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Formelsammlung Astronomie
Constants to know from heart
| Name | Equation | Description |
|---|---|---|
| c - Velocity of light | $c = 3 * 10^{8}\frac{m}{s}$ | |
| AU - Astronomical Unit | $1 AU = 1,5 * 10^{11}m$ | unit 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
| Name | Formula | where | Description |
|---|---|---|---|
| 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 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*}
| Formel | Result |
|---|---|
| $\sum_{n=1}^{\infty} \frac{1}{n}$ | $e$ |
| $\sum_{n=0}^{\infty} n$ | $\infty$ |