Units and Constants

Contents

Multiplication Factors

Common Names in SI Units

SI and British (fps) Unit Conversions

Unit Conversions

• 1 ly. (light year) = 10¹⁸ cm
• 1 pc. (parsec) = 3.26 ly
• 1 AU = 1.496x10¹³ cm
• 1 m (meter) = 100 cm
• 1 micron = 10^-4 cm
• 1 ml = 1 cm³
• 1 liter = 1000 ml
• 1 knot = 1.15 mi/hr = 1.85 km/hr
• Temperature T (in ^oC) = T (in ^oK) - 273.15
• Temperature T (in ^oF) = 1.8 x T (in ^oC) + 32
• 1 ev (electron volt) = 1.602x10^-12 erg
• 1 joule = 10⁷ ergs
• 1 watt = 1 J/sec = 10⁷ erg/sec
• 1 mi/gal = 0.354 km/liter

Natural Units

Physical Quantity	SI Unit	Transition to cm	Natural Unit (cm)	Transition to erg	Natural Unit (erg)
Velocity of Light (c)	2.998x1010 cm/sec		1		1
Planck's Constant ()	1.055x10-27 erg-sec		1		1
Time	sec	cm/c	cm	erg-1	erg-1
Length	cm	cm	cm	(c) erg-1	erg-1
Energy	erg	(c) cm-1	cm-1	erg	erg
Mass	gm	(/c) cm-1	cm-1	erg/c2	erg
Momentum	gm-(cm/sec)	cm-1	cm-1	erg/c	erg
Angular Momentum	gm-(cm/sec)-cm		1		1
Velocity	cm/sec	c	1	c	1
Charge	(erg-cm)1/2	(c)1/2	1	(c)1/2	1
Gravitational Constant	cm3/gm-sec2	(c4/c) cm2	cm2	c4(c) erg-2	erg-2

Table 01 Conversion to Natural Units

There are three examples below to show how to run a reversed conversion from natural unit to SI units :


1. Electromagnetic Wave Equation -
   In natural unit of [cm] (the unit is enclosed within the bracket [ ]) this equation is in the form :
   ²E - E = 0
   Conversion back to SI units in this case is very simple by substituting the natural unit [cm]² with the SI units c²[sec]² in the denominator of the second term. Then the equation in SI units is recovered as:
   ²E - (1/c²)E = 0
2. Total Energy -
   E = (m² + p²)^1/2
   In natural unit of [erg], unit of m is converted back to SI by c²[gm], while the conversion for unit of p is c[gm-cm/sce]. Therefore the formula in SI is :
   E = (m²c⁴ + p²c²)^1/2
3. Schrodinger Equation -
   In natural unit it has the form : -(1/2m) = i
   Converting from the natural unit of [erg], the left-handed side produces a factor of (1/c²[gm])(c/[cm])²=²/[gm-cm²]. On the right-handed side the converting factor is /[sec]. Combining everything together, we recovered the equation in SI :
   -(²/2m) = i
   Incidentally, for all cases the same form in SI units will be recovered whether the natural unit is in [cm] or [erg].

Physical Constants

• Velocity of light c = 2.998x10¹⁰ cm/sec
• Gravitational Constant G = 6.6742x10^-8 cm³/sec²-gm = 6.7087x10^-39 c (Gev / c²)^-2
• Hubble constant H_o = 7.1 km/sec-Mpc
• Luminosity of the Sun = 3.86x10³³ erg/sec
• Mass of the Sun = 2x10³³ gm
• Distance from Sun to Earth = 1 AU = 1.5x10¹³ cm
• Flight time of light from Sun to Earth = 499 sec
• Solar constant = 1.388x10⁶ erg/cm²-sec
• Diameter of the Earth = 1.3x10⁹ cm
• Mass of the Earth = 6x10²⁷ gm
• Mean radius of the Earth = 6371 km
• Standard acceleration of gravity = 980.6 cm/sec²
• 1^o of latitude = 110.5 km (at equator) = 111.7 km (at poles)
• 1^o of longitude at equator = 111.3 km
• Planck's constant = 6.625x10^-27 erg-sec = 4.136x10^-15 ev-sec
• Avogadro's number = 6.023x10²³ molecules/mole
• Normal volume of pergect gas = 2.241x10⁴ cm³/mole
• kT = 0.0258 ev at T = 300^oK
• Gas constant = 8.314x10⁷ erg/K^o-mole
• Boltzmann constant = 1.38x10^-16 erg/K^o
• Speed of sound = 34000 cm/sec
• Electronic charge = 1.602x10^-19 coul
• Fine-structure constant = 1/137
• Bohr radius = 5.29 nm
• Mass of unit atomic weight = 1.6603x10^-24 gm
• Nucleon rest mass = 1.67x10^-24 gm
• Electron rest mass = 9.109x10^-28 gm

Scales of the Universe

Cosmological Constants (WMAP)

Astronomical Symbols

Greek Alphpbets, and Linguistics