2016年IAO理论高低年组第3、4题-天兆

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.