远程星际航行补篇

A Note on Interstellar Astronautics

通过一系列变量置换推导出不同喷气速度和不同加速度条件下,计算恒星际飞船加速段的时间和距离的普遍公式及多级火箭加速情况下加速段的时间和距离的公式。最后以天狼星作为航行目标、计算了用5级和10级火箭加速飞行的时间和距离。结果表明,当火箭的级数很多,且各级加速度相等时,其飞行时间与距离非常接近匀加速飞行的情况。

This paper discusses an extension of Dr.Qian＇s previous work on interstellar travel into the field of multi-stage rocketry.Through the transformation of variables for integration,it was found possible to present some general formulas for the time and distance of accelerating or decelerating part of the trajectory as functions of various parameters such as final speed and exhaust speed.Instead of carrying out the integration for individual values of exhaust speed,the results which are finally plotted in figures have been directly obtained from the general formulas for various practical values of exhaust speed.Numerical examples are also presented and show that a travel to Sirius,a star at a distance of 8.6 light years from the earth,by a five-stage rocket and a ten-stage rocket,both accelerating to V=0.94c with exhaust speed of 0.6c and both at the uniform acceleration of 20m/s2 with respect to the occupants,would require Ta=0.994 years and Ta=0.894 years respectively.The total travel time to Sirius as observed by the occupants would be 4.37 years and 4.20 years respectively.