What is position acceleration

CALCULATING PROBE TRAILS WITH THE TIME STEP METHOD How can

CALCULATING PROBE TRACKS WITH THE TIME STEP METHOD How can trajectories of probes be calculated and simulated?

PROCEDURE Rosetta probe (2 min) Overview trajectory & obstacles Time step method (5 min) General derivation of gravitation Use of the time step method Simulation of probe paths (3 min)

ROSETTA SONDE Space probe of the ESA (European Space Agency) Target: Kommet Tschurjumow-Gerasimenko Launch: March 2, 2004 at 8:17 am, the Ariane 5 G + launcher was launched

ROSETTA FLUGBAHN Swing by maneuvers to Earth & Mars Planet releases kinetic energy to space probe Hibernation (June 2011 - January 2014) Due to the distance to the sun, Rosetta cannot maintain communication. Dropping of the Philae lander (November 2014) Difficulties due to the complicated surface structure of the comet.

GENERAL TIME STEP METHOD Movements are simulated. A program always calculates the new position of an object according to a fixed time step. Advantage: Complex movements can be simulated using simple calculations. Disadvantage: If the time step is too large, the simulation becomes imprecise.

DERIVATION OF THE GRAVITATION Radial gravitational field r P

APPLICATION OF THE TIME STEP METHOD The 2D coordinate system y probe x r x mass

APPLICATION OF THE TIME STEP METHOD From acceleration to position acceleration speed distance

SIMULATION OF PROBE TRACKS [EXAMPLE FILM]