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The Universe by the Numbers

Fundamental Constants


Gravitational constant	6.67 ^. 10^-8	cm³/(g s²)
Velocity of light	3.00 ^. 10¹⁰	cm/s
Planck's constant	6.63 ^. 10^-27	erg s

Atomic Nuclei


Size of proton	0.8 ^. 10^-13	cm
Mass of proton	1.67 ^. 10^-24	g
Proton charge	4.8 ^. 10^-10	e.s.u.
Average density of nuclear matter	2 ^. 10¹⁴	g/cm³
Energy unit 1 eV	1.6 ^. 10^-12	erg
Typical value of binding energy per nucleon		MeV
Mass of proton / mass of electron	1836
Atomic mass unit (amu)	(mass of ¹²C)/12
Rest energy of atomic mass unit	931	MeV
Rest energy of electron	0.511	MeV

Atoms and Photons

Radius of first Bohr orbit	0.5 ^. 10^-8	cm
Typical wavelength of visible light	5 ^. 10^-5 5000	cm angstrom
Ionization energy of hydrogen atom from the ground level	13.6	eV
Ionization energy of various atoms		eV
Boltzmann constant	1.38 ^. 10^-16	erg/K

Man and Humankind
Typical linear size of human being 100 cm

Typical mass of human being 10⁵ g

Typical lifetime of human being 2 ^. 10⁹ s

Density of human body 1 g/cm³

Chemical composition of human body (by mass)

oxygen

carbon

hydrogen

all other elements combined

65%
18%
17%
less than 1%

Rate of energy production 10⁴ erg/(g s)
Mass resolution of human senses 0.1 g
Time resolution of human senses 0.1 s
Linear resolution of human eye 0.01 cm
Angular resolution of human eye 1 arcmin
Number of people on Earth
Number of astronomers

**Man and Humankind**
Typical linear size of human being	100	cm
Typical mass of human being	10⁵	g
Typical lifetime of human being	2 ^. 10⁹	s
Density of human body	1	g/cm³
Chemical composition of human body (by mass) oxygen carbon hydrogen all other elements combined	65% 18% 17% less than 1%
Rate of energy production	10⁴	erg/(g s)
Mass resolution of human senses	0.1	g
Time resolution of human senses	0.1	s
Linear resolution of human eye	0.01	cm
Angular resolution of human eye	1	arcmin
Number of people on Earth
Number of astronomers

Environment
Number of molecules in 1 cm³ of air (Loschmidt's number)

Density of air g/cm³
Molar mass of air 29 g/mol
Thermal velocities of air molecules 0.5 km/s
Thermal energies of air molecules 0.025 eV
Temperature of the environment 300 K
Densities

water

iron

1
7.8

g/cm³

Barometric scale height of Earth's atmosphere 8 km
Size of St.Petersburg, Russia 30 km

**Environment**
Number of molecules in 1 cm³ of air (Loschmidt's number)
Density of air		g/cm³
Molar mass of air	29	g/mol
Thermal velocities of air molecules	0.5	km/s
Thermal energies of air molecules	0.025	eV
Temperature of the environment	300	K
Densities water iron	1 7.8	g/cm³
Barometric scale height of Earth's atmosphere	8	km
Size of St.Petersburg, Russia	30	km

Earth and Moon
Radius of Earth 6400 km
Mass of Earth g
Average density of Earth 5.5 g/cm³
Earth's escape velocity 11.2 km/s
Velocity of Earth's rotation at equator 0.5 km/s
Surface gravity of Earth 980 cm/s²
Earth's magnetic field 0.5 G
Age of Earth yrs
Age of life on Earth yrs
Number of seconds in day 86 400

Number of seconds in year 3 ^. 10⁷

Apparent magnitude of full Moon

Distance to the Moon 400 000
1/400
1.3 km
AU
lightseconds

Mass of Moon / Mass of Earth 1/81

Moon's surface gravity 160 cm/s²
Moon's escape velocity 2.4 km/s
Synodic month 29.5 days
Sidereal month 27.1 days

**Earth and Moon**
Radius of Earth	6400	km
Mass of Earth		g
Average density of Earth	5.5	g/cm³
Earth's escape velocity	11.2	km/s
Velocity of Earth's rotation at equator	0.5	km/s
Surface gravity of Earth	980	cm/s²
Earth's magnetic field	0.5	G
Age of Earth		yrs
Age of life on Earth		yrs
Number of seconds in day	86 400
Number of seconds in year	3 ^. 10⁷
Apparent magnitude of full Moon
Distance to the Moon	400 000 1/400 1.3	km AU lightseconds
Mass of Moon / Mass of Earth	1/81
Moon's surface gravity	160	cm/s²
Moon's escape velocity	2.4	km/s
Synodic month	29.5	days
Sidereal month	27.1	days

Solar System
Astronomical unit (1 AU) 149.6 ^. 10⁶
1.5 ^. 10¹³
500 km
cm
lightseconds

Velocity of Earth orbital motion 30 km/s
Size of Solar System 40

7
AU
cm
lighthours
solar radii

Orbital period of Pluto 250 yrs
Jupiter

orbital period

semi-major axis of orbit

mass

average density

period of rotation

12
5
0.001
300
1.3
10
yrs
AU
solar masses
earth masses
g/cm³
hrs

All planets move around the Sun counterclockwise (when viewed from the direction of North pole)

**Solar System**
Astronomical unit (1 AU)	149.6 ^. 10⁶ 1.5 ^. 10¹³ 500	km cm lightseconds
Velocity of Earth orbital motion	30	km/s
Size of Solar System	40 7	AU cm lighthours solar radii
Orbital period of Pluto	250	yrs
Jupiter orbital period semi-major axis of orbit mass average density period of rotation	12 5 0.001 300 1.3 10	yrs AU solar masses earth masses g/cm³ hrs

Sun
Mass g
Luminosity erg/s
Radius 700 000 km
Average density 1.4 g/cm³
Escape velocity 600 km/s
Period of rotation at equator
synodic

sidereal

27
25
days
"Surface" gravity cm/s²

At the center of visible solar disk 1" corresponds to 750 km

**Sun**
Mass		g
Luminosity		erg/s
Radius	700 000	km
Average density	1.4	g/cm³
Escape velocity	600	km/s
Period of rotation at equator synodic sidereal	27 25	days
"Surface" gravity		cm/s²

Sun as star
Effective temperature 5800 K
Density at the "surface" 10^-7 g/cm³
Chemical composition of solar atmosphere (by mass)

hydrogen
helium
all other elements combined

70%
27%
3%

Absolute magnitude (in V band)

Apparent magnitude

in V band

bolometric

B - V colour index

Spectral class G2V

Magnetic field in sunspots G
Temperature of solar corona K

**Sun as star**
Effective temperature	5800	K
Density at the "surface"	10^-7	g/cm³
Chemical composition of solar atmosphere (by mass) hydrogen helium all other elements combined	70% 27% 3%
Absolute magnitude (in V band)
Apparent magnitude in V band bolometric
B - V colour index
Spectral class	G2V
Magnetic field in sunspots		G
Temperature of solar corona		K

Stars A. Normal stars
Mass range solar mass
Radius range

main sequence

red giants and supergiants

solar radii

Luminosities 10^-4 10⁶ solar luminosities
Rate of energy production erg/(g s)
Largest luminosities erg/s
Average densities

main sequence

red giants and supergiants

g/cm³
"Surface" temperatures K

**Stars** A. Normal stars
Mass range		solar mass
Radius range main sequence red giants and supergiants		solar radii
Luminosities	10^-4 10⁶	solar luminosities
Rate of energy production		erg/(g s)
Largest luminosities		erg/s
Average densities main sequence red giants and supergiants		g/cm³
"Surface" temperatures		K

B. White Dwarfs
Masses:

average

maximum

0.6
1.4
solar masses
Radius c 0.01 solar radii
Average densities 10⁵ 10⁷ g/cm³
Magnetic fields right up to 10⁶ 10⁸ G

B. White Dwarfs
Masses: average maximum	0.6 1.4	solar masses
Radius	c 0.01	solar radii
Average densities	10⁵ 10⁷	g/cm³
Magnetic fields	right up to 10⁶ 10⁸	G

C. Neutron Stars
Masses less than 2 3 solar masses
Radius 10 15 km
Average densities 10¹³ 10¹⁴ g/cm³
Magnetic fields 10¹⁴ G
Rotation periods 0.001 10 s

C. Neutron Stars
Masses	less than 2 3	solar masses
Radius	10 15	km
Average densities	10¹³ 10¹⁴	g/cm³
Magnetic fields	10¹⁴	G
Rotation periods	0.001 10	s

Interstellar medium (ISM)
Mass of stars in Galaxy / Mass of ISM matter 30

Mass of interstellar gas / Mass of interstellar dust 100

Range of temperatures of interstellar gas 10¹ 10⁷ K
Average mass density of ISM 10^-24 g/cm³
Number density of ISM 10^-3 10⁸ cm^-3
Magnetic field (3 $\div$ 5) ^. 10^-6 G
Gaseous nebulae:

number density

temperature

10² 10⁴
(8 $\div$ 12) ^. 10³
cm^-3
K

**Interstellar medium (ISM)**
Mass of stars in Galaxy / Mass of ISM matter	30
Mass of interstellar gas / Mass of interstellar dust	100
Range of temperatures of interstellar gas	10¹ 10⁷	K
Average mass density of ISM	10^-24	g/cm³
Number density of ISM	10^-3 10⁸	cm^-3
Magnetic field	(3 $\div$ 5) ^. 10^-6	G
Gaseous nebulae: number density temperature	10² 10⁴ (8 $\div$ 12) ^. 10³	cm^-3 K

Our Galaxy
Diameter of the optical disk 30 kpc
Vertical thickness of the disk 1 kpc
Mass 10¹¹ 10¹² solar masses
Number of stars 10¹¹
Hubble type Sbc or SBbc
Absolute magnitude (in V band) -20.5^m
Distance from Sun to center of Galaxy 8 kpc
Circular velocity of Sun around Galactic center 200 km/s
Galactic year 2 ^. 10⁸ yrs

Unit of interstellar distances 1 pc = 3.26 lightyears = 206 265 AU = 3 ^. 10¹⁸ cm

Unit of velocities in stellar astronomy
( 1 AU/yr ) 4.74 km/s

Distance to alpha Cen 1.3
4.3 pc
lightyears
Velocity of Sun relative to Local Standard of Rest 20 km/s
Maximum observed proper motion
(Barnard's star) 10 arcsec/yr
Density in solar neighbourhood (stellar matter included) 10^-23
0.1 g/cm³
solar masses/pc³
Globular clusters

estimated number in Galaxy

observed number

stellar content per cluster

c 200
c 140
10⁵ 10⁶

**Our Galaxy**
Diameter of the optical disk	30	kpc
Vertical thickness of the disk	1	kpc
Mass	10¹¹ 10¹²	solar masses
Number of stars	10¹¹
Hubble type	Sbc or SBbc
Absolute magnitude (in V band)	-20.5^m
Distance from Sun to center of Galaxy	8	kpc
Circular velocity of Sun around Galactic center	200	km/s
Galactic year	2 ^. 10⁸	yrs

Extragalactic astronomy and the Universe
Distances to:

Large Magellanic Cloud

Andromeda nebula

Cluster of galaxies in Virgo

55
700
20

kpc
kpc
Mpc
Average distance between
galaxies / average size of galaxy 10 100
Hubble constant H 50 100 km/(s Mpc)
Hubble time (1/H) 10¹⁰ yrs
Hubble distance (c/H) 10²⁸ cm
Temperature of cosmic background radiation 2.7 K
Critical density of the Universe 10^-29 g/cm³
Average density of visible matter in the Universe 10^-30 g/cm³

**Extragalactic astronomy and the Universe**
Distances to: Large Magellanic Cloud Andromeda nebula Cluster of galaxies in Virgo	55 700 20	kpc kpc Mpc
Average distance between galaxies / average size of galaxy	10 100
Hubble constant H	50 100	km/(s Mpc)
Hubble time (1/H)	10¹⁰	yrs
Hubble distance (c/H)	10²⁸	cm
Temperature of cosmic background radiation	2.7	K
Critical density of the Universe	10^-29	g/cm³
Average density of visible matter in the Universe	10^-30	g/cm³

History of Astronomy 1. circa 360 B.C.

Geocentric model of the Universe (Aristotle)
2. 2nd century B.C.

First heliocentric model of the Universe (Aristarchus of Samos)
3. 240 B.C.

First measurement of the Earth's radius (Eratosthenes)
4. 2nd century B.C.

Discovery of precession, scale of stellar magnitudes,

stellar cathalog (Hipparchus)
5. 2nd century A.C.

"Almagest'' by Ptolemy, epicycles
6. 1543

Copernicus: "De revolutionibus orbium coelestium''

("On the Revolutions of the Celestial Orbits'')
7. 1610

Galileo. First use of telescopes in astronomy
8. 1610--1620

Kepler. Laws of planetary motions
9. 1687

Newton: "Philosophiae naturalis principia mathematica''

("Mathematical foundations of natural philosophy'').
10. End of XVIII century

Herschel. The birth of stellar astronomy
11. 1859

Kirchhoff. The birth of spectral analysis
12. 1916

Einstein. General Relativity Theory
13. 1918

Shapley. Galactocentric revolution
14. 1920s

Hubble. Extragalactic astronomy. Expansion of the Universe
15. 1933

Jansky. The birth of radio astronomy
16. 1939

Bethe, von Weizsaecker. Sources of stellar energy
17. 1950s

Stellar evolution
18. 1960s

Quasars, cosmic background radiation, pulsars
19. 1970s

X-ray and gamma-astronomy
20. 1980--1990s

Infrared astronomy. Space based astrometry
21. 1995--1996

Discovery of extrasolar planets

Other Information Sources

Cambridge University Press Handbook of Space Astronomy and Astrophysics
Physical Calculator. It is a JavaScript calculator with some of the astrophysical constants

programmed into it.
Yahoo Constant Page
NIST Constant Index (best one)
Fundamental Physical Constants
NASA Faq - numbers and equations

Next: Preface Previous: Elucidations, advice and preceptions

�

V.V.Ivanov,A.V.Krivov,P.A.Denissenkov
Translation by Sergei Nikolaev
HTML by Igor Drozdovsky
Last modified on:

Unit of velocities in stellar astronomy ( 1 AU/yr )	4.74	km/s
Distance to Cen	1.3 4.3	pc lightyears
Velocity of Sun relative to Local Standard of Rest	20	km/s
Maximum observed proper motion (Barnard's star)	10	arcsec/yr
Density in solar neighbourhood (stellar matter included)	10^-23 0.1	g/cm³ solar masses/pc³
Globular clusters estimated number in Galaxy observed number stellar content per cluster	c 200 c 140 10⁵ 10⁶