2016年IAO理论高低年组第3、4题-天兆
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本题为高低年组共用，并且有共用题干。
英文原题
Common introduction for problem 3 and 4, Heaven omen. On June 22, 813A.D, after 15 days of standing opposite to each other, Bulgarian Khan Krum defeated the Byzantine army of Emperor Michael I Rhangabe near Adrianople (currently Edirme, Turkey) and took over the city. After the victory, the Bulgarian army marched on to Constantinople and besieged the capital of the Byzantine Empire. It is possible that the outcome of the battle was affected by superstitious generals. Fear of astronomical events is described in the Byzantine chronicles:" When the two armies, Bulgarian in north-west and Greek in south-east, converged, a terrible celestial omen was the gaze of warriors: two comets, bright as moons, separated from one another." Some historians of astronomy believe that it is one of the first descriptions of a cometary nucleus fragmentation. However, there are other options.
3. Heaven omen. Two comets. Imagine two comets, moving one by one strictly on the same trajectory. Supposing orbital period of the comets is exactly 3 years, let us assume that they come in opposition for an observer on the Earth during the aphelion passage of their orbit (reaching the middle of asteroid belt), but their apparent positions in this position are so close to each other, that the comets merge into one visible point for the naked eye. At what maximum angular distance from each other the comets can be observed at the time of perihelion passage? (At this angular distance, perhaps two comets were seen in June 813 A.D.).
4. Heaven omen. Moon and comet. Even more surprising, but nonetheless, a possible explanation for this phenomenon may be the end of the occultation of a bright comet by the Moon in thin crescent phase. Then the warriors can see how the comet comes out from behind the illuminated part of the Moon and two crescents break up in the sky. In this case:
4.1 At what time of day could this phenomenon have been observed?
4.2 In what constellation could this phenomenon have been observed?
4.3 For which of the two armies the omen has given more fright? Why?
4.4 Include an artistic picture with an image of warriors before the battle. Necessary sizes or angular sizes should be pointed out in the picture.
4.5 Calculate (or explain what data is missing for the calculation), in which of the 15 days of standing armies before the battle, could this phenomenon have been observed.
中文翻译
问题3和4的共用说明。天兆。 公元813年6月22日，经过15天的对峙，保加利亚可汗 Krum 率军在Adrianople （今土耳其 Edirne ）击败了拜占庭帝国皇帝 Michael I Rhangabe 的军队并占领了这座城市，之后乘胜追击，包围了拜占庭帝国首都君士坦丁堡。不过，战争的结局可能被迷信的将领们左右。史书记载了人们对天象的恐惧：“两支军队在原野上对峙，保加利亚人在西北方，希腊人在东南方。此时，可怕的天兆注视着勇士们：有两颗月亮一样明亮的彗星，彼此分开。”一些天文历史学家认为这是人类首次观测到的彗核分裂现象，然而还有别的观点。
3. 天兆 两颗彗星。 想象一下，有两颗彗星，一颗接一颗严格按着相同的轨道运行。假设彗星的轨道周期恰好是3年；在远日点（差不多是小行星带带中央）的时候，对于地球上的观测者而言，两颗彗星恰好冲日，不过在此时，两颗彗星离得很近，以至于裸眼看来它们是一个光点。那么在它们过近日点的时候，两颗彗星彼此分开的最大角距离是多少（也许在这个角距离上，两颗彗星在公元813年6月能被看到）？
4. 天兆 月球和彗星。 有一种十分惊人但也不是不可能的观点是，极细的月牙掩住了一颗明亮的彗星，而这个景象发生在掩星即将结束时。这样当两国的勇士们看到彗星从月球被照亮的一侧出现时，他们发现月牙一分为二。在这种情况下：
4.1 在一天中的什么时候可以观测到这个现象？
4.2 在哪个星座中可以观测到这个现象？
4.3 哪一只军队将会更害怕这个天象？为什么？
4.4 画一张包含了激战之前的双方勇士的战场艺术画。必要的大小和角度需要在图里标出来。
4.5 计算（或者解释缺少了什么数据）这对峙的15天里，哪一天会观测到这个现象。
