Marslanding

This project is a simulation of a mars landing.

Demo Hostet at mars.hobbylos.org.

To run the project locally just start the docker compose file with docker compose up and open the browser at localhost:80.

Math

Force over time with changing mass

$\displaystyle \Delta v = F * \frac{t}{m}$ (Change in velocity)

$\displaystyle \Delta t$: Time Interval
$\displaystyle m_{0}$: Mass at $\displaystyle t_{0}$
$\displaystyle \Delta m$: Change in Mass in Time Interval $\displaystyle \Delta t$

$\displaystyle m(t) = m_{0} - \frac{\Delta m * t}{\Delta t}$ (Linear Equation)

$\displaystyle \Delta v = \int_{0}^{\Delta t} \frac{F}{m_{0} - \frac{\Delta m * t}{\Delta t}} ,dt = \ -F {\left(\frac{\Delta t \log(-\Delta m + m_{0})}{\Delta m} - \frac{\Delta t \log(m_{0})}{\Delta m}\right)} = \ F {\left(\frac{\Delta t \log(m_{0})}{\Delta m} - \frac{\Delta t \log(m_{0} - \Delta m)}{\Delta m}\right)} = \ F * \frac{\Delta t}{\Delta m} {(\log(m_{0}) - \log(m_{0} - \Delta m))} = \ F * \frac{\Delta t}{\Delta m} * \log\left(\frac{m_{0}}{m_{0}-\Delta m}\right)$

Calculation

Sources

(1) Barometrische Höhenformel [Zitat vom 10.06.2024]
(2) Schwerefeld [Zitat vom 10.06.2024]
(3) Gravitationskonstante [Zitat vom 10.06.2024]
(4) Drag [Zitat vom 10.06.2024]
(5) Specific Impulse [Zitat vom 10.06.2024]
(6) Barometrische Höhenformel für die Marsatmosphäre [Zitat vom 11.06.2024]

Image-Sources

(1) Bild des Raumschiffs [Abgerufen am 11.06.2024]
(2) Bild der Flamme [Abgerufen am 11.06.2024]