Physical & Astronomical Constants

Physical Constants

Name Symbol Number Exp CGS Units
speed of light in a vacuum c 2.99792458 10  cm s-1
Planck constant h 6.6260755(40) -27  erg s
hbar 1.05457266(63) -27  erg s
Gravitational constant G 6.67259(85) -8  cm3 g-1 s-2
Electron charge e 4.8032068(14) -10  esu
Mass of electron me 9.1093897(54) -28  g
Mass of proton mp 1.6726231(10) -24  g
Mass of neutron mn 1.6749286(10) -24  g
Mass of hydrogen mH 1.6733 -24  g
Atomic mass unit amu 1.6605402(10) -24  g
Avagadro's number NA 6.0221367(36) 23
Boltzmann constant k 1.380658(12) -16  erg k-1
Electron volt eV 1.6021772(50) -12  erg
Radiation density constant a 7.5646 -15  erg cm-3 K-4
Stefan-Boltzmann constant sigma 5.67051(19) -5  erg cm-2 K-4 s-1
Fine structure constant alpha 7.29735308(33) -3
Rydberg constant R 2.1798741(13) -11  erg


Astronomical Units

Name   Symbol    Number    Exp     CGS Units  
Astronomical unit   AU 1.496 13 cm
Parsec pc 3.086 18 cm
Light year ly 9.496 17 cm
Solar mass Msun 1.99 33 g
Solar radius Rsun 6.96 10 cm
Solar luminosity Lsun 3.9 33 erg s-1
Solar temperature Tsun 5.780 3 K



Planetary Data

                                     MSun=1.989x1033 g
                                     MJ=1.898x1030 g
                                     ME=5.974x1027 g
  NAME     MASS  (M_E)   RADIUS (cm)    PERIOD (yr)    SEMI-MAJOR (AU)    ECCENTRICITY 
Mercury 0.06 2.439x108 0.24085 0.387096 0.205622
Venus 0.82 6.050x108 0.61521 0.723342 0.006783
Earth 1.0 6.378x108 1.00004 0.999987 0.016684
Mars 0.11 3.397x108 1.88089 1.523705 0.093404
Jupiter 317.89 7.140x109 11.8622 5.204529 0.047826
Saturn 95.18 6.000x109 29.4577 9.575133 0.052754
Uranus 14.53 2.615x109 84.0139 19.30375 0.050363
Neptune 17.14 2.43x109 16.47932 30.20652 0.004014



Physical Properties of Main-Sequence Stars

           Columns give:
           1) spectral class, temperature increases going from class M to class O. The spectral type of the sun is G2.
           2) Logarithm of the mass in solar mass units. The mass of the sun is 2x1033 grams.
           3) Logarithm of the luminosity in solar units. The luminosity of the sun is 4x1033 erg/s.
           4) Bolometric magnitude.
           5) Visual magnitude.
           6) Logarithm of the radius in solar units. The radius of the sun is 6.96x108 m.
           7) 8) 9) 10) Give the magnitude difference (the color) for varius bands
Class Teff Lg(M/Msun) Lg(L/Lsun) Mbol MV Lg(R/Rsun) (U-B) (B-V) (V-R) (V-I)
M6 .. -1.0 -2.9 +12.1 +15.5 -0.9 ... ... ... ...
M5 3170 -0.8 -2.5 +10.9 +13.9 -0.56 1.22 1.61 ... 3.47
M4 .. -0.6 -2.0 +9.7 +12.2 -0.5 ... ... ... ...
M2 3520 -0.4 -1.5 +8.4 +10.2 -0.3 ... ... ... ...
M0 3840 -0.3 -1.6 +7.5 +8.8 -0.22 1.25 1.40 ... ...
K5 4410 -0.2 -0.8 +6.6 +7.5 -0.14 1.09 1.16 0.8 1.62
K0 5150 -0.1 -0.4 +5.6 +5.9 -0.07 0.47 0.85 0.74 1.06
G5 5560 -0.04 -0.1 +4.9 +5.2 -0.04 0.20 0.69 ... 0.89
G2 5790 +0.0 +0.0 +4.7 +4.8 +0.00 0.13 0.65 0.41 0.86
G0 5940 +0.02 +0.2 +4.2 +4.4 +0.04 0.05 0.58 0.52 0.81
F5 6650 +0.11 +0.6 +3.3 +3.4 +0.11 0.01 0.42 ... 0.64
F0 7300 +0.20 +0.8 +2.6 +2.7 +0.18 0.06 0.29 0.30 0.47
A5 8180 +0.30 +1.2 +1.8 +1.9 +0.23 0.11 0.15 ... 0.22
A2 9000 +0.4 +1.6 +0.7 +1.1 +0.32 ... ... ... ...
A0 9790 +0.46 +1.8 +0.3 +0.6 +0.38 -0.06 0.00 0.00 0.00
B8 11400 +0.56 +2.3 -1.1 -0.2 +0.49 -0.34 -0.10 ... ...
B5 15200 +0.77 +3.0 -2.9 -1.1 +0.58 -0.56 -0.16 ... ...
B3 .. +0.88 +3.7 -4.6 -2.2 +0.72 -0.71 -0.20 ... ...
B0 30000 +1.24 +4.4 -6.3 3.4 +0.86 -1.08 -0.30 ... ...
O8 .. +1.36 +4.9 -7.6 -4.6 +0.93 -1.13 -0.31 ... ...
O5 42000 +1.77 +5.4 -8.9 -5.6 +1.08 -1.15 -0.32 ... ...
O4 .. +1.8 +6.0 -10.2 -6.3 +1.3 ... ... ... ...
           Source: ``Galactic Astronomy'' by Mihalas & Binney; Ed. Freeman & Company

Teff of Giants Stars

Class Teff
M5 3380
M2 3540
M0 3690
K5 4050
K2 4390
K0 4660
G8 4800
G5 5050
           Source: ``Allen's Astrophysical Quantities'' by Arthur N. Cox

Stellar Surface Gravity & Radius

Main-Sequence Stars

Class Lg(g/gsun) R/Rsun
M8 +0.50.10
M5 +0.50.27
M2 +0.20.50
M0 +0.150.65
K5 +0.10.72
K0 +0.050.85
G5 +0.050.92
G0 -0.051.1
F5 -0.11.3
F0 -0.11.5
A5 -0.151.7
A0 -0.32.4
B8 -0.43.0
B5 -0.43.9
B3 -0.54.8
B0 -0.57.4
O8 -0.58.5
O6 -0.4510
O5 -0.412
O3 -0.315
           Source: ``Allen's Astrophysical Quantities'' by Arthur N. Cox

Giants Stars

Class Lg(g/gsun) R/Rsun
M0 -3.140
K5 -2.725
K0 -2.315
G5 -1.910
G0 -1.55
A0 ..5
B5 -0.958
B0 -1.115
           Source: ``Allen's Astrophysical Quantities'' by Arthur N. Cox

Photon Flux:

Given the passband and the magnitude of an object, the number of tphotons incident at the top of the atmosphere may be estimated using the data in this table:

Band lambda_c dlambda/lambda Flux at m=0 Reference
um Jy
U 0.36 0.15 1810 Bessel (1979)
B 0.44 0.22 4260 Bessel (1979)
V 0.55 0.16 3640 Bessel (1979)
R 0.64 0.23 3080 Bessel (1979)
I 0.79 0.19 2550 Bessel (1979)
J 1.26 0.16 1600 Campins, Reike, & Lebovsky (1985)
H 1.60 0.23 1080 Campins, Reike, & Lebovsky (1985)
K 2.22 0.23 670 Campins, Reike, & Lebovsky (1985)
g 0.52 0.14 3730 Schneider, Gunn, & Hoessel (1983)
r 0.67 0.14 4490 Schneider, Gunn, & Hoessel (1983)
i 0.79 0.16 4760 Schneider, Gunn, & Hoessel (1983)
z 0.91 0.13 4810 Schneider, Gunn, & Hoessel (1983)

Also useful are these identities:

1 Jy = 10^-23 erg sec^-1 cm^-2 Hz^-1
1 Jy = 1.51e7 photons sec^-1 m^-2 (dlambda/lambda)^-1
Example: How many V-band photons are incident per second on an area of 1 m^2 at the top of the atmosphere from a V=23.90 star? From the table, the flux at V=0 is 3640 Jy; hence, at V=23.90 the flux is diminished by a factor 10^(-0.4*V)=2.75e-10, yielding a flux of 1.e-6 Jy. Since dlambda/lambda=0.16 in V, the flux per second on a 1 m^2 aperture is
f=1.e-6 Jy * 1.51e7 * 0.16 = 2.42 photons sec^-1

References:


Linear Limb-darkening Coefficieints:

'Claret 2000 table' From Vizier Astronomical Table & Catalogue( http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/363/1081 )

log g log(g/gsun) Teff Gamma
[cm/s2] [sun:27400cm/s2] [K] U B V R I
3.5 -0.93775 2000 1.250271 1.257329 1.211991 1.115265 1.024194
4 -0.43775 2000 1.213712 1.232759 1.188098 1.09119 1.004507
4.5 0.062249 2000 1.188098 1.208556 1.169572 1.078502 0.997003
5 0.562249 2000 1.162889 1.17965 1.149606 1.064351 0.989537
3.5 -0.93775 2200 1.191489 1.217158 1.201708 1.118503 1.031834
4 -0.43775 2200 1.164557 1.19659 1.174603 1.088008 1.007519
4.5 0.062249 2200 1.143007 1.184713 1.161222 1.07377 1.003003
5 0.562249 2200 1.116883 1.157895 1.138075 1.058104 0.995507
3.5 -0.93775 2400 1.089598 1.136435 1.152916 1.083248 1.007519
4 -0.43775 2400 1.084833 1.123373 1.126628 1.053435 0.98359
4.5 0.062249 2400 1.078502 1.125 1.118503 1.041054 0.98359
5 0.562249 2400 1.05033 1.108808 1.102378 1.024194 0.980626
3.5 -0.93775 2600 0.939735 0.998501 1.030303 0.968827 0.899952
4 -0.43775 2600 0.974715 1.019628 1.039514 0.971768 0.911208
4.5 0.062249 2600 0.977667 1.02267 1.031834 0.95858 0.904163
5 0.562249 2600 0.965892 1.033367 1.034901 0.957122 0.915452
3.5 -0.93775 2800 0.822201 0.880461 0.890173 0.819549 0.756086
4 -0.43775 2800 0.857143 0.909796 0.922552 0.847651 0.790698
4.5 0.062249 2800 0.86533 0.911208 0.925402 0.853067 0.791996
5 0.562249 2800 0.872188 0.929688 0.938296 0.859867 0.805049
3.5 -0.93775 3000 0.766252 0.827521 0.814259 0.733485 0.680965
4 -0.43775 3000 0.738476 0.788104 0.797203 0.722323 0.653693
4.5 0.062249 3000 0.743484 0.785515 0.802429 0.73224 0.654867
5 0.562249 3000 0.771363 0.820874 0.834199 0.758621 0.685765
3.5 -0.93775 3200 0.752294 0.838221 0.81294 0.711252 0.684564
4 -0.43775 3200 0.70514 0.763703 0.766252 0.682164 0.618944
4.5 0.062249 3200 0.685765 0.729754 0.744739 0.669039 0.588438
5 0.562249 3200 0.682164 0.722323 0.740978 0.669039 0.580645
3.5 -0.93775 3400 0.754821 0.897151 0.858504 0.721088 0.728513
4 -0.43775 3400 0.692998 0.782931 0.7894 0.684564 0.631579
4.5 0.062249 3400 0.654867 0.712477 0.729754 0.647838 0.564103
5 0.562249 3400 0.635046 0.679768 0.697842 0.62697 0.531646
3.5 -0.93775 3600 0.76116 0.962963 0.928258 0.758621 0.779064
4 -0.43775 3600 0.676182 0.826189 0.842255 0.707581 0.665482
4.5 0.062249 3600 0.624672 0.714932 0.743484 0.65252 0.560819
5 0.562249 3600 0.592913 0.656042 0.679768 0.608696 0.504174
3.5 -0.93775 3800 0.771363 1.004507 1 0.832861 0.818225
4 -0.43775 3800 0.65252 0.870813 0.901354 0.764977 0.695418
4.5 0.062249 3800 0.594034 0.74223 0.781641 0.690583 0.580645
5 0.562249 3800 0.557545 0.650177 0.676182 0.610966 0.49066
3.5 -0.93775 4000 0.597403 0.81294 0.81558 0.740978 0.591793
4 -0.43775 4000 0.612103 0.838221 0.873563 0.790698 0.642008
4.5 0.062249 4000 0.564103 0.779064 0.823529 0.735978 0.603037
5 0.562249 4000 0.532714 0.667852 0.690583 0.628121 0.498959
3.5 -0.93775 4200 0.586207 0.786809 0.757353 0.664298 0.544529
4 -0.43775 4200 0.625821 0.847651 0.855783 0.784223 0.620087
4.5 0.062249 4200 0.598528 0.855783 0.887392 0.810304 0.651348
5 0.562249 4200 0.54022 0.738476 0.757353 0.685765 0.547771
3.5 -0.93775 4400 0.604167 0.788104 0.739726 0.637363 0.528445
4 -0.43775 4400 0.665482 0.859867 0.826189 0.743484 0.598528
4.5 0.062249 4400 0.581756 0.807674 0.790698 0.70514 0.569593
5 0.562249 4400 0.553191 0.803738 0.808989 0.727273 0.588438
3.5 -0.93775 4600 0.62697 0.780352 0.708804 0.607562 0.505219
4 -0.43775 4600 0.703921 0.866699 0.799813 0.702703 0.580645
4.5 0.062249 4600 0.608696 0.811621 0.757353 0.660754 0.544529
5 0.562249 4600 0.564103 0.794597 0.758621 0.664298 0.546689
3.5 -0.93775 4800 0.647838 0.775208 0.683363 0.586207 0.488594
4 -0.43775 4800 0.743484 0.868069 0.779064 0.677376 0.568493
4.5 0.062249 4800 0.637363 0.807674 0.737226 0.635046 0.528445
5 0.562249 4800 0.580645 0.784223 0.727273 0.62697 0.521008
3.5 -0.93775 5000 0.682164 0.773925 0.673797 0.57732 0.48139
4 -0.43775 5000 0.718623 0.810304 0.710027 0.612103 0.513615
4.5 0.062249 5000 0.642008 0.781641 0.699055 0.599653 0.5
5 0.562249 5000 0.595156 0.768805 0.701486 0.60078 0.5
3.5 -0.93775 5200 0.680965 0.75989 0.649007 0.556455 0.464066
4 -0.43775 5200 0.724796 0.793296 0.683363 0.589555 0.494802
4.5 0.062249 5200 0.658396 0.768805 0.674989 0.579536 0.483444
5 0.562249 5200 0.612103 0.757353 0.678571 0.581756 0.484472
3.5 -0.93775 5400 0.673797 0.745995 0.628121 0.536998 0.446982
4 -0.43775 5400 0.723559 0.776492 0.660754 0.568493 0.476269
4.5 0.062249 5400 0.670227 0.756086 0.65252 0.560819 0.467105
5 0.562249 5400 0.631579 0.745995 0.656042 0.563007 0.469136
3.5 -0.93775 5600 0.667852 0.73224 0.610966 0.521008 0.431118
4 -0.43775 5600 0.719855 0.76116 0.640845 0.55102 0.461034
4.5 0.062249 5600 0.676182 0.74223 0.632734 0.542373 0.451982
5 0.562249 5600 0.645503 0.727273 0.632734 0.543451 0.453988
3.5 -0.93775 5800 0.663116 0.717391 0.594034 0.506266 0.417405
4 -0.43775 5800 0.717391 0.745995 0.624672 0.534854 0.445985
4.5 0.062249 5800 0.679768 0.728513 0.615519 0.52738 0.438033
5 0.562249 5800 0.656042 0.713704 0.61324 0.52738 0.439024
3.5 -0.93775 7000 0.603037 0.645503 0.52738 0.440016 0.355713
4 -0.43775 7000 0.658396 0.667852 0.554278 0.46812 0.382844
4.5 0.062249 7000 0.642008 0.644337 0.536998 0.454992 0.373418
5 0.562249 7000 0.638522 0.633889 0.531646 0.45098 0.371542
3.5 -0.93775 7200 0.590674 0.635046 0.518892 0.432104 0.348337
4 -0.43775 7200 0.642008 0.649007 0.539145 0.455997 0.373418
4.5 0.062249 7200 0.630425 0.633889 0.52738 0.445985 0.364998
5 0.562249 7200 0.628121 0.623524 0.522068 0.442002 0.363135
3.5 -0.93775 7400 0.57732 0.625821 0.511511 0.425222 0.342835
4 -0.43775 7400 0.629273 0.638522 0.530578 0.44798 0.366864
4.5 0.062249 7400 0.616659 0.622378 0.517835 0.437043 0.357564
5 0.562249 7400 0.616659 0.61324 0.512563 0.434077 0.355713
3.5 -0.93775 7600 0.564103 0.614379 0.501042 0.415459 0.33463
4 -0.43775 7600 0.61324 0.625821 0.51995 0.438033 0.358491
4.5 0.062249 7600 0.604167 0.612103 0.508361 0.42915 0.350176
5 0.562249 7600 0.603037 0.601908 0.503129 0.425222 0.348337
3.5 -0.93775 7800 0.556455 0.607562 0.49273 0.405774 0.327386
4 -0.43775 7800 0.599653 0.614379 0.50941 0.428167 0.350176
4.5 0.062249 7800 0.591793 0.601908 0.501042 0.422285 0.344666
5 0.562249 7800 0.589555 0.590674 0.493766 0.416432 0.341007
3.5 -0.93775 8000 0.556455 0.608696 0.483444 0.396166 0.319289
4 -0.43775 8000 0.587322 0.604167 0.5 0.419355 0.342835
4.5 0.062249 8000 0.576213 0.589555 0.489627 0.411576 0.336449
5 0.562249 8000 0.57732 0.581756 0.485501 0.409639 0.33463
3.5 -0.93775 8200 0.556455 0.610966 0.475248 0.384738 0.311248
4 -0.43775 8200 0.580645 0.603037 0.49584 0.412545 0.336449
4.5 0.062249 8200 0.564103 0.579536 0.479339 0.402883 0.328289
5 0.562249 8200 0.564103 0.569593 0.475248 0.40096 0.327386
3.5 -0.93775 8400 0.547771 0.596279 0.464066 0.377179 0.305919
4 -0.43775 8400 0.580645 0.599653 0.49066 0.409639 0.335539
4.5 0.062249 8400 0.552105 0.570694 0.470152 0.393299 0.321083
5 0.562249 8400 0.55102 0.558635 0.465078 0.391391 0.320186
3.5 -0.93775 8600 0.535926 0.580645 0.452984 0.368733 0.299732
4 -0.43775 8600 0.57732 0.603037 0.477291 0.392344 0.320186
4.5 0.062249 8600 0.544529 0.567394 0.465078 0.386635 0.314815
5 0.562249 8600 0.536998 0.547771 0.454992 0.382844 0.31303
3.5 -0.93775 8800 0.52419 0.566296 0.442997 0.360346 0.293578
4 -0.43775 8800 0.563007 0.594034 0.463054 0.376238 0.306805
4.5 0.062249 8800 0.545609 0.569593 0.459016 0.380952 0.309469
5 0.562249 8800 0.526316 0.54022 0.445985 0.373418 0.305033
3.5 -0.93775 9000 0.52419 0.556455 0.438033 0.359418 0.293578
4 -0.43775 9000 0.544529 0.570694 0.445985 0.364066 0.29709
4.5 0.062249 9000 0.532714 0.567394 0.439024 0.356638 0.28833
5 0.562249 9000 0.515723 0.54022 0.439024 0.364066 0.294455
3.5 -0.93775 9200 0.512563 0.544529 0.428167 0.352019 0.287457
4 -0.43775 9200 0.541296 0.560819 0.439024 0.360346 0.295333
4.5 0.062249 9200 0.521008 0.553191 0.42915 0.349256 0.283105
5 0.562249 9200 0.51046 0.538071 0.42915 0.352941 0.285714
3.5 -0.93775 9400 0.511511 0.534854 0.423263 0.348337 0.285714
4 -0.43775 9400 0.531646 0.548853 0.431118 0.354788 0.290076
4.5 0.062249 9400 0.51046 0.54022 0.419355 0.34192 0.27704
5 0.562249 9400 0.505219 0.54022 0.417405 0.339181 0.273588
3.5 -0.93775 9600 0.498959 0.52419 0.414487 0.34192 0.279635
4 -0.43775 9600 0.517835 0.536998 0.421308 0.347418 0.283105
4.5 0.062249 9600 0.5 0.529511 0.411576 0.335539 0.271867
5 0.562249 9600 0.496879 0.534854 0.413516 0.33463 0.268431
3.5 -0.93775 9800 0.493766 0.514669 0.409639 0.339181 0.278769
4 -0.43775 9800 0.50941 0.526316 0.414487 0.34192 0.279635
4.5 0.062249 9800 0.493766 0.521008 0.40481 0.331002 0.268431
5 0.562249 9800 0.486531 0.516779 0.4 0.325581 0.262443

Sloan filters

log g log(g/gsun) Teff Gamma in Sloan filter (wavelength)
u' g' r' i' z'
[cm/s2] [sun:27400cm/s2] [K] (3543 A) (4770 A) (6231 A) (7625 A) (9134 A)
0 -4.43775 3500 0.702216 0.84212 0.807937 0.665719 0.571465
0.5 -3.93775 3500 0.731121 0.862049 0.801251 0.651582 0.563007
1 -3.43775 3500 0.759382 0.874114 0.790698 0.63771 0.556455
1.5 -2.93775 3500 0.780352 0.880046 0.77855 0.624902 0.551671
2 -2.43775 3500 0.791477 0.881568 0.766252 0.613354 0.548528
2.5 -1.93775 3500 0.792646 0.877974 0.754947 0.603376 0.546797
3 -1.43775 3500 0.779322 0.855375 0.741479 0.591681 0.540005
3.5 -0.93775 3500 0.732365 0.777906 0.70697 0.565418 0.506789
4 -0.43775 3500 0.68769 0.704652 0.663944 0.53464 0.46812
4.5 0.062249 3500 0.657572 0.660754 0.632618 0.513089 0.441804
5 0.562249 3500 0.636667 0.634699 0.610852 0.498855 0.424536
0 -4.43775 3750 0.78061 0.831524 0.76485 0.647954 0.552974
0.5 -3.93775 3750 0.796551 0.850492 0.769316 0.642473 0.545069
1 -3.43775 3750 0.811885 0.860957 0.769955 0.635625 0.538178
1.5 -2.93775 3750 0.821936 0.864782 0.768294 0.628006 0.5325
2 -2.43775 3750 0.822334 0.862595 0.76485 0.619973 0.528232
2.5 -1.93775 3750 0.811885 0.855511 0.760017 0.611989 0.52504
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