_SI 1.6605402e-27 |
| | Atomic mass unit, kg.
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| #define | LAL_MP_SI 1.6726231e-27 |
| | Proton mass, kg.
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| #define | LAL_ME_SI 9.1093897e-31 |
| | Electron mass, kg.
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| #define | LAL_QE_SI 1.60217733e-19 |
| | Electron charge, C.
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| #define | LAL_ALPHA 7.297354677e-3 |
| | Fine structure constant, dimensionless.
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| #define | LAL_RE_SI 2.81794092e-15 |
| | Classical electron radius, m.
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| #define | LAL_LAMBDAE_SI 3.86159323e-13 |
| | Electron Compton wavelength, m.
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| #define | LAL_AB_SI 5.29177249e-11 |
| | Bohr radius, m.
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| #define | LAL_MUB_SI 9.27401543e-24 |
| | Bohr magneton, J T^-1.
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| #define | LAL_MUN_SI 5.05078658e-27 |
| | Nuclear magneton, J T^-1.
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The following parameters are derived from measured properties of the Earth and Sun.
The values are taken from Barnet (1996), except for the obliquity of the ecliptic plane and the eccentricity of Earth's orbit, which are taken from Lang (1992). All values are given in the SI units shown.
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| #define | LAL_REARTH_SI 6.378140e6 |
| | Earth equatorial radius, m.
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| #define | LAL_AWGS84_SI 6.378137e6 |
| | Semimajor axis of WGS-84 Reference Ellipsoid, m.
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| #define | LAL_BWGS84_SI 6.356752314e6 |
| | Semiminor axis of WGS-84 Reference Ellipsoid, m.
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| #define | LAL_MEARTH_SI 5.97370e24 |
| | Earth mass, kg.
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| #define | LAL_IEARTH 0.409092804 |
| | Earth inclination (2000), radians.
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| #define | LAL_EEARTH 0.0167 |
| | Earth orbital eccentricity.
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| #define | LAL_RSUN_SI 6.960e8 |
| | Solar equatorial radius, m.
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| #define | LAL_MSUN_SI 1.98892e30 |
| | Solar mass, kg.
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| #define | LAL_MRSUN_SI 1.47662504e3 |
| | Geometrized solar mass, m.
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| #define | LAL_MTSUN_SI 4.92549095e-6 |
| | Geometrized solar mass, s.
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| #define | LAL_LSUN_SI 3.846e26 |
| | Solar luminosity, W.
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| #define | LAL_AU_SI 1.4959787066e11 |
| | Astronomical unit, m.
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| #define | LAL_PC_SI 3.0856775807e16 |
| | Parsec, m.
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| #define | LAL_YRTROP_SI 31556925.2 |
| | Tropical year (1994), s.
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| #define | LAL_YRSID_SI 31558149.8 |
| | Sidereal year (1994), s.
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| #define | LAL_DAYSID_SI 86164.09053 |
| | Mean sidereal day, s.
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| #define | LAL_LYR_SI 9.46052817e15 |
| | ``Tropical'' lightyear (1994), m
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| #define | LAL_H0FAC_SI 3.2407792903e-18 |
| | Hubble constant prefactor, s^-1.
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| #define | LAL_H0_SI 2e-18 |
| | Approximate Hubble constant, s^-1.
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| #define | LAL_RHOCFAC_SI 1.68860e-9 |
| | Critical density prefactor, J m^-3.
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| #define | LAL_RHOC_SI 7e-10 |
| | Approximate critical density, J m^-3.
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| #define | LAL_TCBR_SI 2.726 |
| | Cosmic background radiation temperature, K.
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| #define | LAL_VCBR_SI 3.695e5 |
| | Solar velocity with respect to CBR, m s^-1.
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| #define | LAL_RHOCBR_SI 4.177e-14 |
| | Energy density of CBR, J m^-3.
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| #define | LAL_NCBR_SI 4.109e8 |
| | Number density of CBR photons, m^-3.
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| #define | LAL_SCBR_SI 3.993e-14 |
| | Entropy density of CBR, J K^-1 m^-3.
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Functions |
| | NRCSID (LALCONSTANTSH,"$Id: LALConstants.h,v 1.12 2007/06/08 14:41:52 bema Exp $") |
D.
1.5.2
and 
are taken from Barnet (1996), 
is from Lang (1992), while 
and 
are computed from 
is equal to the actual Hubble constant 
divided by 
. Thus the Hubble constant can be written as: 
. Similarly, the critical energy density 
required for spatial flatness is given by: 
. Current estimates give