2019年IAO理论高年组第5题-两颗卫星

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英文题目

5. Two satellites. Two artificial satellites move around an unknown planet in circular orbits. The satellite S1 moves in an equatorial orbit with the angular velocity ω1, and the satellite S2 moves in a polar orbit with the angular velocity ω2, as shown in Fig.5. The planet rotates around its axis with the angular velocity ω0. At the initial time, the satellites are in zenith for observer O.

5.1. It is known that for observer O, the duration of the visibility (from the zenith to setting) of satellite S2 is t2. Find the similar visibility duration t1 of satellite Sl.

5.2. Find the azimuth ζ, of the satellite S2 setting point (the point of its "disappearance" for the observer). Consider the South direction as the zero azimuth point (0°).

中文翻译

5.两颗卫星。两颗人造卫星在圆轨道上环绕一颗未知行星。第一颗卫星S1以角速度ω1在沿赤道绕转,而第二颗卫星S2以角速度ω2沿极轨道运转,如图5所示。行星绕自转轴旋转的角速度为ω0。在开始时,两颗卫星都位于观测者O的天顶。

5.1 对观测者O,已知卫星S2的可见时间(从天顶到落下)为t2。计算卫星Sl的可见时间t1

5.2 计算卫星S2落入地平线时的方位角(对观测者来说卫星“消失”的点)。南点为方位角0°。