Formelsammlung Astronomie

\section{Constants to know from heart}

\subsection{Velocity of light} \begin{equation} c = 3 * 10^{8}\frac{m}{s} \end{equation}

\subsection{AU - Astronomical unit} The mean distance from earth to sun \begin{equation} 1 AU = 1,5 * 10^{11}m \end{equation}

\subsection{pc - parsec} One parsec is the dinstance, from wich 1 AU looks like an angle of 1 second. \begin{equation} 1 pc \approx 3 lightyears \end{equation}

\section{Formulars}

\subsection{Keplers 3rd Law} \begin{equation} \label{Kepler's 3rd law} a^3 = \frac{GMP^2}{4\pi^2} \end{equation} where: \begin{align*} a &= \text{Semi-major axis of elliptical orbit}\\ G &=\text{constant}\\ M &=\text{total mass of orbiting bodies}\\ P &=\text{orbital periode}\\ \end{align*}

\subsection{Keplers 3rd Law in simplified units} \begin{equation} a^3 = P^2M \end{equation} where: \begin{align*} a &= \text{Semi-major axis of elliptical orbit in Units of AU}\\ M &=\text{total mass of bodies in masses of sun}\\ P &=\text{orbital periode in years}\\ \end{align*}

when mass of planet is much smaller than the star, then $\frac{M}{M_\odot} \approx 1$, so: \begin{equation} a^3 = P^2 \end{equation}

\subsection{Small angle formular} \begin{equation} \frac{D2}{D1} = \sin{\alpha} \approx \alpha \end{equation} where: \begin{align*} \alpha &= \text{viewing angle (for small angles) in rad}\\ D1 &=\text{Distance to object in parsec}\\ D2 &=\text{Extension distance in AU}\\ \end{align*}