2015IOAA理论短问题第5题-卫星轨道

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英文题目

An observer is trying to determine an approximate value of the orbital eccentricity of a man-made satellite. When the satellite was at apogee, it was observed to have moved by $$∆𝜃_{1}$$ = 2′44" in a short time. When the radius vector connecting Earth and the satellite is perpendicular to the major axis (true anomaly is equal to 90o), within the same duration of time, it was observed to have moved by $$∆𝜃_{2}$$ = 21′17". Assume that the observer is located at the center of the Earth. Find an approximate value of the eccentricity of the satellite’s orbit.

中文翻译

一个观察者正在尝试确定一颗人造卫星轨道的偏心率。当卫星位于远地点时，观察到它在短时间内移动了 $$∆𝜃_{1}$$ = 2′44"。当连接地球和卫星的半径向量与长轴垂直（真近点角为90°）时，在相同时间内，观察到它移动了 $$∆𝜃_{2}$$ = 21′17"。假设观察者位于地球中心。求卫星轨道偏心率的近似值。