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--- public:fs_astronomie [2023/05/16 17:02]
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+++ public:fs_astronomie [2023/05/16 17:14] (current)
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-====== Formelsammlung Astronomie ======
+====== Astronomy cheat sheet ======
 ===== Constants to know from heart =====
 ^Name ^Equation ^Description ^
-|c - Velocity of light |$c = 3 * 10^{8}\frac{m}{s}$ | |
+|c - Velocity of light |$c = 3 * 10^{8}\frac{m}{s}$ |Velocity of light in vacuum |
-|AU - Astronomical Unit |$1 AU = 1,5 * 10^{11}m$ |unit The mean distance from earth to sun |
+|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 ====
+===== Formulars =====
+==== Keplers 3rd Law  ====
-^Name ^Formula ^where ^Description ^
+^Name  ^  Formula  ^  where  ^
-|Keplers 3rd Law|\begin{align*}a^3 = \frac{GMP^2}{4\pi^2} \end{align*}|\begin{align*}
+|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*}|
+\end{align*}  |
-|Keplers 3rd Law in simplified units|\begin{equation}
+|Keplers 3rd law in simplified units|\begin{equation}
     a^3 = P^2M
-\end{equation}|\begin{align*}
+\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 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}
-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}
+\end{equation} |\begin{align*}
+a &= \text{Semi-major axis of elliptical orbit in Units of AU}\\
+P &=\text{orbital period in years}\\
+\end{align*}  |
-\subsection{Small angle formular}
+==== Small angle  ====
-\begin{equation}
+|\begin{equation}
     \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}\\
 D1 &=\text{Distance to object in parsec}\\
 D2 &=\text{Extension distance in AU}\\
-\end{align*}
+\end{align*}|
-^ Formel                             ^ Result    ^
-| $\sum_{n=1}^{\infty} \frac{1}{n}$  | $e$       |
-| $\sum_{n=0}^{\infty} n$            | $\infty$  |