Effects of interstellar drag on minimumtime trajectories with thrustlimited relativistic rockets
Abstract
An analysis is presented of the effects of drag due to the presence of interstellar matter which acts on a relativistic thrustlimited rocket traveling a minimumtime trajectory between fixed points with zero initial and final velocities. Two rockets are considered: an ideal photon rocket with an effective exhaust velocity equal to the speed of light (c) and an ideal nuclearfusion rocket with an effective exhaust velocity of 0.0893c. The mathematical problem is outlined, and a twopoint boundaryvalue problem is derived using the necessary conditions for a minimumtime trajectory. Solution of the latter problem indicates that the main effect of interstellar drag is that a singular arc (where thrust equals drag) may have to be incorporated into the minimumtime trajectory. It is concluded, however, that no singular arcs occur with realistic drag coefficients and that the effects of drag are very small for a flight time of 40 years and a maximum acceleration of 1 light year per year per year (as recorded on the rocket).
 Publication:

Lisbon International Astronautical Federation Congress
 Pub Date:
 September 1975
 Bibcode:
 1975lisb.iafcU....A
 Keywords:

 Drag;
 Flight Time;
 Interstellar Travel;
 Relativistic Velocity;
 Time Optimal Control;
 Trajectory Optimization;
 Aerodynamic Coefficients;
 Mass Ratios;
 Mathematical Models;
 Rocket Thrust;
 Astrodynamics