Simon Jeffery's Software Store
TAP global constants
Quick Reference
| MODULE TAP_PAR |
TAP public global constants.
|
| MODULE TAPM_PAR |
TAP public mathematical constants.
|
| MODULE TAPP_PAR |
TAP public physical constants.
|
| MODULE TAPA_PAR |
TAP public astronomical constants.
|
| MODULE TAPC_PAR |
TAP public chemical constants.
|
| MODULE MCH_PAR |
TAP public global constants.
|
Long Reference
Purpose:
Theoretical Astrophysics Library public global constants.
Invocation:
USE TAP_PAR
Description:
This file defines all the TAP public global constants which refer
to the way the package is accessed. It does not include physical
values, these are contained in modules TAPA_PAR, TAPC_PAR, TAPM_PAR
and TAPP_PAR for the astrophysical, chemical,
mathematical and physical public global constants respectively.
Purpose:
Theoretical Astrophysics Library public global mathematical constants.
Invocation:
USE TAPM_PAR [, ONLY .name. [ => .newname. ][, name2 ...] ]
Examples:
USE TAPM_PAR
USE TAPM_PAR, ONLY TAPM__PIB2
USE TAPM_PAR, ONLY TAPM__PIB2 => pi_by_2, TAPM__E => e
Description:
This file defines the mathematical global constants used by the
Theoretical Astrophysics Library. All values were generated using
the MAPLE symbolic computation package (Char, B.W., Geddes, K.O.,
Gonnet, G.H., Monagan, M.B., and Watt, S.M., 1988, Watcom
Publications, Waterloo, Ontario, Canada). All values are accurate
to 34 decimal digits and are declared as DOUBLE PRECISION constants.
Constants by name:
TAPM__PI :: PI
TAPM__PIB2 :: PI / 2.0D+00
TAPM__2PI :: 2.0D+00 * PI
TAPM__1B2PI :: 1.0D+00 / ( 2.0D+00 * PI )
TAPM__4PI :: 4.0D+00 * PI
TAPM__1B4PI :: 1.0D+00 / ( 4.0D+00 * PI )
TAPM__PISQ :: PI**2
TAPM__SQTPI :: SQRT( PI )
TAPM__LGPI :: LOG10( PI )
TAPM__LNPI :: LOG( PI )
TAPM__DTOR :: PI / 180.0D+00
TAPM__RTOD :: 180.0D+00 / PI
TAPM__ASTOR :: PI / ( 180.0D+00 * 3600.0D+00 )
TAPM__RTOAS :: ( 180.0D+00 * 3600.0D+00 ) / PI
TAPM__HTOR :: PI / 12.0D+00
TAPM__RTOH :: 12.0D+00 / PI
TAPM__STOR :: PI / ( 12.0D+00 * 3600.0D+00 )
TAPM__RTOS :: ( 12.0D+00 * 3600.0D+00 ) / PI
TAPM__E :: E
TAPM__LGE :: LOG10( E )
TAPM__EPI :: E**PI
TAPM__GAMMA :: LIM (M -> INF.) [ 1 + 1/2 + 1/3 + 1/4 + ... + 1/M - ln M ]
TAPM__LNGAM :: LOG ( GAMMA )
TAPM__SQT2 :: SQRT( 2.0D+00 )
TAPM__LG2 :: LOG10( 2.0D+00 )
TAPM__LN2 :: LOG( 2.0D+00 )
TAPM__SQT3 :: SQRT( 3.0D+00 )
TAPM__LG3 :: LOG10( 3.0D+00 )
TAPM__LN3 :: LOG( 3.0D+00 )
TAPM__SQT10 :: SQRT( 10.0D+00 )
TAPM__LN10 :: LOG( 10.0D+00 )
Purpose:
Theoretical Astrophysics Library public global physical constants.
Invocation:
USE TAPP_PAR [, ONLY .name. [ => .newname. ][, name2 ...] ]
Examples:
USE TAPP_PAR
USE TAPP_PAR, ONLY: TAPP__C
USE TAPP_PAR, ONLY: TAPP__G, TAPP__C => CLIGHT
Description:
This file defines the physical global constants used by the
Theoretical Astrophysics Library. Most values were taken from the
1986 CODATA Recommended Values of the Fundamental Physical
Constants (Cohen, E.R., and Taylor, B.N., 1987, Journal of
Research of the National Bureau of Standards, Vol. 92, 85).
Other sources were used where necessary and given in the comments
for the constants concerned. All values are declared as DOUBLE
PRECISION constants. Experimentally determined values are are
accurate to their specified standard deviations given in the
comment script. Exact values are given to 34 decimal digits and
were evaluated using the MAPLE symbolic computation package
(Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B., and Watt,
S.M., 1988, Watcom Publications, Waterloo, Ontario, Canada).
Constants by name:
TAPP__C :: Speed of light in a vacuum: c = 2.99792458E+08 m/s (exact).
TAPP_M0 :: Permeability of a vacuum: mu(0) = 4.0E-07Pi N/A**2 (exact).
TAPP__E0 :: Permittivity of a vacuum: epsilon(0) = 1/mu(0)c**2 F/m (exact).
TAPP__G :: Newtonian constant of gravitation: G = 6.67259E-11 m**3/kg s**2,
error = 0.00085E-11.
TAPP__H :: Planck constant: h = 6.6260755E-34 J s,
error = 0.0000040E-34.
TAPP__HB2PI :: Planck constant: h(bar) = h/2Pi = 1.05457266E-34 J s,
error = 0.00000063E-34.
TAPP__E :: Elementary charge: e = 1.60217733E-19 C,
error = 0.00000049E-19.
TAPP__P0 :: Magnetic flux quantum: Phi(0) = h/2e = 2.06783461E-15 Wb,
error = 0.00000061E-15.
TAPP__ME :: Electron mass: m(e) = 9.1093897E-31 kg,
error = 0.0000054E-31.
TAPP__MP :: Proton mass: m(p) = 1.6726231E-27 kg,
error = 0.0000010E-27.
TAPP__MPBME :: Proton-electron mass ratio: m(p)/m(e) = 1.836152701E+03
error = 0.000000037E+03.
TAPP__MN :: Neutron mass: m(n) = 1.6749286E-27 kg,
error = 0.0000010E-27.
TAPP__A :: Fine-structure constant: alpha = mu(0)ce**2/2h = 7.29735308E-03,
error = 0.00000033E-03.
TAPP__RYD :: Rydberg constant: R(infty) = m(e)c alpha**2/2h = 1.0973731534E+07 m**(-1),
error = 0.0000000013E+07.
TAPP__A0 :: Bohr radius: a(0) = alpha/((4pi R(infty)) = 0.529177249E-10 m
error = 0.000000024E-10.
TAPP__NA :: Avogadro constant: N(A) = L = 6.0221367E+23 mol**(-1),
error = 0.0000036E+23.
TAPP__F :: Faraday constant: F = N(A)e = 9.6485309E+04 C/mol,
error = 0.0000029E+04.
TAPP__R :: Molar gas constant: R = 8.314510 J/mol K,
error = 0.000070.
TAPP__K :: Boltzmann constant: k = R/N(A) = 1.380658E-23 J/K,
error = 0.000012E-23.
TAPP__S :: Stefan-Boltzmann constant: sigma = (Pi**2/60) k**4/h**3 c**2
= 5.67051E-08 W/m**2 K**4,
error = 0.00019E-08.
TAPP__EV :: Electron volt: eV = e/C = 1.60217733E-19 J,
error = 0.00000049E-19.
TAPP__U :: (Unified) atomic mass unit: u = m(u) = m(12C)/12 = 1.6605402E-27 kg,
error = 0.0000010E-27.
Purpose:
Theoretical Astrophysics Library public astronomical constants
Invocation:
USE TAPA_PAR [, ONLY .name. [ => .newname. ][, name2 ...] ]
Examples:
USE TAPA_PAR
USE TAPA_PAR, ONLY: TAPA__MSOL
USE TAPA_PAR, ONLY: TAPA__MSOL => Msun
Description:
This file contains the astronomical global constants used by the
Theoretical Astrophysics Library. These come from a number of
sources, including:
a) IAU (1976) System of Astronomical Constants
The IAU recognises a set of astronomical units of length, mass
and time for use in connection with motions in the Solar System;
they are related to each other through the adopted value of the
constant of gravitation when expressed in these units. The unit
of length is the au (A), the unit of time is 1 day (D) of 86 400
SI seconds (s), the unit of mass is equal to the mass of the Sun
(S). For larger quantities, the IAU recommend that the parsec,
defined in au, and the Julian year (365.25 d) should be used.
The defining constants in this system are the Gaussian
gravitational constant (k) and the speed of light (c).
Primary constants are best values from observations and
derived constants are calculated from defining and primary
constants.
The question of combining constants from two systems (CODATA and
IAU) in the TAP library raises certain difficulties. For
example, the recommended value for the gravitational constant is
specified with greater precision in CODATA than in IAU (1976).
The IAU recommendations are given without errors.
To overcome possible conflicts, TAP adopts CODATA constants
where available. Errors for IAU (1976) constants are estimated
from the modifications required to prepare and fit ephemerides
to observation (Astronomical Almanac 1992). Derived constants are
calculated accordingly.
b) Astrophysical Quantities (1973).
Observed values for the solar radius and luminosity are mean
values (1973). A variation in luminosity of 0.05 percent around
the 22 year solar cycle has been measured. Larger amplitude
variations over other timescales are indicated. Historical
measurements of the solar radius indicate a reduction by 0.3 per
cent since observations by Picard and others during the Maunder
minimum (1640 - 1700).
References:
Transactions of the International Astronomical Union. Vol. XVIB
1976. Proceedings of the Sixteenth General Assembly, Grenoble
1976, p.58. eds. E.A.Mueller & A.Jappel. Reidel, Dordrecht.
Astronomical Almanac, 1992. p K6. US Government Printing Office,
Washington, & HM Stationery Office, London
Allen C.W., 1973. Astrophysical Quantities (3rd edn), p. 161.
Constants by name:
TAPA__PI :: PI (needed locally)
TAPA__K :: Gaussian gravitational constant: k = 0.01720209895 (exact).
TAPA__DAY :: Day: d = 8.64E+04 s (exact).
TAPA__JYEAR :: Julian Year: Jyear = 365.25 d = 3.15576E+07 s (exact).
TAPA__AU :: Astronomical Unit: AU = 1.49597870E+11 m
error = 0.00000001E+11.
TAPA__PC :: Parsec: pc = 360 * 60 * 60 / 2pi * A m (derived).
TAPA__MSOL :: Solar Mass: M(sol) = 1.98892E+30 kg
error = 0.00025E+30.
TAPA__RSOL :: Solar radius: R(sol) = 6.9599E+08 m
error = 0.0007E+08.
TAPA__GSOL :: Solar surface gravity: g(sol) = G * M(sol) / R(sol)**2
= 2.7397E+02 m/s**2
error = 0.0005E+02.
TAPA__LSOL :: Solar luminosity: L(sol) = 3.826E+26 J/s
error = 0.008E+26.
TAPA__TESOL :: Solar effective temperature:
Teff(sol) = ( L / ( 4 * pi * sigma * R**2 ) ) ** (1/4)
= 5.770E+03 K
error = 0.006E+03.
Purpose:
Theoretical Astrophysics Library chemical global constants.
Invocation:
USE TAPC_PAR [, ONLY .name. [ => .newname. ][, name2 ...] ]
Description:
This file is a holder to define chemical public global constants
used by the Theoretical Astrophysics library. There are currently
no constants provided by this module.
Purpose:
Machine-dependent constants.
Invocation:
USE MCH_PAR [, ONLY .name. [ => .newname. ][, name2 ...] ]
Machine:
Compaq Alpha
Description:
This file defines the machine dependent constants relevant for
Fortran floating point arithmetic.
In order to write certain numerical procedures, numbers such as the
machine precision and the smallest and largest allowed positive
numbers allowed need to be known. Such important properties of
floating-point arithmetic may be characterised by a simplified
_model_ containing a small number of (machine-dependent) parameters,
which may be chosen to describe closely the behaviour of floating point
arithmetic.
The model adopted here is based on that developed by Brown (1981),
and implemented in the NAG library (chapter X02). It is characterized
five parameters, B, P, EMIN, EMAX and ROUNDS. The machine precision (EPS),
smallest (SMALL) and largest (LARGE) positive model numbers, and the safe
range (SAFE) parameter, can be characterized in terms of these quantities.
Both the primitive parameters, and selected dependent quantities are
given in this file, to avoid the need for additional computations.
The file also contains parameters relating to other aspects of the
computing environment.
Reference:
Brown W.S., 1981. ACM Trans. Math. Software 7, 445.
NAG Fortran Library ...
Constants by name:
MCH__B :: Model parameter B.
MCH__P :: Model parameter P.
MCH__EMIN :: Model parameter EMIN.
MCH__EMAX :: Model parameter EMAX.
MCH__ROUND :: Model parameter ROUNDS.
MCH__EPS :: Machine precision EPS.
MCH__SMALL :: Smallest positive model number SMALL.
MCH__LARGE :: Largest positive model number LARGE.
MCH__SAFE :: Safe range parameter SAFE.
MCH__ILARGE :: Largest positive integer ILARGE.
MCH__DIGITS :: Precision in decimal digits DIGITS.