【摘要】 <正> 向大行星,特别是向火星发射宇宙火箭,已成当前现突的问题.在文献中看到的方案,一般是霍曼(Hohman)轨道,速度大小虽然不同,但火箭方向在脱离地球引力范围时都与地球轨道相切.这样,发射速度愈大,到达火星的时间也愈短.但在相同的地面发射速度情况下,用不同方向发射,到达火星的时间是不同的.其中是否有极值存在,使得到达更多还原

【Abstract】 In general,the time required for a spaceship to go from Earth to another planet varies inversely with initial velocity （from Earth’s surface）.If absolute value of the initial velo- city is given,then there exists a direction of this velocity such that the time spent by the spaceship on the way is minimum.This is the result of our investigation of the minimum- time orbit from Earth to Mars. Suppose the orbits of Earth and Mars be circular,and lie in the same plane.The gravitational region of the Earth is a sphere with radius ρ=930,000 km （Egoroff’s value）. In this gravitational region,in determining the spaceship’s motion it is only necessary to consider the Earth’s attraction,and it is necessary to consider the Sun’s attraction only, when the spaceship gets out of the Earth’s gravitational region. Let v denote the initial velocity on Earth’s surface,α denotes its direction with respect to the radius vector of the Earth from the Sun.v_1a,α′ denote the values of v and α res- pectively at the boundary of Earth’s gravitational region,and V₁,α₁ denote respectively the values of v_1a,α′ relative to the Sun.The time spent by the spaceship inside and outside the Esrth’s gravitational region are T₁,T₂ expressed by formulae （2）,（6）. If v is given there exists a certain value of α,such that T=T₁+T₂ is minimum, for the case v=14-16 km/sec,numerical calculation shows that α=42°-46°.更多还原