Hamas

hjfgmuyf

Notes

Newtonian Physics

\[v = \frac{ds}{dt}\]

\[a = \frac{d^2s}{dt^2}\]

\[\vec{p} = m\vec{v}\]

and ~

\[\vec{F} = m\frac{d^2}{dt^2} \vec{s}\]

Kepler’s Third Law

\[mr\left(\frac{2\pi}{T}\right)^2 = G\frac{mM}{r^2} \rightarrow T^2 = \left(\frac{4\pi^2}{GM} \right)r^3 \rightarrow T^2 \propto r^3\]

Lorentz Factor

\[\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{1}{\sqrt{1 - \beta}} = \frac{dt}{d\tau}\]

Maxwell’s Equations

\[\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}\]

\[\nabla \cdot \mathbf{B} = 0\]

\[\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}\]

\[\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)\]

Einstein-Maxwell equations

\[G^{\alpha \beta} + \Lambda g^{\alpha \beta} = \frac{\kappa}{\mu_0} \left( {F^\alpha}^\psi {F_{\psi}\beta + \frac{1}{4} g^{\alpha \beta} F}_{\psi\tau} F^{\psi\tau}\right)\]

Eyring equation

\[\ln \frac{k}{T} = \frac{-\Delta H^\ddagger}{R} \cdot \frac{1}{T} + \ln \frac{\kappa k_\mathrm{B}}{h} + \frac{\Delta S^\ddagger}{R}\]

together