# Astr 734 - Order of Magnitude Astrophysics - Fall 2017

## Useful constants and conversions

### Constants

• 1 AU = 150 million km = 1.5x1011 m = 500 light-sec = 1.5x1013 cm
• 1 year = $$\pi$$x107 seconds (pi-ty million)
• Earth Radius = 6000 km = 6x106 m
• $$\sigma_T = 6.7 \times 10^{-29}$$ m2
• Proton mass = Neutron mass = 1.7x10-27 kg
• Electron mass = 9.1x10-31 kg or roughly 10-3 smaller than a proton
• G = 6.67 x 10-11 m3 / kg / s2 = 0.0043 $$\frac{km}{s}$$2 pc / M_sun

### Conversions

• 1 parsec = 206256 AU
• 1 radian = 57.296 deg = 206265 arcsec
• 1 eV = 1.6x10-19 J
• 1 erg = 10-7 J = 6.2x1011 eV

## Formulae

• Gravitational force FG = GMm/r2
• Inline latex can be rendered with $$F_G = {GMm \over r^2}$$
• Display latex can be rendered with

$F_G = {GMm \over r^2}$

• Another way to render a latex formula is
• Eddington Luminosity

$L_{\rm{Edd}} = 1.25\times 10^{38} \big(\frac{M}{M_{\rm{Sun}}}\big) \rm{erg}\; \rm s^{-1} = 3.2\times 10^4 \big(\frac{M}{M_{\rm{Sun}}}\big) L_{\rm{Sun}}$

## Data

• Heat
• 9 kcal/g = burning fat
• 4 kcal/g = burning protein
• 4 kcal/g = burning carbohydrates
• 1 kcal/g = explosives (TNT)
• 0.6 kcal/g = boiling water
• 0.1 kcal/g = heating water (0-100C)
• 0.08 kcal/g = melting water
• ISM Densities
• 1 cm-3 = approximate particle density in Milky Way
• 10-3 to 10-4 cm-3 = approximate coronal gas (hot ISM) particle density

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