# Physical Constants¶

This chapter describes macros for the values of physical constants, such as the speed of light, , and gravitational constant, . The values are available in different unit systems, including the standard MKSA system (meters, kilograms, seconds, amperes) and the CGSM system (centimeters, grams, seconds, gauss), which is commonly used in Astronomy.

The full list of constants is described briefly below. Consult the header files themselves for the values of the constants used in the library.

## Fundamental Constants¶

CML_CONST_MKSA_SPEED_OF_LIGHT

The speed of light in vacuum, .

CML_CONST_MKSA_VACUUM_PERMEABILITY

The permeability of free space, . This constant is defined in the MKSA system only.

CML_CONST_MKSA_VACUUM_PERMITTIVITY

The permittivity of free space, . This constant is defined in the MKSA system only.

CML_CONST_MKSA_PLANCKS_CONSTANT_H

Planck’s constant, .

CML_CONST_MKSA_PLANCKS_CONSTANT_HBAR

Planck’s constant divided by , .

CML_CONST_NUM_AVOGADRO

CML_CONST_MKSA_FARADAY

The molar charge of 1 Faraday.

CML_CONST_MKSA_BOLTZMANN

The Boltzmann constant, .

CML_CONST_MKSA_MOLAR_GAS

The molar gas constant, .

CML_CONST_MKSA_STANDARD_GAS_VOLUME

The standard gas volume, .

CML_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT

CML_CONST_MKSA_GAUSS

The magnetic field of 1 Gauss.

## Astronomy and Astrophysics¶

CML_CONST_MKSA_ASTRONOMICAL_UNIT

The length of 1 astronomical unit (mean earth-sun distance), .

CML_CONST_MKSA_GRAVITATIONAL_CONSTANT

The gravitational constant, .

CML_CONST_MKSA_LIGHT_YEAR

The distance of 1 light-year, .

CML_CONST_MKSA_PARSEC

The distance of 1 parsec, .

CML_CONST_MKSA_GRAV_ACCEL

The standard gravitational acceleration on Earth, .

CML_CONST_MKSA_SOLAR_MASS

The mass of the Sun.

## Atomic and Nuclear Physics¶

CML_CONST_MKSA_ELECTRON_CHARGE

The charge of the electron, .

CML_CONST_MKSA_ELECTRON_VOLT

The energy of 1 electron volt, .

CML_CONST_MKSA_UNIFIED_ATOMIC_MASS

The unified atomic mass, .

CML_CONST_MKSA_MASS_ELECTRON

The mass of the electron, .

CML_CONST_MKSA_MASS_MUON

The mass of the muon, .

CML_CONST_MKSA_MASS_PROTON

The mass of the proton, .

CML_CONST_MKSA_MASS_NEUTRON

The mass of the neutron, .

CML_CONST_NUM_FINE_STRUCTURE

The electromagnetic fine structure constant .

CML_CONST_MKSA_RYDBERG

The Rydberg constant, , in units of energy. This is related to the Rydberg inverse wavelength by .

CML_CONST_MKSA_BOHR_RADIUS

CML_CONST_MKSA_ANGSTROM

The length of 1 angstrom.

CML_CONST_MKSA_BARN

The area of 1 barn.

CML_CONST_MKSA_BOHR_MAGNETON

The Bohr Magneton, .

CML_CONST_MKSA_NUCLEAR_MAGNETON

The Nuclear Magneton, .

CML_CONST_MKSA_ELECTRON_MAGNETIC_MOMENT

The absolute value of the magnetic moment of the electron, . The physical magnetic moment of the electron is negative.

CML_CONST_MKSA_PROTON_MAGNETIC_MOMENT

The magnetic moment of the proton, .

CML_CONST_MKSA_THOMSON_CROSS_SECTION

The Thomson cross section, .

CML_CONST_MKSA_DEBYE

The electric dipole moment of 1 Debye, .

## Measurement of Time¶

CML_CONST_MKSA_MINUTE

The number of seconds in 1 minute.

CML_CONST_MKSA_HOUR

The number of seconds in 1 hour.

CML_CONST_MKSA_DAY

The number of seconds in 1 day.

CML_CONST_MKSA_WEEK

The number of seconds in 1 week.

## Imperial Units¶

CML_CONST_MKSA_INCH

The length of 1 inch.

CML_CONST_MKSA_FOOT

The length of 1 foot.

CML_CONST_MKSA_YARD

The length of 1 yard.

CML_CONST_MKSA_MILE

The length of 1 mile.

CML_CONST_MKSA_MIL

The length of 1 mil (1/1000th of an inch).

## Speed and Nautical Units¶

CML_CONST_MKSA_KILOMETERS_PER_HOUR

The speed of 1 kilometer per hour.

CML_CONST_MKSA_MILES_PER_HOUR

The speed of 1 mile per hour.

CML_CONST_MKSA_NAUTICAL_MILE

The length of 1 nautical mile.

CML_CONST_MKSA_FATHOM

The length of 1 fathom.

CML_CONST_MKSA_KNOT

The speed of 1 knot.

## Printers Units¶

CML_CONST_MKSA_POINT

The length of 1 printer’s point (1/72 inch).

CML_CONST_MKSA_TEXPOINT

The length of 1 TeX point (1/72.27 inch).

## Volume, Area and Length¶

CML_CONST_MKSA_MICRON

The length of 1 micron.

CML_CONST_MKSA_HECTARE

The area of 1 hectare.

CML_CONST_MKSA_ACRE

The area of 1 acre.

CML_CONST_MKSA_LITER

The volume of 1 liter.

CML_CONST_MKSA_US_GALLON

The volume of 1 US gallon.

CML_CONST_MKSA_CANADIAN_GALLON

The volume of 1 Canadian gallon.

CML_CONST_MKSA_UK_GALLON

The volume of 1 UK gallon.

CML_CONST_MKSA_QUART

The volume of 1 quart.

CML_CONST_MKSA_PINT

The volume of 1 pint.

## Mass and Weight¶

CML_CONST_MKSA_POUND_MASS

The mass of 1 pound.

CML_CONST_MKSA_OUNCE_MASS

The mass of 1 ounce.

CML_CONST_MKSA_TON

The mass of 1 ton.

CML_CONST_MKSA_METRIC_TON

The mass of 1 metric ton (1000 kg).

CML_CONST_MKSA_UK_TON

The mass of 1 UK ton.

CML_CONST_MKSA_TROY_OUNCE

The mass of 1 troy ounce.

CML_CONST_MKSA_CARAT

The mass of 1 carat.

CML_CONST_MKSA_GRAM_FORCE

The force of 1 gram weight.

CML_CONST_MKSA_POUND_FORCE

The force of 1 pound weight.

CML_CONST_MKSA_KILOPOUND_FORCE

The force of 1 kilopound weight.

CML_CONST_MKSA_POUNDAL

The force of 1 poundal.

## Thermal Energy and Power¶

CML_CONST_MKSA_CALORIE

The energy of 1 calorie.

CML_CONST_MKSA_BTU

The energy of 1 British Thermal Unit, .

CML_CONST_MKSA_THERM

The energy of 1 Therm.

CML_CONST_MKSA_HORSEPOWER

The power of 1 horsepower.

## Pressure¶

CML_CONST_MKSA_BAR

The pressure of 1 bar.

CML_CONST_MKSA_STD_ATMOSPHERE

The pressure of 1 standard atmosphere.

CML_CONST_MKSA_TORR

The pressure of 1 torr.

CML_CONST_MKSA_METER_OF_MERCURY

The pressure of 1 meter of mercury.

CML_CONST_MKSA_INCH_OF_MERCURY

The pressure of 1 inch of mercury.

CML_CONST_MKSA_INCH_OF_WATER

The pressure of 1 inch of water.

CML_CONST_MKSA_PSI

The pressure of 1 pound per square inch.

## Viscosity¶

CML_CONST_MKSA_POISE

The dynamic viscosity of 1 poise.

CML_CONST_MKSA_STOKES

The kinematic viscosity of 1 stokes.

## Light and Illumination¶

CML_CONST_MKSA_STILB

The luminance of 1 stilb.

CML_CONST_MKSA_LUMEN

The luminous flux of 1 lumen.

CML_CONST_MKSA_LUX

The illuminance of 1 lux.

CML_CONST_MKSA_PHOT

The illuminance of 1 phot.

CML_CONST_MKSA_FOOTCANDLE

The illuminance of 1 footcandle.

CML_CONST_MKSA_LAMBERT

The luminance of 1 lambert.

CML_CONST_MKSA_FOOTLAMBERT

The luminance of 1 footlambert.

CML_CONST_MKSA_CURIE

The activity of 1 curie.

CML_CONST_MKSA_ROENTGEN

The exposure of 1 roentgen.

CML_CONST_MKSA_RAD

The absorbed dose of 1 rad.

## Force and Energy¶

CML_CONST_MKSA_NEWTON

The SI unit of force, 1 Newton.

CML_CONST_MKSA_DYNE

The force of 1 Dyne = Newton.

CML_CONST_MKSA_JOULE

The SI unit of energy, 1 Joule.

CML_CONST_MKSA_ERG

The energy 1 erg = Joule.

## Prefixes¶

These constants are dimensionless scaling factors.

CML_CONST_NUM_YOTTA

CML_CONST_NUM_ZETTA

CML_CONST_NUM_EXA

CML_CONST_NUM_PETA

CML_CONST_NUM_TERA

CML_CONST_NUM_GIGA

CML_CONST_NUM_MEGA

CML_CONST_NUM_KILO

CML_CONST_NUM_MILLI

CML_CONST_NUM_MICRO

CML_CONST_NUM_NANO

CML_CONST_NUM_PICO

CML_CONST_NUM_FEMTO

CML_CONST_NUM_ATTO

CML_CONST_NUM_ZEPTO

CML_CONST_NUM_YOCTO

## Examples¶

The following program demonstrates the use of the physical constants in a calculation. In this case, the goal is to calculate the range of light-travel times from Earth to Mars.

The required data is the average distance of each planet from the Sun in astronomical units (the eccentricities and inclinations of the orbits will be neglected for the purposes of this calculation). The average radius of the orbit of Mars is 1.52 astronomical units, and for the orbit of Earth it is 1 astronomical unit (by definition). These values are combined with the MKSA values of the constants for the speed of light and the length of an astronomical unit to produce a result for the shortest and longest light-travel times in seconds. The figures are converted into minutes before being displayed.

#include <stdio.h>
#include <cml.h>

int
main(void)
{
double c  = CML_CONST_MKSA_SPEED_OF_LIGHT;
double au = CML_CONST_MKSA_ASTRONOMICAL_UNIT;
double minutes = CML_CONST_MKSA_MINUTE;

/* distance stored in meters */
double r_earth = 1.00 * au;
double r_mars  = 1.52 * au;

double t_min, t_max;

t_min = (r_mars - r_earth) / c;
t_max = (r_mars + r_earth) / c;

printf("light travel time from Earth to Mars:\n");
printf("minimum = %.1f minutes\n", t_min / minutes);
printf("maximum = %.1f minutes\n", t_max / minutes);

return 0;
}


Here is the output from the program,

light travel time from Earth to Mars:
minimum = 4.3 minutes
maximum = 21.0 minutes