1 @cindex physical constants
2 @cindex constants, physical
3 @cindex conversion of units
4 @cindex units, conversion of
5 This chapter describes macros for the values of physical constants, such
6 as the speed of light, @math{c}, and gravitational constant, @math{G}.
7 The values are available in different unit systems, including the
8 standard MKSA system (meters, kilograms, seconds, amperes) and the CGSM
9 system (centimeters, grams, seconds, gauss), which is commonly used in
12 The definitions of constants in the MKSA system are available in the file
13 @file{gsl_const_mksa.h}. The constants in the CGSM system are defined in
14 @file{gsl_const_cgsm.h}. Dimensionless constants, such as the fine
15 structure constant, which are pure numbers are defined in
16 @file{gsl_const_num.h}.
19 * Fundamental Constants::
20 * Astronomy and Astrophysics::
21 * Atomic and Nuclear Physics::
22 * Measurement of Time::
24 * Speed and Nautical Units::
26 * Volume Area and Length::
28 * Thermal Energy and Power::
31 * Light and Illumination::
35 * Physical Constant Examples::
36 * Physical Constant References and Further Reading::
39 The full list of constants is described briefly below. Consult the
40 header files themselves for the values of the constants used in the
43 @node Fundamental Constants
44 @section Fundamental Constants
45 @cindex fundamental constants
46 @cindex constants, fundamental
48 @item GSL_CONST_MKSA_SPEED_OF_LIGHT
49 The speed of light in vacuum, @math{c}.
51 @item GSL_CONST_MKSA_VACUUM_PERMEABILITY
52 The permeability of free space, @math{\mu_0}. This constant is defined
53 in the MKSA system only.
55 @item GSL_CONST_MKSA_VACUUM_PERMITTIVITY
56 The permittivity of free space, @math{\epsilon_0}. This constant is
57 defined in the MKSA system only.
59 @item GSL_CONST_MKSA_PLANCKS_CONSTANT_H
60 Planck's constant, @math{h}.
62 @item GSL_CONST_MKSA_PLANCKS_CONSTANT_HBAR
63 Planck's constant divided by @math{2\pi}, @math{\hbar}.
65 @item GSL_CONST_NUM_AVOGADRO
66 Avogadro's number, @math{N_a}.
68 @item GSL_CONST_MKSA_FARADAY
69 The molar charge of 1 Faraday.
71 @item GSL_CONST_MKSA_BOLTZMANN
72 The Boltzmann constant, @math{k}.
74 @item GSL_CONST_MKSA_MOLAR_GAS
75 The molar gas constant, @math{R_0}.
77 @item GSL_CONST_MKSA_STANDARD_GAS_VOLUME
78 The standard gas volume, @math{V_0}.
80 @item GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT
81 The Stefan-Boltzmann radiation constant, @math{\sigma}.
83 @item GSL_CONST_MKSA_GAUSS
84 The magnetic field of 1 Gauss.
87 @node Astronomy and Astrophysics
88 @section Astronomy and Astrophysics
89 @cindex astronomical constants
91 @item GSL_CONST_MKSA_ASTRONOMICAL_UNIT
92 The length of 1 astronomical unit (mean earth-sun distance), @math{au}.
94 @item GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT
95 The gravitational constant, @math{G}.
97 @item GSL_CONST_MKSA_LIGHT_YEAR
98 The distance of 1 light-year, @math{ly}.
100 @item GSL_CONST_MKSA_PARSEC
101 The distance of 1 parsec, @math{pc}.
103 @item GSL_CONST_MKSA_GRAV_ACCEL
104 The standard gravitational acceleration on Earth, @math{g}.
106 @item GSL_CONST_MKSA_SOLAR_MASS
110 @node Atomic and Nuclear Physics
111 @section Atomic and Nuclear Physics
112 @cindex atomic physics, constants
113 @cindex nuclear physics, constants
115 @item GSL_CONST_MKSA_ELECTRON_CHARGE
116 The charge of the electron, @math{e}.
118 @item GSL_CONST_MKSA_ELECTRON_VOLT
119 The energy of 1 electron volt, @math{eV}.
121 @item GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS
122 The unified atomic mass, @math{amu}.
124 @item GSL_CONST_MKSA_MASS_ELECTRON
125 The mass of the electron, @math{m_e}.
127 @item GSL_CONST_MKSA_MASS_MUON
128 The mass of the muon, @math{m_\mu}.
130 @item GSL_CONST_MKSA_MASS_PROTON
131 The mass of the proton, @math{m_p}.
133 @item GSL_CONST_MKSA_MASS_NEUTRON
134 The mass of the neutron, @math{m_n}.
136 @item GSL_CONST_NUM_FINE_STRUCTURE
137 The electromagnetic fine structure constant @math{\alpha}.
139 @item GSL_CONST_MKSA_RYDBERG
140 The Rydberg constant, @math{Ry}, in units of energy. This is related to
141 the Rydberg inverse wavelength @math{R} by @math{Ry = h c R}.
143 @item GSL_CONST_MKSA_BOHR_RADIUS
144 The Bohr radius, @math{a_0}.
146 @item GSL_CONST_MKSA_ANGSTROM
147 The length of 1 angstrom.
149 @item GSL_CONST_MKSA_BARN
152 @item GSL_CONST_MKSA_BOHR_MAGNETON
153 The Bohr Magneton, @math{\mu_B}.
155 @item GSL_CONST_MKSA_NUCLEAR_MAGNETON
156 The Nuclear Magneton, @math{\mu_N}.
158 @item GSL_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT
159 The absolute value of the magnetic moment of the electron, @math{\mu_e}.
160 The physical magnetic moment of the electron is negative.
162 @item GSL_CONST_MKSA_PROTON_MAGNETIC_MOMENT
163 The magnetic moment of the proton, @math{\mu_p}.
165 @item GSL_CONST_MKSA_THOMSON_CROSS_SECTION
166 The Thomson cross section, @math{\sigma_T}.
168 @item GSL_CONST_MKSA_DEBYE
169 The electric dipole moment of 1 Debye, @math{D}.
173 @node Measurement of Time
174 @section Measurement of Time
177 @item GSL_CONST_MKSA_MINUTE
178 The number of seconds in 1 minute.
180 @item GSL_CONST_MKSA_HOUR
181 The number of seconds in 1 hour.
183 @item GSL_CONST_MKSA_DAY
184 The number of seconds in 1 day.
186 @item GSL_CONST_MKSA_WEEK
187 The number of seconds in 1 week.
192 @section Imperial Units
193 @cindex imperial units
194 @cindex units, imperial
196 @item GSL_CONST_MKSA_INCH
197 The length of 1 inch.
199 @item GSL_CONST_MKSA_FOOT
200 The length of 1 foot.
202 @item GSL_CONST_MKSA_YARD
203 The length of 1 yard.
205 @item GSL_CONST_MKSA_MILE
206 The length of 1 mile.
208 @item GSL_CONST_MKSA_MIL
209 The length of 1 mil (1/1000th of an inch).
213 @node Speed and Nautical Units
214 @section Speed and Nautical Units
215 @cindex nautical units
218 @item GSL_CONST_MKSA_KILOMETERS_PER_HOUR
219 The speed of 1 kilometer per hour.
221 @item GSL_CONST_MKSA_MILES_PER_HOUR
222 The speed of 1 mile per hour.
224 @item GSL_CONST_MKSA_NAUTICAL_MILE
225 The length of 1 nautical mile.
227 @item GSL_CONST_MKSA_FATHOM
228 The length of 1 fathom.
230 @item GSL_CONST_MKSA_KNOT
236 @section Printers Units
237 @cindex printers units
240 @item GSL_CONST_MKSA_POINT
241 The length of 1 printer's point (1/72 inch).
243 @item GSL_CONST_MKSA_TEXPOINT
244 The length of 1 TeX point (1/72.27 inch).
248 @node Volume Area and Length
249 @section Volume, Area and Length
253 @item GSL_CONST_MKSA_MICRON
254 The length of 1 micron.
256 @item GSL_CONST_MKSA_HECTARE
257 The area of 1 hectare.
259 @item GSL_CONST_MKSA_ACRE
262 @item GSL_CONST_MKSA_LITER
263 The volume of 1 liter.
265 @item GSL_CONST_MKSA_US_GALLON
266 The volume of 1 US gallon.
268 @item GSL_CONST_MKSA_CANADIAN_GALLON
269 The volume of 1 Canadian gallon.
271 @item GSL_CONST_MKSA_UK_GALLON
272 The volume of 1 UK gallon.
274 @item GSL_CONST_MKSA_QUART
275 The volume of 1 quart.
277 @item GSL_CONST_MKSA_PINT
278 The volume of 1 pint.
282 @comment @node Cookery
283 @comment @section Cookery
284 @comment @commentindex cookery units
286 @comment @table @commentode
287 @comment @item GSL_CONST_MKSA_CUP
288 @comment The volume of 1 cup.
290 @comment @item GSL_CONST_MKSA_FLUID_OUNCE
291 @comment The volume of 1 fluid ounce.
293 @comment @item GSL_CONST_MKSA_TABLESPOON
294 @comment The volume of 1 tablespoon.
296 @comment @item GSL_CONST_MKSA_TEASPOON
297 @comment The volume of 1 teaspoon.
301 @node Mass and Weight
302 @section Mass and Weight
303 @cindex mass, units of
304 @cindex weight, units of
306 @item GSL_CONST_MKSA_POUND_MASS
309 @item GSL_CONST_MKSA_OUNCE_MASS
312 @item GSL_CONST_MKSA_TON
315 @item GSL_CONST_MKSA_METRIC_TON
316 The mass of 1 metric ton (1000 kg).
318 @item GSL_CONST_MKSA_UK_TON
319 The mass of 1 UK ton.
321 @item GSL_CONST_MKSA_TROY_OUNCE
322 The mass of 1 troy ounce.
324 @item GSL_CONST_MKSA_CARAT
327 @item GSL_CONST_MKSA_GRAM_FORCE
328 The force of 1 gram weight.
330 @item GSL_CONST_MKSA_POUND_FORCE
331 The force of 1 pound weight.
333 @item GSL_CONST_MKSA_KILOPOUND_FORCE
334 The force of 1 kilopound weight.
336 @item GSL_CONST_MKSA_POUNDAL
337 The force of 1 poundal.
341 @node Thermal Energy and Power
342 @section Thermal Energy and Power
343 @cindex energy, units of
344 @cindex power, units of
345 @cindex thermal energy, units of
347 @item GSL_CONST_MKSA_CALORIE
348 The energy of 1 calorie.
350 @item GSL_CONST_MKSA_BTU
351 The energy of 1 British Thermal Unit, @math{btu}.
353 @item GSL_CONST_MKSA_THERM
354 The energy of 1 Therm.
356 @item GSL_CONST_MKSA_HORSEPOWER
357 The power of 1 horsepower.
363 @cindex pressure, units of
365 @item GSL_CONST_MKSA_BAR
366 The pressure of 1 bar.
368 @item GSL_CONST_MKSA_STD_ATMOSPHERE
369 The pressure of 1 standard atmosphere.
371 @item GSL_CONST_MKSA_TORR
372 The pressure of 1 torr.
374 @item GSL_CONST_MKSA_METER_OF_MERCURY
375 The pressure of 1 meter of mercury.
377 @item GSL_CONST_MKSA_INCH_OF_MERCURY
378 The pressure of 1 inch of mercury.
380 @item GSL_CONST_MKSA_INCH_OF_WATER
381 The pressure of 1 inch of water.
383 @item GSL_CONST_MKSA_PSI
384 The pressure of 1 pound per square inch.
389 @cindex viscosity, units of
391 @item GSL_CONST_MKSA_POISE
392 The dynamic viscosity of 1 poise.
394 @item GSL_CONST_MKSA_STOKES
395 The kinematic viscosity of 1 stokes.
399 @node Light and Illumination
400 @section Light and Illumination
401 @cindex light, units of
402 @cindex illumination, units of
405 @item GSL_CONST_MKSA_STILB
406 The luminance of 1 stilb.
408 @item GSL_CONST_MKSA_LUMEN
409 The luminous flux of 1 lumen.
411 @item GSL_CONST_MKSA_LUX
412 The illuminance of 1 lux.
414 @item GSL_CONST_MKSA_PHOT
415 The illuminance of 1 phot.
417 @item GSL_CONST_MKSA_FOOTCANDLE
418 The illuminance of 1 footcandle.
420 @item GSL_CONST_MKSA_LAMBERT
421 The luminance of 1 lambert.
423 @item GSL_CONST_MKSA_FOOTLAMBERT
424 The luminance of 1 footlambert.
429 @section Radioactivity
430 @cindex radioactivity, units of
432 @item GSL_CONST_MKSA_CURIE
433 The activity of 1 curie.
435 @item GSL_CONST_MKSA_ROENTGEN
436 The exposure of 1 roentgen.
438 @item GSL_CONST_MKSA_RAD
439 The absorbed dose of 1 rad.
443 @node Force and Energy
444 @section Force and Energy
445 @cindex force and energy, units of
447 @item GSL_CONST_MKSA_NEWTON
448 The SI unit of force, 1 Newton.
450 @item GSL_CONST_MKSA_DYNE
451 The force of 1 Dyne = @c{$10^{-5}$}
454 @item GSL_CONST_MKSA_JOULE
455 The SI unit of energy, 1 Joule.
457 @item GSL_CONST_MKSA_ERG
458 The energy 1 erg = @c{$10^{-7}$}
466 @cindex constants, prefixes
468 These constants are dimensionless scaling factors.
471 @item GSL_CONST_NUM_YOTTA
475 @item GSL_CONST_NUM_ZETTA
479 @item GSL_CONST_NUM_EXA
483 @item GSL_CONST_NUM_PETA
487 @item GSL_CONST_NUM_TERA
491 @item GSL_CONST_NUM_GIGA
494 @item GSL_CONST_NUM_MEGA
497 @item GSL_CONST_NUM_KILO
500 @item GSL_CONST_NUM_MILLI
504 @item GSL_CONST_NUM_MICRO
508 @item GSL_CONST_NUM_NANO
512 @item GSL_CONST_NUM_PICO
516 @item GSL_CONST_NUM_FEMTO
520 @item GSL_CONST_NUM_ATTO
524 @item GSL_CONST_NUM_ZEPTO
528 @item GSL_CONST_NUM_YOCTO
533 @node Physical Constant Examples
536 The following program demonstrates the use of the physical constants in
537 a calculation. In this case, the goal is to calculate the range of
538 light-travel times from Earth to Mars.
540 The required data is the average distance of each planet from the Sun in
541 astronomical units (the eccentricities and inclinations of the orbits
542 will be neglected for the purposes of this calculation). The average
543 radius of the orbit of Mars is 1.52 astronomical units, and for the
544 orbit of Earth it is 1 astronomical unit (by definition). These values
545 are combined with the MKSA values of the constants for the speed of
546 light and the length of an astronomical unit to produce a result for the
547 shortest and longest light-travel times in seconds. The figures are
548 converted into minutes before being displayed.
551 @verbatiminclude examples/const.c
555 Here is the output from the program,
558 @verbatiminclude examples/const.out
561 @node Physical Constant References and Further Reading
562 @section References and Further Reading
564 The authoritative sources for physical constants are the 2002 CODATA
565 recommended values, published in the articles below. Further information
566 on the values of physical constants is also available from the cited
567 articles and the NIST website.
570 @item Journal of Physical and Chemical Reference Data, 28(6), 1713-1852, 1999
571 @item Reviews of Modern Physics, 72(2), 351-495, 2000
572 @item @uref{http://www.physics.nist.gov/cuu/Constants/index.html}
573 @item @uref{http://physics.nist.gov/Pubs/SP811/appenB9.html}