public:fs_astronomie

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public:fs_astronomie [2023/05/16 11:42]
psio 		public:fs_astronomie [2023/05/16 17:14] (current)
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-====== Formelsammlung Astronomie ======+====== Astronomy cheat sheet ======
  
-\section{Constants to know from heart}+===== Constants to know from heart =====
  
-\subsection{Velocity of light} +^Name ^Equation ^Description ^ 
-\begin{equation} +|c - Velocity of light |$c = 3 * 10^{8}\frac{m}{s}$ |Velocity of light in vacuum | 
-    c = 3 * 10^{8}\frac{m}{s} +|AU - Astronomical Unit |$1 AU = 1,5 * 10^{11}m$ |The mean distance from earth to sun | 
-\end{equation}+|Ly - Lightyear|$1Ly \approx 9,5 * 10^{15}m$ |Distance light travels in one year| 
 +|pc - Parsec|$1 pc \approx 3Ly$|One parsec is the dinstance, from wich 1 AU looks like an angle of 1 second|    
  
-\subsection{AU - Astronomical unit} +===== Formulars ===== 
-The mean distance from earth to sun +==== Keplers 3rd Law  ==== 
-\begin{equation} +^Name  ^  Formula  ^  where  ^ 
-    1 AU = 1,5 * 10^{11}m +|Keplers 3rd Law  |\begin{align*}a^3 = \frac{GMP^2}{4\pi^2} \end{align*}  |\begin{align*}
-\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}\\ a &= \text{Semi-major axis of elliptical orbit}\\
 G &=\text{constant}\\ G &=\text{constant}\\
 M &=\text{total mass of orbiting bodies}\\ M &=\text{total mass of orbiting bodies}\\
 P &=\text{orbital periode}\\ P &=\text{orbital periode}\\
-\end{align*} +\end{align*}  | 
- +|Keplers 3rd law in simplified units|\begin{equation}
- +
-\subsection{Keplers 3rd Law in simplified units} +
-\begin{equation}+
     a^3 = P^2M     a^3 = P^2M
-\end{equation} +\end{equation} |\begin{align*}
-where: +
-\begin{align*}+
 a &= \text{Semi-major axis of elliptical orbit in Units of AU}\\ a &= \text{Semi-major axis of elliptical orbit in Units of AU}\\
 M &=\text{total mass  of bodies in masses of sun}\\ M &=\text{total mass  of bodies in masses of sun}\\
-P &=\text{orbital periode in years}\\ +P &=\text{orbital period in years}\\ 
-\end{align*}+\end{align*}  | 
 +|Keplers 3rd law when mass of planet is much smaller than the star $\frac{M}{M_\odot} \approx 1$ | \begin{equation} 
 +    a^3 = P^2 
 +\end{equation} |\begin{align*} 
 +a &= \text{Semi-major axis of elliptical orbit in Units of AU}\\ 
 +P &=\text{orbital period in years}\\ 
 +\end{align*}  |
  
-when mass of planet is much smaller than the star, then $\frac{M}{M_\odot} \approx 1$, so: +==== Small angle  ====
-\begin{equation} +
-    a^3 = P^2 +
-\end{equation}+
  
-\subsection{Small angle formular} +|\begin{equation}
-\begin{equation}+
     \frac{D2}{D1} = \sin{\alpha} \approx \alpha      \frac{D2}{D1} = \sin{\alpha} \approx \alpha 
-\end{equation} +\end{equation} |\begin{align*}
-where: +
-\begin{align*}+
 \alpha &= \text{viewing angle (for small angles) in rad}\\ \alpha &= \text{viewing angle (for small angles) in rad}\\
 D1 &=\text{Distance to object in parsec}\\ D1 &=\text{Distance to object in parsec}\\
 D2 &=\text{Extension distance in AU}\\ D2 &=\text{Extension distance in AU}\\
-\end{align*}+\end{align*}|