496de8c7a9
* Disambiguate python use #1250 Changed all calls to /usr/bin/python to /usr/bin/env python3. Removed execute permissions on a lot of files that are not executable. closes #1250 |
||
|---|---|---|
| .. | ||
| images | ||
| .gitignore | ||
| Flyby.cpp | ||
| makefile | ||
| plot_position.py | ||
| plot_stepsize.py | ||
| README.md | ||
Flyby
The Flyby program uses the SA::RKF45Integrator class to simulate an asteroid passing near Earth.
For each numerical integration time-step, the simulation program prints:
- time (s)
- the size of the last time step
- 2D position vector (m)
- 2D velocity vector (m/s)
to stdout, in Comma Separated Values (CSV) format.
Building & Running the Simulation Program
Generate the results as follows:
$ make
$ ./Flyby > flyby.csv
Plotting the Results
The Python script, plot_position.py is provided to plot the results
in flyby.csv using (Python) matplotlib.
Plot the asteroid path as follows:
$ python plot_position.py
The following shows the path of the asteroid for 25000 seconds (about 7 hours).
The asteroid starts about 20 Earth-radii from the Earth, traveling at 10000 meters per second ( about 22000 miles per hour). The Earth is at 0,0.
The normal (maximum) step-size (dt) for this simulation is 60 seconds. As the asteroid approaches Earth, and gravitational acceleration increases, the RKF45Integrator decreases its step-size to maintain accurancy. The step-size reaches a minimum of about 3 seconds when closest to Earth. As the asteroid retreats, the step-size returns to normal.
With RKF45, a max step-size of 60 seconds, and epsilon = 0.000000001, this 25000 second simulation requires 1513 steps. With RK4 and a step-size of 3 seconds (to maintain the required accuracy), this simulation would require about 8300 steps. So, it would appear that the overhead of RKF45 can be a worthwhile investment in time.
In a simulation where the asteroid were mostly flying through open space, and rarely encountering another planet, the payoff would be much bigger.
