## Astronomical Constants - **c (speed of light)** = 299,792,458 $m s^{-1}$ - **G (gravitational constant)** = 6.674×10$^{-11}$ $m^3$ $kg^{-1}$ $s^{-2}$ - **AU (astronomical unit)** = 149,597,870.7 $km$ - **M☉ (solar mass)** = 1.989×10$^{30}$ $kg$ - **M⊕ (Earth mass)** = 5.972×10$^{24}$ $kg$ - **L☉ (solar luminosity)** = 3.828×10$^{26}$ $W$ - **pc (parsec)** = 3.0857×10$^{16}$ $m$ - **H₀ (Hubble constant)** = 70 $km$ $s^{-1}$ $Mpc^{-1}$ *(value subject to change)* - **h (Planck constant)** = 6.626×10$^{-34}$ $m^2$ $kg$ $s^{-1}$ - **k (Boltzmann constant)** = 1.381×10$^{-23}$ $J$ $K^{-1}$ - **σ (Stefan-Boltzmann constant)** = 5.670×10$^{-8}$ $W$ $m^{-2}$ $K^{-4}$ - **eV (electronvolt)** = 1.602×10$^{-19}$ $J$ - **sec in a year** = 3.16 x 10$^7$ ## Fundamental Astronomical Equations - **Newton's Law of Universal Gravitation** - $F = G \frac{m_1 m_2}{r^2}$ - **Kepler's Third Law (for orbital periods and distances)** - $P^2 = \frac{4\pi^2}{G(M_1 + M_2)} a^3$ - **Einstein's Mass-Energy Equivalence** - $E = mc^2$ - **Hubble's Law (velocity-distance relation)** - $v = H_0 d$ - **Stefan-Boltzmann Law (luminosity of a star)** - $L = 4\pi R^2 \sigma T^4$ - **Wien's Displacement Law (peak wavelength of blackbody radiation)** - $\lambda_{\text{max}} = \frac{b}{T}$ - **Escape Velocity** - $v_{\text{esc}} = \sqrt{\frac{2GM}{r}}$ - **Hydrostatic Equilibrium in Stars (balance of gravity and pressure)** - $\frac{dP}{dr} = -\frac{G\rho M(r)}{r^2}$ - **Chandrasekhar Limit (maximum mass for white dwarf stability)** - $M_{\text{limit}} \approx 1.4 M_{\odot}$ - **Drake Equation (estimate the number of active, communicative extraterrestrial civilizations)** - $N = R_* \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L$ - **Schwarzschild Radius (radius of a black hole)** - $r_s = \frac{2GM}{c^2}$ - **Virial Theorem (relation between potential energy and kinetic energy in a stable system)** - $2\langle K \rangle = -\langle U \rangle$ **ref** [[Chapters/Astronomy]]