#------UNITS, PHYSICAL CONSTANTS, AND DATA----
#-------Warren D. Smith 1998-------------
#This useful file causes MAPLE to know about
#fundamental physical constants, useful data, and units.

#I feel cgs, emu, esu units are an abomination.
#If you want to have no units, go totally dimensionless
#(for example, the Planck units). If you want to have units,
#use SI. The cgs, emu, esu systems are a silly halfassed attempt
#to have it both ways and get rid of some units and keep others.

#   The present file features conversion factors to random non-SI
#units like foot, horsepower, pound, ounce. The entire group
#of units is known to it, so all quantities are dimensioned
#automatically. Meter, second, coulomb, kelvin, and kg are
#my fundamental units. (Arguably kelvin is not needed.
#Also for radiation dose units, I use the "disintegration", e.g. 
#disintegration/second.)

#  I have so far been unable to stomach the "candela".
#The old definition was...
#candle =  1/60 the luminous intensity of 1 cm^2 of a Blackbody at the
#melting Temperature of platinum (2042.15 kelvin) = 1.6437 *watt
#= meter^2 / 600000 * sigmasb * platinummelttemp^4;
#a candela is the light intensity from a candle (now redefined
#as "1/683 watt per steradian" of 555nm wavelength light (which the eye
#is maximally sensitive to). 
#Note, this seems to be a lot smaller than the old defn.
#Huh? Then   lumen = candela*steradian = 1/683 *watt;  
#lux = lumen/meter^2 = 1/683 *watt/meter^2; candlepower = candela.
#Yuk!

#I also hate the "radian" and "steradian"; they should be
#dimensionless, in my view.

#   Finally, decibels and bels are another abomination.
#  decibels = 10*bels = 10*log10(Intensity/ReferenceIntensity);
#and for use in auditory work, one uses
#ReferenceIntensity = 1 phon = 10^(-16) *watt/cm^2/sec at 1000 *hertz.
#Idiotic - haven't these guys heard of scientific notation to deal with
#logarithms?

#  This MAPLE code does not know about precision (usually the
#last 2 digits of our numbers are imprecise). My values
#are CODATA values plus miscellaneous sources like
#CRC handbook. If you really care about errors you have to know
#about the correlations among the errors in the 
#fundamental constants (many errors are highly correlated)
#and that would require a lot of extra software, which I
#didn't feel like trying to write.

#Update 1999: 
#PJ Mohr BN Taylor
#CODATA recommended values of the fundamental physical constants 1998
#J Phys Chem Ref Data 28 (1999) 
#finally came out
#http://physics.nist.gov/cgi-bin/cuu/
#  http://physics.nist.gov/PhysRefData/contents.html

#The  1998  CODATA
#Recommended Values of the Fundamental Physical
#Constants, Web Version 3.0," available at
#http://physics.nist.gov/constants (National Institute of
#Standards and Technology, Gaithersburg, MD 20899,
#release date 23 July 1999).
#http://physics.nist.gov/cuu/Constants/index.html
#http://physics.nist.gov/constants
#http://www.codata.org/ 
#http://pdg.lbl.gov/1998/astrorpp.ps
#these sites very recommended - can now download any correlation coeff too

#A detailed description of the data and its analysis that led to these
#values will be published by early 2000 in the Journal of Physical
#and Chemical Reference Data.

#"Review of particle properties", Phys Rev D50 (1994) 1-.
#PRD 54 (July 1996) 1-720.
#C.Caso et al.: Review of particle physics, Europ. Phys. J. C3 (1998) 1-.
#http://pdg.lbl.gov

#---------units (and data):---------------

#prefixes:
zepto := 10^(-21):
atto := 10^(-18):
femto := 10^(-15):
pico := 10^(-12):
nano := 10^(-9):
micro := 10^(-6):
milli := 10^(-3):
centi := 10^(-2):
kilo := 10^3:
mega := 10^6:
giga := 10^9:
tera := 10^12:
peta := 10^15:
exa := 10^18:
zetta := 10^21:

joule := meter^2 * kg / second^2:
watt := joule/second:
mole := 6.02214199 * 10^(23):  #79 ppb uncert
ampere := coulomb/second:
hertz := 1/second:
newton := meter*kg/second^2:   #force
pascal := newton/meter^2:      #pressure
poise := pascal*second:        #absolute viscosity
stokes := meter^2 /second:     #kinematic viscosity
volt := watt/ampere:
farad := coulomb/volt:
ohm := volt/ampere:
mho := 1/ohm;
siemens := 1/ohm:
weber := volt*second:
tesla := weber/meter^2:
henry := weber/ampere:

sipole := meter*coulomb/second; #my own unit of magentic monopole charge
#One SIpole is the amount of magnetic charge that would
#experience a force of 1 Newton if placed in a 1 Tesla magnetic
#field.

becquerel := disintegration/second:  #radioactivity unit
gray := joule/kg:  #for measuring absorbed radiation dose
#a sievert is the amount of radiation equivalent in health effect to 1 gray
#of some kind of standard type of radiation.

minute := 60*second:
hour := 60*minute:
solarday := 24*hour:  #increases 1 millisecond/century
starday := 86164.09 * second:
year := 365.24219879  *solarday:
month := year/12:
century := 100*year:

denier := kg/meter:
dyne := 10^(-5) *newton:
erg := 10^(-7) *joule:

gauss := 10^(-4) * tesla:
maxwell := 10^(-8) *weber:

horsepower := 746 * watt:  #several definitions exist 735 to 746 watt.

jansky := 10^(-26) * watt * second / meter^2;

oersted := 7.957747 * ampere/meter: #says CRC handbook

parsec := cot(1 * angularsecond) * astronomicalunit: #3.085678*10^(16) *meter: 3.26*lightyear

lb := .45359237  *kg:  #exact
poundmass := lb:
ounce := lb/16:
shortton := 2000 *lb:
longton :=  2240 *lb:
grain := lb/7000:
slug := 14.59390 *kg:

lbf := 4.4482216152605 * newton: #exact
poundforce := lbf:
psi := lbf/inch^2:  #6895*pascal
torr := 133.322 *pascal:
mmhg := torr:

liter := 10^(-3) *meter^3:

sverdrup := 10^6 *meter^3/second: #volume flux. Used in oceanography.
kayser := 1/(centi*meter): #used in spectroscopy
cc := (centi*meter)^3:
micron := 10^(-6) * meter;

metricton := 10^3 *kg:  #also "tonne"
#electron-volt
ev := 1.602176462 * 10^(-19) *joule:
km := 10^3 *meter:
mm := 10^(-3) *meter:
cm := 10^(-2) *meter:
astronomicalunit := 149597900 *km:  #earth-sun distance
nauticalmile := 1852*meter:
#nauticalmile := 6076.115486*foot:

angstrom := 10^(-10) * meter:
barn := 10^(-28) *meter^2:
fermi := 10^(-15) *meter:

bar := 10^(5) *pascal:

abampere := ampere/10:
abcoulomb := coulomb/10:
statampere := 3.335641 * 10^(-10) *ampere:
statcoulomb := 3.335641 * 10^(-10) *coulomb:
curie := 3.7*10^(10) *becquerel:
roentgen := 2.58 * 10^(-4) *coulomb/kg:
rad := 10^(-2) *gray:
remunit := 10^(-2) *sievert:

pi := evalf(Pi);

radian := 1:
revolution := evalf(2*Pi*radian):
angulardegree := evalf(Pi/180 *radian):
angularminute := angulardegree/60:
angularsecond := angularminute/60:

fullsphere := evalf(4*Pi*steradian):

knot := nauticalmile/hour:
hectare := 10^4 *meter^2:
angstrom := 10^(-10)*meter:
inch := 2.54 * 10^(-2)*meter:
foot := 12*inch:
yard := 3*foot:
printerpoint := 0.13837 *inch:  #or is it inch/72? close
mile := 5280*foot:
acre := mile^(2) /640: #acre := 43560 *foot^2

usgallon := 231 * inch^3:
brgallon := 277.420 *inch^3:
quart := usgallon/4:
pint := quart/2:
cup := pint/2:
gill := cup/2; #british cups, pints, gills are each a bit bigger
fluidounce := cup/8:
tablespoon := fluidounce/2:
teaspoon  :=  tablespoon/3:
boardfoot := 144 *inch^3:

gram := 10^(-3) *kg:
carat := .2 *gram:

btu := 1.055056 * 10^(3) * joule:
ustherm := 1.054804 * 10^(8) *joule:  #used by US natural gas industry

watertripletemp := 273.16 *kelvin: #exact

watertriplepressure := 611.73 *pascal:
platinummelttemp := (1769.0+273.15) *kelvin:
waterfreezetemp := 273.15 *kelvin:
waterboiltemp := 373.15 *kelvin:
#celsius := waterfreeze + kelvin. fahrenheit := celsius * (5/9) + 32:

caloriethermo := 4.184 *joule:
calorieintl := 4.1868 *joule:
calorie := calorieintl:

#weapons kiloton is by convention 10^(12) calories.
kiloton := 10^(12) * calorie:
mageaton := 10^(3) * kiloton:

rankine := (5/9) *kelvin:
standardatmosphere := 101325 *pascal:
standardgravity := 9.80665 *meter/second^2:
vsoundair := 331.4 *meter/second:
specheatair := 1010 *joule/kg/kelvin: #at const pressure
densityair := 1.21 * kg/meter^3:
vsoundwater := 1496.7 *meter/second:
densitywater := 1000*kg/meter^3:
specheatwater := 4190 *joule/kg/kelvin: #at const pressure
heatfusionwater := 333 * kilo*joule/kg:
heatvapwater := 2260* kilo*joule/kg:
indexrefwater := 1.33: #at 589 nm

resistivitysilver := 1.587 * 10^(-8) * ohm * meter; #at 293 Kelvin

radgeosync := 42200 * kilo * meter:
vescapeearth := 11200 * meter/second:
muearth := 8.0*10^(22) *joule/tesla: #magnetic dipole moment
efieldearth := 150 * volt/meter:  #down. At earth's surface. mean.

suntemp := 5780*kelvin;
sunluminosity := 3.846 * 10^(26) * joule/second:
solarconst := evalf(sunluminosity / (4*Pi*astronomicalunit^2)): #varies 2%

mmilkyway := 2.2*10^(41) *kg:
moceans := 1.4 *10^(21) *kg:

velocorbitalgalaxy := 220 * km/second: #of solar system round milky way galaxy
velocwrtcosmicbackground := 369.3 * km/second: #+-2.5

disttocenterofmilkyway := 8.0 * mega * parsec:

distproximacentauri := 4.22 * c*year:
#**Alpha  Centauri system:
#Separation between  Alpha  Centauri A and B varies from 11 to 35 AU;
#they take 80 years to orbit around each other.
#Proxima  Centauri is currently 13,000 AUs from A and B; no orbital
#parameters of it are known.
#  A            B           proxima     sun
# 5800K        5300K       2700K      5800K
#  4.35         4.35        4.22         0 lightyears away
#  Yellow       Orange         Red    Yellow
distandromedagalaxy := 2*10^(22) *meter:
distlargemagellaniccloud := 55*kilo*parsec:
distvirgocluster := 20*mega*parsec:
disttouniverseedge := 10^(26) * meter;
distearthmoon := 384404 *km:  #+3 cm per year
periodmoon := 27 *solarday:  #??? +2 milliseconds/century 

distsunmercury := .38  * astronomicalunit:
distsunvenus   := .72  * astronomicalunit:
distsunearth   := 1.0  * astronomicalunit:
distsunmars    := 1.52 * astronomicalunit:
distsunjupiter := 5.20 * astronomicalunit:
distsunsaturn  := 9.5  * astronomicalunit:
distsunuranus  := 19.2 * astronomicalunit:
distsunneptune := 30.0 * astronomicalunit:
distsunpluto   := 39.5 * astronomicalunit:
#pluto has 1 satellite "charon" with about .1 its mass; 
#it has day 6.38 earth days.

#radiusearth   := 6371.006 *km:
radiusearth   := 6378.140 *km:#equatorial
radiusmoon    := 1738 *km:

radiusmercury := .38  * radiusearth:
radiusvenus   := .96  * radiusearth:
radiusmars    := .53  * radiusearth:
radiusjupiter := 10.8 * radiusearth:
radiussaturn  := 9.0  * radiusearth:
radiusuranus  := 4.1  * radiusearth:
radiusneptune := 3.85 * radiusearth:
radiuspluto   := 1137 *km:  #+-8
radiussun     := 695990 *km:  #equatorial
radiussunschwarzschild     := 2.95325008 * km:
radiusmilkyway := 15 * kilo *parsec:
thicknessmilkyway := 1 * kilo *parsec:

mmercury := .33022 * 10^(24) * kg:
mvenus   := 4.8690 * 10^(24) * kg:
mearth   := 5.97370 * 10^(24) * kg:
mmoon    := .073483 * 10^(24) * kg:
mmars    := .64191 * 10^(24) * kg:
mjupiter := 1898.8 * 10^(24) * kg:
msaturn  := 568.50 * 10^(24) * kg:
muranus  := 86.625 * 10^(24) * kg:
mneptune := 102.78 * 10^(24) * kg:
mpluto   := 1.27 * 10^(22) * kg:
msun := 1.98892 * 10^(30) *kg:

hubnum := .5: #could be anywhere .2 to 1.0
hubbleconst := 70*hubnum*km/second/(mega*parsec);
#http://ucsu.colorado.edu/~lisle/main.html
#``The cosmological implications of Hipparcus''
#direct trig parallax distance measurement to nearby Cepheids with
#Hipparcus satellite. Leads to 10% revision of Hubble constant, now
#about 60  km/s/Mpc.
#another place claims 60-80 is the range; I'm going with it.

criticaldensity := 3*hubbleconst^2/(8*pi*G); #needed to close the universe
#matter density is supposed to be .2 to 1.0 times this

entropydensityofuniverse := 2899.3 * (2.853/2.728)^3 * kb / cc; 

tempuniversebackground := 2.853 * kelvin:  #plus or minus .002

lightyear := c*year;

#various rough estimates of universe-quantities on Misner-Thorne-Wheeler p738:
#max radius 19*10^9 lightyear
#time start to max 3*10^10 year
#time bang to crunch 6*10^10 year
#age now 10^10 year
#radius now 13*10^9 lightyear    note: larger than age
#volume now 3.83*10^79 meter^3
#density at maximum   5*10^(-30) * gram/cc
#rate of increase of radius now   .66 lightyear/year
#amount of matter   5.68*10^(53) kg
#baryon number      3.39*10^(80)

#MTW 29.6p796
#density of universe now is <10^(-28) g/cc and >2*10^(-31) g/cc

#MTW when universe about 10^5 years old, density was 10^(-20) g/cc and temp 3000K
#and then: 
#1. radiation ceased to domaine, now matter
#2. universe became transparent
#3. hydrogen atoms began to form (no longer ionized perpetually)

#------------------fundamental constants:-----------------

#these constants suffice to define the planck units:

#speed of light in vacuum    exact
c := 299792458 * meter/second:

#boltzmann constant
kb := 1.3806503 * 10^(-23) *joule/kelvin:  #1700 ppb uncert

#permittivity & permeability of vacuum
mu0 := evalf(4*Pi*1.0 * 10^(-7)) *henry/meter: #exact
eps0 := 1/(c^2 * mu0): #exact
#eps0 := 8.854187817 * 10^(-12) *farad/meter
#mu0*eps0*c^2=1

#newton gravitational constant (force = G*m1*m2/r^2)
G := 6.673 * 10^(-11) *newton*meter^2/kg^2:  
#+- .010; huge relative uncert .0015

#coulomb law constant (force = coulombconst * q1*q2/r^2)
coulombconst := 1/ (4 * pi *eps0):

#planck's constant
h := 6.62606876 * 10^(-34) *joule*second:
hbar := 1.054571596 * 10^(-34) *joule*second:
#hbar = evalf(h/(2*Pi)):
#78 ppb uncert

#------------planck length, mass, time, charge:--------------
#These are the fundamental units of 
#length, mass, time, charge, temperature
#in a unit system where c=G=hbar=kb=1 and 
#where coulombconst*qplanck^2 = G*mplanck^2.

lplanck := sqrt(hbar*G/c^3):
mplanck := sqrt(hbar*c/G):
tplanck := sqrt(hbar*G/c^5):
qplanck := evalf(sqrt(4*Pi*hbar*c*eps0)):
#qplanck / qe = 1/sqrt(alpha), reciprocal sqrt of fine structure constant!

tempplanck := (mplanck*c^2)/kb:

# lplanck    := 1.616048609*10^(-35) *meter:
# tplanck    := 5.390557920*10^(-44) *second:
# mplanck    := 2.176714074*10^(-8)  *kg:
# qplanck    := 1.875546788*10^(-18) *coulomb: 
# tempplanck := 1.416957021*10^(32)  *kelvin:

# qplanck = 11.7062 charge quanta = sqrt(137).
# mplanck = 2.389527889 * 10^(22) electron masses.

#------other fundamental constants:-----------------

#charge of proton
qe := 1.602176462 * 10^(-19) *coulomb:
#39 ppb uncert

#atomic mass unit
amu := 10^(-3) * kg/mole:
#amu := 1.66053873*10^(-27) *kg:  #79 ppb uncert
#mole is number of carbon-12 atoms in 12 grams, amu is
#1/12 mass of a carbon-12 atom.

#rest mass of electron, proton, neutron, muon, deuteron, alpha particle
#me := 9.10938188 * 10^(-31) *kg:   #79 ppb uncert
me := 5.48579903 * 10^(-4) * amu:   # +-   .00000013
me := .510998902 * mega * ev/c^2:  #40 ppb uncert
#failed excited lepton searches: e >86 GeV, muon >=86 GeV, tau>72 GeV

mp := 1.67262158* 10^(-27) *kg:  #79 ppb uncert
mp := 938.271998 * mega * ev / c^2:   #40 ppb uncert
mp := 1.00727646688 * amu:  # .13ppb uncert

mpbyme := 1836.1526675: #2.1ppb uncert

#mn := 1.6749286 * 10^(-27) *kg:
mn := 1.008664904 * amu:
#    +-.000000014

#mmu := 1.8835327*10^(-28) *kg:
mmu := .113428913 * amu:  # +-   .000000017
mmu := 105.658389 * mega * ev/c^2: #+-.000034  (1998 value)

mdeuteron := 3.3435860 * 10^(-27) *kg:
mdeuteron := 1875.612762 * mega * ev/c^2: #40 ppb
mtriton   := 3.015500 * amu;
m3he      := 3.014932 * amu;
malpha := me / (1.37093354 * 10^(-4)):
#malpha :=       4.001505 * amu;
mpi  := 135.0 * mega*ev/c^2; #mass of pi
mpi0 := 139.6 * mega*ev/c^2; #mass of pi_0^{+-}
mtau := 1777.05 * mega * ev / c^2: #+.29, -.26  (1998 value)

#heavy lepton searches supposedly go up to 81.5GeV now with 95% conf 
#nothing charged there. Ackerstaff Euro Phys J C1 (1998) 45 
#also 95% conf nothing uncharged below 69GeV

mquarku := 3.25 * mega * ev/c^2: #charge +2/3  (1.5 to 5)
mquarkd := 6    * mega * ev/c^2: #charge -1/3 #??? wrong way ???  (3 to 9)
mquarks := 115 * mega * ev/c^2: #charge -1/3  (60 to 170)
mquarkc := 1.25  * giga * ev/c^2: #charge +2/3  (1.25 +-.15)
mquarkb := 4.25  * giga * ev/c^2: #charge -1/3  (4.25 +- .15)
mquarkt := 174.3 * giga * ev/c^2: #charge +2/3. 174.3+-5.1
#all quarks spin 1/2, baryon # 1/3, RGB or anti-RGB color.

mw := 80.41  * giga * ev/c^2: #+-.4 Gev. Charge +-1. Spin 1. W boson.
mz := 91.187 * giga * ev/c^2: #+-.031 Gev. Charge 0. Spin 1. Z boson.

#particle mean lifetimes
meanlifemu := 2.19703 * micro * second:#uncert .00004
meanlifetau := .2900 * pico * second:  #+-.0012
meanlifen := 888.6 * second: #+- 3.5 second
#meanlifep > 10^31 years for some investigated modes

#Bohr magneton
bohrmag := qe*hbar/(2*me):
#bohrmag = mue/1.001159652:
#bohrmag := 9.2740154 * 10^(-24) *joule/tesla:

#Nuclear magneton
nucmag := qe*hbar/(2*mp)::
#nucmag := 5.0507866*10^(-27) * joule/tesla:

#magnetic moment of electron, proton, neutron, muon, deuteron
#mue := 9.2847701 * 10^(-24) *joule/tesla:
mue := 1.001159652193 * bohrmag:
# +-    .000000000010

#mup := 1.41060761 * 10^(-26) *joule/tesla:
mup := 2.792847386 * nucmag:
# +-    .000000063

#mun := 9.6623707 * 10^(-27) *joule/tesla:
mun := 1.91304275 * nucmag: #has negative sign, incidentally
#     +-.00000045

mumu := 4.4904514 * 10^(-26) *joule/tesla:
mudeuteron := 4.3307375 * 10^(-27) *joule/tesla:

#------------"atomic units":--------------
#mass     me
#charge   qe
#action   hbar
#length   rbohr
#energy   hartree

#Bohr radius (estimate, for hydrogen atom)
rbohr := evalf(4*Pi*eps0*hbar^2/(me*qe^2)):
#rbohr := 5.29177208 * 10^(-11) *meter: #3.7ppb

#hartree energy unit, about 27 ev
#hartree := 2*rydberg*h*c := 4.3598 * 10^(-18) *joule:
hartree := hbar^2 / (me*rbohr^2):

atomictimeunit := hbar / hartree:
atomicvelocityunit := rbohr / atomictimeunit:   #about c/137
atomicforceunit := hartree / rbohr:
atomicmomentumunit := hbar / rbohr:
atomiccurrentunit := qe / atomictimeunit:
atomicefieldunit := hartree/(qe*rbohr):
atomicpotentialunit := hartree/qe:
atomicedipoleunit := qe*rbohr:
atomicmagfieldunit := hbar / (qe*rbohr^2):

atomicmagdipoleunit :=  2*bohrmag:

#------derived constants:-----------------

#magnetic flux quantum
phi0 := h/(2*qe):
#phi0 := 2.06783461 * 10^(-15) *weber

#alpha = fine structure constant
#alpha := 1/137.0359895:
alpha := evalf(qe^2 / (4*Pi*eps0*hbar*c)):

#stefan-boltzmann constant
sigmasb := evalf(Pi^2*kb^4/(60*hbar^3*c^2)):
#sigmasb :=  5.670400*10^(-8) *watt/meter^2/kelvin^4: #7000 ppb

#first radiation constant
c1radiation := evalf(2*Pi*h*c^2):
#c1radiation := 3.7417749 * 10^(-16) watt/meter^2:
c2radiation := h*c/kb:
#c2radiation := 0.01438769 *meter*kelvin:
#The max intensity lambda in blackbody radiation is
#wienconst*T*cm/kelvin, where
wienconst := c2radiation / 4.965114231:
#wienconst := 0.2897756 *cm/kelvin:

#rydberg (approx hydrogen waves per meter, infinite mass nuc)
rydberg := me*c*alpha^2/(2*h):
#rydberg := 10973731.56834(24) /meter:

#classical electron radius
#re := 2.817940285 * 10^(-15) *meter: #11 ppb
re := alpha^2 * rbohr:

#compton wavelengths of electron, proton, neutron, muon
e_compton := h/(me*c):
p_compton := h/(mp*c):
n_compton := h/(mn*c):
mu_compton := h/(mmu*c):

fermicouplingconst := 1.16639 * 10^(-5) / (giga * ev)^2: #9000 ppb
sinsquaredweakmixingangle := 0.23124:  #.001 relative uncert
#codata says .2235 +- .0023

strongcouplingconst := .119: