 For example, when modeling the motion of a satellite about the earth as a standard Kepler orbit, a fixed time-stepping method such as the Euler method may be sufficient.However things are more difficult if one wishes to model the motion of a spacecraft taking into account both the Earth and the Moon as in the Three-body problem.There, scenarios emerge where one can take large time steps when the spacecraft is far from the Earth and Moon, but if the spacecraft gets close to colliding with one of the planetary bodies, then small time steps are needed.