LAL  7.1.7.1-f7f2ccf
LALConstants.h
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1 /*
2 * Copyright (C) 2007 Jolien Creighton
3 *
4 * This program is free software; you can redistribute it and/or modify
5 * it under the terms of the GNU General Public License as published by
6 * the Free Software Foundation; either version 2 of the License, or
7 * (at your option) any later version.
8 *
9 * This program is distributed in the hope that it will be useful,
10 * but WITHOUT ANY WARRANTY; without even the implied warranty of
11 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 * GNU General Public License for more details.
13 *
14 * You should have received a copy of the GNU General Public License
15 * along with with program; see the file COPYING. If not, write to the
16 * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
17 * MA 02110-1301 USA
18 */
19 
20 /**
21  * @defgroup LALConstants_h Header LALConstants.h
22  * @ingroup lal_std
23  * @author Creighton, T. D.
24  * @brief Provides standard numerical constants for LAL.
25  *
26  * This header defines a number of useful numerical constants
27  * for use in LAL routines. These constants come in three basic
28  * flavours: arithmetic and mathematical constants, fundamental (or
29  * defined) physical constants, and measured astrophysical and
30  * cosmological parameters.
31  *
32  * Note that this header is not included automatically by the header
33  * <tt>LALStdlib.h</tt>. Include it explicitly if you need any of these
34  * constants.
35  *//** @{ */
36 
37 /** @{ */
38 #ifndef _LALCONSTANTS_H
39 #define _LALCONSTANTS_H
40 
41 #ifdef __cplusplus
42 extern "C" {
43 #endif
44 
45 /**
46  * @name Floating-point constants
47  * The following constants define the precision and range of
48  * floating-point arithmetic in LAL. They are taken from the IEEE
49  * standard 754 for binary arithmetic. All numbers are dimensionless.
50  * @see http://dx.doi.org/10.1109/IEEESTD.2008.4610935
51  */
52 /** @{ */
53 #if __STDC_VERSION__ >= 199901L
54 #define LAL_REAL4_MANT 24 /**< Bits of precision in the mantissa of a REAL4 */
55 #define LAL_REAL4_MAX 0x1.fffffe0000000p+127 /**< Largest normalized REAL4 number (2-2^-23)*2^127 */
56 #define LAL_REAL4_MIN 0x1.0000000000000p-126 /**< Smallest normalized REAL4 number 2^-126 */
57 #define LAL_REAL4_EPS 0x1.0000000000000p-23 /**< Difference between 1 and the next resolvable REAL4 2^-23 */
58 #define LAL_REAL8_MANT 53 /**< Bits of precision in the mantissa of a REAL8 */
59 #define LAL_REAL8_MAX 0x1.fffffffffffffp+1023 /**< Largest normalized REAL8 number (2-2^-52)*2^1023 */
60 #define LAL_REAL8_MIN 0x1.0000000000000p-1022 /**< Smallest normalized REAL8 number 2^-1022 */
61 #define LAL_REAL8_EPS 0x1.0000000000000p-52 /**< Difference between 1 and the next resolvable REAL8 2^-52 */
62 #else
63 #define LAL_REAL4_MANT 24
64 #define LAL_REAL4_MAX 3.4028234663852886e+38
65 #define LAL_REAL4_MIN 1.1754943508222875e-38
66 #define LAL_REAL4_EPS 1.1920928955078125e-07
67 #define LAL_REAL8_MANT 53
68 #define LAL_REAL8_MAX 1.797693134862315708145274237317043568e308
69 #define LAL_REAL8_MIN 2.225073858507201383090232717332404064e-308
70 #define LAL_REAL8_EPS 2.220446049250313080847263336181640625e-16
71 #endif
72 /** @} */
73 
74 /**
75  * @name Integer constants
76  * Extremal integer values, all expressed as unsigned long long.
77  */
78 /** @{ */
79 #define LAL_UINT8_MAX LAL_UINT8_C(18446744073709551615)
80 #define LAL_UINT4_MAX LAL_UINT8_C(4294967295)
81 #define LAL_UINT2_MAX LAL_UINT8_C(65535)
82 #define LAL_INT8_MAX LAL_UINT8_C(9223372036854775807)
83 #define LAL_INT4_MAX LAL_UINT8_C(2147483647)
84 #define LAL_INT2_MAX LAL_UINT8_C(32767)
85 /** @} */
86 
87 /**
88  * @name Mathematical constants
89  * All are dimensionless.
90  *
91  * @def LAL_E
92  * @brief Euler's constant, e
93  * @see https://oeis.org/A001113
94  *
95  * @def LAL_LOG2E
96  * @brief base-2 logarithm of e, log_2(e)
97  * @see http://oeis.org/A007525
98  *
99  * @def LAL_LOG10E
100  * @brief common logarithm of e, log_10(e)
101  * @see http://oeis.org/A002285
102  *
103  * @def LAL_LN2
104  * @brief natural log of 2, ln(2)
105  * @see http://oeis.org/A002162
106  *
107  * @def LAL_LN10
108  * @brief natural log of 10, ln(10)
109  * @see http://oeis.org/A002392
110  *
111  * @def LAL_SQRT2
112  * @brief Pythagoras's constant, sqrt(2)
113  * @see https://oeis.org/A002193
114  *
115  * @def LAL_SQRT1_2
116  * @brief 1/sqrt(2)
117  * @see https://oeis.org/A010503
118  *
119  * @def LAL_GAMMA
120  * @brief Euler-Mascheroni constant, gamma
121  * @see https://oeis.org/A001620
122  *
123  * @def LAL_EXPGAMMA
124  * @brief exp(gamma)
125  * @see https://oeis.org/A073004
126  *
127  * @def LAL_PI
128  * @brief Archimedes's constant, pi
129  * @see https://oeis.org/A000796
130  *
131  * @def LAL_TWOPI
132  * @brief 2*pi is circumference of a circle divided by its radius
133  * @see https://oeis.org/A019692
134  *
135  * @def LAL_PI_2
136  * @brief pi/2
137  * @see http://oeis.org/A019669
138  *
139  * @def LAL_PI_4
140  * @brief pi/4 is the least positive solution to sin(x) = cos(x)
141  * @see http://oeis.org/A003881
142  *
143  * @def LAL_1_PI
144  * @brief 1/pi is the ratio of the volume of a regular octahedron
145  * to the volume of the circumscribed sphere
146  * @see http://oeis.org/A049541
147  *
148  * @def LAL_2_PI
149  * @brief 2/pi is Buffon's constant
150  * @see http://oeis.org/A060294
151  *
152  * @def LAL_2_SQRTPI
153  * @brief 2/sqrt(pi)
154  * @see http://oeis.org/A190732
155  *
156  * @def LAL_PI_180
157  * @brief 180/pi is the number of degrees in one radian
158  * @see http://oeis.org/A072097
159  *
160  * @def LAL_180_PI
161  * @brief pi/180 is the number of radians in one degree
162  * @see http://oeis.org/A019685
163  *
164  * @def LAL_LNPI
165  * @brief natural log of pi, ln(pi)
166  * @see http://oeis.org/A053510
167  */
168 /** @{ */
169 #define LAL_E 2.718281828459045235360287471352662498
170 #define LAL_LOG2E 1.442695040888963407359924681001892137
171 #define LAL_LOG10E 0.434294481903251827651128918916605082
172 #define LAL_LN2 0.693147180559945309417232121458176568
173 #define LAL_LN10 2.302585092994045684017991454684364208
174 #define LAL_SQRT2 1.414213562373095048801688724209698079
175 #define LAL_SQRT1_2 0.707106781186547524400844362104849039
176 #define LAL_GAMMA 0.577215664901532860606512090082402431
177 #define LAL_EXPGAMMA 1.781072417990197985236504103107179549
178 /* Assuming we're not near a black hole or in Tennessee... */
179 #define LAL_PI 3.141592653589793238462643383279502884
180 #define LAL_TWOPI 6.283185307179586476925286766559005768
181 #define LAL_PI_2 1.570796326794896619231321691639751442
182 #define LAL_PI_4 0.785398163397448309615660845819875721
183 #define LAL_1_PI 0.318309886183790671537767526745028724
184 #define LAL_2_PI 0.636619772367581343075535053490057448
185 #define LAL_2_SQRTPI 1.128379167095512573896158903121545172
186 #define LAL_PI_180 1.745329251994329576923690768488612713e-2
187 #define LAL_180_PI 57.295779513082320876798154814105170332
188 #define LAL_LNPI 1.144729885849400174143427351353058712
189 /** @} */
190 
191 /**
192  * @name Exact physical constants
193  * The following physical constants are defined to have exact values.
194  * The dimensions in SI units are as shown.
195  * @see 2018 CODATA adjustment: http://physics.nist.gov/constants
196  */
197 /** @{ */
198 #define LAL_C_SI 299792458e0 /**< Speed of light in vacuum, m s^-1 */
199 #define LAL_H_SI 6.62607015e-34 /**< Planck constant, J s */
200 #define LAL_QE_SI 1.602176634e-19 /**< Electron charge, C */
201 #define LAL_MOL 6.02214076e+23 /**< Avogadro constant, dimensionless */
202 #define LAL_K_SI 1.380649e-23 /**< Boltzmann constant, J K^-1 */
203 #define LAL_GEARTH_SI 9.80665 /**< Standard gravity, m s^-2 */
204 #define LAL_PATM_SI 101325e0 /**< Standard atmosphere, Pa */
205 
206 /**
207  * @brief Reduced Planck constant, J s
208  * @details
209  * LAL_HBAR_SI = LAL_H_SI / (2 * LAL_PI)
210  */
211 #define LAL_HBAR_SI 1.054571817646156391262428003302280745e-34
212 
213 /**
214  * @brief Molar gas constant, J mol^-1 K^-1
215  * @details
216  * LAL_R_SI = LAL_MOL * LAL_K_SI
217  */
218 #define LAL_R_SI 8.31446261815324
219 
220 /**
221  * @brief Stefan-Boltzmann constant, W m^-2 K^-4
222  * @details
223  * 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))
224  */
225 #define LAL_SIGMA_SI 5.670374419184429453970996731889230876e-8
226 
227 /**
228  * @brief Second radiation constant, m K
229  * @details
230  * LAL_C2RAD_SI = (LAL_H_SI * LAL_C_SI / LAL_K_SI)
231  */
232 #define LAL_C2RAD_SI 1.438776877503933802146671601543911595e-2
233 
234 /**
235  * @brief Wien displacement law constant, m K
236  * @details
237  * LAL_BWIEN_SI = (LAL_C2RAD_SI / X)
238  *
239  * where the factor X satisfies
240  *
241  * X * exp(X) = 5 * (exp(X) - 1)
242  */
243 #define LAL_BWIEN_SI 2.897771955185172661478605448092884727e-3
244 /** @} */
245 
246 /**
247  * @name Primary physical constants
248  * These physical constants are given to the precision
249  * to which they are known. Other physical constants
250  * derived from these are given in the next section.
251  * @see 2018 CODATA adjustment: http://physics.nist.gov/constants
252  */
253 /** @{ */
254 #define LAL_ALPHA 0.0072973525693 /**< Fine structure constant, dimensionless */
255 #define LAL_RYD_SI 10973731.568160 /**< Rydberg constant, m^-1 */
256 #define LAL_MP_ME 1836.15267343 /**< Proton-electron mass ratio, dimensionless */
257 #define LAL_ME_AMU 0.000548579909065 /**< Electron mass, atomic mass units */
258 #define LAL_G_SI 6.67430e-11 /**< Gravitational constant, N m^2 kg^-2 */
259 /** @} */
260 
261 /**
262  * @name Derived physical constants
263  * The following constants are derived from the primary
264  * physical constants. When not dimensionless, they are
265  * given in the SI units shown. Precision beyond the
266  * accuracy is retained for these constants in order
267  * that equivalent combinations yield the same value.
268  */
269 /** @{ */
270 
271 /**
272  * @brief Permeability of free space, N A^-2
273  * @details
274  * LAL_MU0_SI = 4 * LAL_PI * LAL_ALPHA * LAL_HBAR_SI / (LAL_QE_SI * LAL_QE_SI * LAL_C_SI)
275  */
276 #define LAL_MU0_SI 1.256637062123837330602573817851770477e-6
277 
278 /**
279  * @brief Permittivity of free space, C^2 N^-1 m^-2
280  * @details
281  * LAL_EPSILON0_SI = 1 / (LAL_MU0_SI * LAL_C_SI * LAL_C_SI)
282  */
283 #define LAL_EPSILON0_SI 8.854187812773347391812964575762341677e-12
284 
285 /**
286  * @brief Planck mass, kg
287  * @details
288  * LAL_MPL_SI = sqrt(LAL_HBAR_SI * LAL_C_SI / LAL_G_SI)
289  */
290 #define LAL_MPL_SI 2.176434342717898213927914919024147041e-8
291 
292 /**
293  * @brief Planck length, m
294  * @details
295  * LAL_LPL_SI = (LAL_HBAR_SI / (LAL_MPL_SI * LAL_C_SI))
296  */
297 #define LAL_LPL_SI 1.616255024423705286500047697249314157e-35
298 
299 /**
300  * @brief Planck time, s
301  * @details
302  * LAL_TPL_SI = (LAL_LPL_SI / LAL_C_SI)
303  */
304 #define LAL_TPL_SI 5.391246448313603961644851309932934193e-44
305 
306 /**
307  * @brief Planck luminosity, J s^-1
308  * @details
309  * LAL_LUMPL_SI = (LAL_C_SI * LAL_C_SI * LAL_C_SI * LAL_C_SI * LAL_C_SI) / (LAL_G_SI)
310  */
311 #define LAL_LUMPL_SI 3.628254904411280064474144638555430509e52
312 
313 /**
314  * @brief Proton mass, atomic mass units
315  * @details
316  * LAL_MP_AMU = (LAL_ME_AMU * LAL_MP_ME)
317  */
318 #define LAL_MP_AMU 1.00727646661968604164295
319 
320 /**
321  * @brief Electron mass, kg
322  * @details
323  * LAL_ME_SI = ((2 * LAL_RYD_SI * LAL_H_SI) / (LAL_C_SI * LAL_ALPHA * LAL_ALPHA))
324  */
325 #define LAL_ME_SI 9.109383701517728819842163772087735080e-31
326 
327 /**
328  * @brief Proton mass, kg
329  * @details
330  * LAL_MP_SI = (LAL_ME_SI * LAL_MP_ME)
331  */
332 #define LAL_MP_SI 1.672621923684144692109494784075478798e-27
333 
334 /**
335  * @brief Atomic mass unit, kg
336  * @details
337  * LAL_AMU_SI = (LAL_ME_SI / LAL_ME_AMU)
338  */
339 #define LAL_AMU_SI 1.660539066595378801332508797951914123e-27
340 
341 /**
342  * @brief Bohr radius, m
343  * @details
344  * LAL_AB_SI = (LAL_ALPHA / (4 * LAL_PI * LAL_RYD_SI))
345  */
346 #define LAL_AB_SI 5.291772109034624983506063293620795401e-11
347 
348 /**
349  * @brief Electron Compton wavelength, m
350  * @details
351  * LAL_LAMBDAE_SI = (2 * LAL_PI * LAL_ALPHA * LAL_AB_SI)
352  */
353 #define LAL_LAMBDAE_SI 2.426310238678370231942278247906312873e-12
354 
355 /**
356  * @brief Classical electron radius, m
357  * @details
358  * LAL_RE_SI = (LAL_ALPHA * LAL_ALPHA * LAL_AB_SI)
359  */
360 #define LAL_RE_SI 2.817940326207927528347087481623789683e-15
361 
362 /**
363  * @brief Bohr magneton, J T^-1
364  * @details
365  * LAL_MUB_SI = (LAL_LAMBDAE_SI * LAL_C_SI * LAL_QE_SI / (4 * LAL_PI))
366  */
367 #define LAL_MUB_SI 9.274010078344114556082608495144137435e-24
368 
369 /**
370  * @brief Nuclear magneton, J T^-1
371  * @details
372  * LAL_MUN_SI = (LAL_MUB_SI / LAL_MP_ME)
373  */
374 #define LAL_MUN_SI 5.050783746114056140501321131006282803e-27
375 /** @} */
376 
377 /**
378  * @name Exact astrophysical parameters
379  * The following astrophysical constants are defined to have exact values.
380  * The dimensions in SI units are as shown.
381  * @see http://asa.hmnao.com/SecK/Constants.html
382  */
383 /** @{ */
384 #define LAL_ROT_DAY 1.00273781191135448 /**< Number of Earth rotations in one UT1 day, dimensionless */
385 #define LAL_DAYJUL_SI 86400e0 /**< Julian day, s */
386 #define LAL_YRJUL_SI 31557600e0 /**< Julian year, s */
387 #define LAL_LYR_SI 9460730472580800e0 /**< (Julian) Lightyear, m */
388 #define LAL_AU_SI 149597870700e0 /**< Astronomical unit, m */
389 #define LAL_PC_SI 3.085677581491367278913937957796471611e16 /**< Parsec, m */
390 /** @} */
391 
392 /**
393  * @name Primary astrophysical parameters
394  * These astrophysical constants are given to the precision
395  * to which they are known. Other physical constants
396  * derived from these are given in the next section.
397  */
398 /** @{ */
399 
400 /**
401  * @brief Earth equatorial radius, m
402  * @see http://asa.hmnao.com/SecK/Constants.html
403  */
404 #define LAL_REARTH_SI 6378136.6
405 
406 /**
407  * @brief Semimajor axis of WGS-84 Reference Ellipsoid, m
408  * @see Department of Defense World Geodedic System 1984 http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
409  */
410 #define LAL_AWGS84_SI 6378137e0
411 
412 /**
413  * @brief Semiminor axis of WGS-84 Reference Ellipsoid, m
414  * @details
415  * LAL_BWGS84_SI = LAL_AWGS84_SI * (1 - f)
416  *
417  * where f is the flattening
418  *
419  * 1/f = 298.257223563
420  *
421  * @note This constant is not given to full precision for compatibility.
422  * @see Department of Defense World Geodedic System 1984 http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
423  */
424 #define LAL_BWGS84_SI 6356752.314
425 
426 /**
427  * @brief Earth inclination (2000), radians
428  * @details
429  * This is the measured value of the mean obliquity of the
430  * ecliptic, 84381.406 arcseconds, converted to radians.
431  * @see http://asa.hmnao.com/SecK/Constants.html
432  */
433 #define LAL_IEARTH 0.409092600600582871467239393761915655
434 
435 /**
436  * @brief Earth orbital eccentricity, dimensionless
437  * @see 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
438  */
439 #define LAL_EEARTH 0.0167
440 
441 /**
442  * @brief Rate of Earth precession (2000), Hz
443  * @details
444  * This is the rate of precession of the Earth,
445  * 4612.156534 arcseconds per Julian century,
446  * converted to cycles per second, at the epoch J2000.0
447  * (=2000-01-01T12:00:00Z):
448  *
449  * LAL_EPREC_SI = 4612.156534 / 36525 / 15 / 86400 / LAL_DAYJUL_SI
450  *
451  * @see Linear (in t) term in Eq. (42) of
452  * N. Capitaine, P. T. Wallace and J. Chapront
453  * "Expressions for IAU 2000 precession quantities",
454  * Astronomy & Astrophysics 412 567 (2003)
455  * https://doi.org/10.1051/0004-6361:20031539
456  */
457 #define LAL_EPREC_SI 1.127703867758020059420250393792953007e-12
458 
459 /**
460  * @brief Geocentric gravitational constant, m^3 s^-2 (TCB)
461  * @see http://asa.hmnao.com/SecK/Constants.html
462  */
463 #define LAL_GMEARTH_SI 3.986004418e+14
464 
465 /**
466  * @brief Solar equatorial radius, m
467  * @see http://dx.doi.org/10.1088/0004-637X/750/2/135
468  */
469 #define LAL_RSUN_SI 6.96342e+8
470 
471 /**
472  * @brief Solar luminosity, W
473  * @see http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
474  */
475 #define LAL_LSUN_SI 3.846e+26
476 
477 /**
478  * @brief Solar mass parameter, m^3 s^-2 (TCB)
479  * @see http://asa.hmnao.com/SecK/Constants.html
480  */
481 #define LAL_GMSUN_SI 1.32712442099e+20
482 
483 /**
484  * @brief Tropical year (2000), s
485  * @see 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
486  */
487 #define LAL_YRTROP_SI 31556925.1874707200
488 
489 /**
490  * @brief Sidereal year (2000), s
491  * @see http://hpiers.obspm.fr/eop-pc/models/constants.html
492  */
493 #define LAL_YRSID_SI 31558149.763545600
494 /** @} */
495 
496 /**
497  * @name Derived astrophysical parameters
498  * The following constants are derived from the primary
499  * astrophysical constants. When not dimensionless, they are
500  * given in the SI units shown. Precision beyond the
501  * accuracy is retained for these constants in order
502  * that equivalent combinations yield the same value.
503  */
504 /** @{ */
505 
506 /**
507  * @brief Cosine of Earth inclination (2000)
508  * @details
509  * LAL_COSIEARTH = cos(LAL_IEARTH)
510  */
511 #define LAL_COSIEARTH 0.917482143065241841533315838574859003
512 
513 /**
514  * @brief Sine of Earth inclination (2000)
515  * @details
516  * LAL_SINIEARTH = sin(LAL_IEARTH)
517  */
518 #define LAL_SINIEARTH 0.397776969112605992551264763661918798
519 
520 /**
521  * @brief Earth mass, kg
522  * @details
523  * LAL_MEARTH_SI = LAL_GMEARTH_SI / LAL_G_SI
524  */
525 #define LAL_MEARTH_SI 5.972168494074284943739418365970963247e24
526 
527 /**
528  * @brief Solar mass, kg
529  * @details
530  * LAL_MSUN_SI = LAL_GMSUN_SI / LAL_G_SI
531  */
532 #define LAL_MSUN_SI 1.988409902147041637325262574352366540e30
533 
534 /**
535  * @brief Geometrized solar mass, m
536  * @details
537  * LAL_MRSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI)
538  */
539 #define LAL_MRSUN_SI 1.476625061404649406193430731479084713e3
540 
541 /**
542  * @brief Geometrized solar mass, s
543  * @details
544  * LAL_MTSUN_SI = LAL_GMSUN_SI / (LAL_C_SI * LAL_C_SI * LAL_C_SI)
545  */
546 #define LAL_MTSUN_SI 4.925491025543575903411922162094833998e-6
547 
548 /**
549  * @brief Ratio of mean solar day to sidereal day, dimensionless
550  * @details
551  * This quantity is evaluated at the epoch J2000.0 (=2000-01-01T12:00:00Z) as:
552  *
553  * LAL_SOL_SID = LAL_ROT_DAY + LAL_DAYJUL_SI * LAL_EPREC_SI
554  */
555 #define LAL_SOL_SID 1.002737909344968654292933133909634024
556 
557 /**
558  * @brief Mean sidereal day, s
559  * @details
560  * This quantity is evaluated at the epoch J2000.0 (=2000-01-01T12:00:00Z) as:
561  *
562  * LAL_DAYSID_SI = LAL_DAYJUL_SI / LAL_SOL_SID
563  */
564 #define LAL_DAYSID_SI 86164.090531333536768710524462700317733190
565 /** @} */
566 
567 /**
568  * @name Cosmological parameters
569  * The following cosmological parameters are derived from measurements of
570  * the Hubble expansion rate and of the cosmic microwave background radiation.
571  * In what follows, the normalized Hubble constant \f$h_0\f$ is equal to the
572  * actual Hubble constant \f$H_0\f$ divided by
573  * \f$\langle H \rangle=100\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}\f$.
574  * Thus the Hubble constant can be written as:
575  * \f$H_0 = \langle H \rangle * h_0\f$. Similarly, the critical energy density
576  * \f$\rho_c\f$ required for spatial flatness is given by:
577  * \f$\rho_c = \langle\rho\rangle h_0^2\f$.
578  * Current estimates give \f$h_0\f$ a value of around 0.69
579  * which is what is assumed below.
580  * All values are in the SI units shown.
581  * @see http://arxiv.org/abs/1303.5062
582  * @see http://dx.doi.org/10.1088/0067-0049/208/2/20
583  */
584 /** @{ */
585 
586 /**
587  * @brief Hubble constant prefactor, s^-1
588  * @details
589  * LAL_H0FAC_SI = 100 km s^-1 Mpc^-1
590  */
591 #define LAL_H0FAC_SI 3.240779289444365023237687716352957261e-18
592 
593 /**
594  * @brief Approximate Hubble constant, s^-1
595  * @details
596  * LAL_H0_SI = h0 * LAL_H0FAC_SI
597  *
598  * where h0 is approximately 0.69 (the value adopted here).
599  * @see http://arxiv.org/abs/1303.5062
600  * @see http://dx.doi.org/10.1088/0067-0049/208/2/20
601  */
602 #define LAL_H0_SI (0.69 * LAL_H0FAC_SI)
603 
604 /**
605  * @brief Critical energy density prefactor, J m^-3
606  * @details
607  * LAL_RHOCFAC_SI = 3 * (LAL_H0FAC_SI * LAL_C_SI)^2 / (8 * LAL_PI * LAL_G_SI)
608  */
609 #define LAL_RHOCFAC_SI 1.688169255655572064052978218230767915e-9
610 
611 /**
612  * @brief Approximate critical energy density, J m^-3
613  * @details
614  * LAL_RHOC_SI = h0^2 * LAL_RHOCFAC_SI
615  *
616  * where h0 is approximately 0.69 (the value adopted here).
617  * @see http://arxiv.org/abs/1303.5062
618  * @see http://dx.doi.org/10.1088/0067-0049/208/2/20
619  */
620 #define LAL_RHOC_SI (0.69 * 0.69 * LAL_RHOCFAC_SI)
621 
622 /**
623  * @brief Cosmic microwave background radiation temperature, K
624  * @see http://dx.doi.org/10.1088/0004-637X/707/2/916
625  */
626 #define LAL_TCMB_SI 2.72548
627 
628 /**
629  * @brief Solar velocity with respect to the cosmic microwave background radiation, m s^-1
630  * @details
631  * Adopted value is v/c = 0.0012338
632  * @see http://dx.doi.org/10.1088/0004-637X/707/2/916
633  */
634 #define LAL_VCMB_SI 369883.9346804
635 
636 /**
637  * @brief Number density of cosmic microwave background radiation photons, m^-3
638  * @details
639  * LAL_NCMB_SI = 16 * zeta(3) * LAL_PI * (LAL_K_SI * LAL_TCMB_SI / (LAL_C_SI * LAL_H_SI))^3
640  *
641  * where zeta is the Riemann zeta function and zeta(3) is Apery's constant.
642  * @see http://oeis.org/A002117
643  */
644 #define LAL_NCMB_SI 4.107178061233267795913602167900672966e8
645 
646 /**
647  * @brief Entropy density of cosmic microwave background radiation, J K^-1 m^-3
648  * @details
649  * LAL_SCMB_SI = 4 * LAL_PI^2 * LAL_K_SI * (LAL_K_SI * LAL_TCMB_SI / (LAL_C_SI * LAL_HBAR_SI))^3 / 45
650  */
651 #define LAL_SCMB_SI 2.042296344521760298284258925842980552e-14
652 /** @} */
653 
654 /** @} */
655 /** @} */
656 #ifdef __cplusplus
657 }
658 #endif
659 #endif /* _LALCONSTANTS_H */