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--- public:fs_astronomie [2023/05/16 11:41]
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+++ public:fs_astronomie [2023/05/16 17:14] (current)
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-====== Formelsammlung Astronomie ======
+====== Astronomy cheat sheet ======
-\subsection{Velocity of light}
+===== Constants to know from heart =====
-\begin{equation}
-    c = 3 * 10^{8}\frac{m}{s}
-\end{equation}
-\subsection{AU - Astronomical unit}
+^Name ^Equation ^Description ^
-The mean distance from earth to sun
+|c - Velocity of light |$c = 3 * 10^{8}\frac{m}{s}$ |Velocity of light in vacuum |
-\begin{equation}
+|AU - Astronomical Unit |$1 AU = 1,5 * 10^{11}m$ |The mean distance from earth to sun |
-AU = 1,5 * 10^{11}m
+|Ly - Lightyear|$1Ly \approx 9,5 * 10^{15}m$ |Distance light travels in one year|
-\end{equation}
+|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*}|