public:fs_astronomie [Psiox

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====== Astronomy cheat sheet ======

===== Constants to know from heart =====

^Name ^Equation ^Description ^
|c - Velocity of light |$c = 3 * 10^{8}\frac{m}{s}$ |Velocity of light in vacuum |
|AU - Astronomical Unit |$1 AU = 1,5 * 10^{11}m$ |The mean distance from earth to sun |
|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|    

===== Formulars =====
==== Keplers 3rd Law  ====
^Name  ^  Formula  ^  where  ^
|Keplers 3rd Law  |\begin{align*}a^3 = \frac{GMP^2}{4\pi^2} \end{align*}  |\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*}  |
|Keplers 3rd law in simplified units|\begin{equation}
    a^3 = P^2M
\end{equation} |\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 period in years}\\
\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*}  |

==== Small angle  ====

|\begin{equation}
    \frac{D2}{D1} = \sin{\alpha} \approx \alpha 
\end{equation} |\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*}|