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一、从一道试题讲起如图1所示是一个绕地球作椭圆轨道运行的人造地球卫星。卫星在远地点b距地心的距离是近地点a距地心距离的2倍。设卫星在a点的速度是v_1,角速度是ω_1,向心加速度是a_1;在b点的速度是v_2,角速度是ω_2,向心加速度是a_2.则v_1=()v_2,ω_1=()ω_2,a_1=()a_2。(选自哈尔滨出版社,“北大、清华、人大附中高中毕业班各科试题解”p.200第5题) 书中给出答案是:v_1=(2v_2)~(1/2),ω_1=(2ω_2)~(1/2),a_1=4a_2。我认为前二个答案是错误的,其解答过程书中虽未给出,但要得到上面的结论必采用了如下推理过程。根据动
First, from a test question, as shown in Figure 1, it is a man-made earth satellite orbiting the earth in an elliptical orbit. The distance of the satellite from the apogee b to the center of the earth is twice the distance from the geocentric distance a. Let the speed of the satellite at point a be v_1, the angular velocity be ω_1, the centripetal acceleration be a_1, the velocity at b is v_2, the angular velocity be ω_2, and the centripetal acceleration be a_2. Then v_1=()v_2, ω_1=()ω_2 ,a_1=()a_2. (From Harbin Publishing House, “Questionnaires for the subjects of the senior high school graduating class at Peking University, Tsinghua University, and Renmin University” p.200 question 5) The answer given in the book is: v_1=(2v_2)~(1/2), ω_1= (2ω_2)~(1/2), a_1=4a_2. I think the first two answers are wrong. Although the answer process book is not given, the following reasoning process must be used to obtain the above conclusions. According to the move