2017年IOAA理论第8题-圣诞星
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IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题
英文原题
(T8) The Star of Bethlehem [20 marks]
A great conjunction is a conjunction of Jupiter and Saturn for observers on Earth. Assume that Jupiter and Saturn have circular orbits in the ecliptic plane.
The time between successive conjunctions may vary slightly as viewed from the Earth. However, the average time period of the great conjunctions is the same as that of an observer at the centre of the Solar system.
a) Find the average great conjunction period (in years) and average heliocentric angle between two successive great conjunctions (in degrees). [6]
b) The next great conjunction will be on 21st December 2020 with an elongation of 30.3° East of the Sun. Suggest the constellation in which the conjunction on 21st December 2020 will occur. (Give the IAU Latin name or IAU three-letter abbreviation of the constellation, i.e. Ursa Major or UMa) [2]
In 1606, Johannes Kepler determined that in some years the great conjunction can be happen three times in the same year due to the retrograde motions of the planets. He also determined that such an event happened in the year 7 BC, which could have been the event commonly known as “The Star of Bethlehem”. For the calculations below you may ignore the precession of the axis of the Earth.
c) Suggest the constellation in which the great conjunctions in 7 BC occurred. (Give the IAU Latin name or IAU three-letter abbreviation of the constellation, i.e. Ursa Major or UMa)[8]
d) During the second conjunction of the series of three conjunctions in 7 BC, suggest the constellation the Sun was in as viewed by the observer on Earth. (Give the IAU Latin name or IAU three-letter abbreviation of the constellation, i.e. Ursa Major or UMa) [4]
中文翻译
圣诞星
对于地球上的观测者来说，木星合土星是非常帅气的。设木星和土星在黄道面上的公转轨道为圆轨道。从地球上观测，木星合土星发生的周期是很稳定的，变化微乎其微。对于太阳系中心的观测者，木星合土星发生的周期可认为和在地球上观测是相同的。
（a）请计算木星合土星的平均周期（以年为单位），以及连续两次木星合土星位置的黄经差（以度为单位）
（b）下次木星合土星将会发生在2020年12月21日，位置位于太阳以东30.3°。请推算发生时刻它们所在的星座。（给出标准星座名或标准星座名的三字母缩写，例如 Ursa Major 或 UMa）
1606年，开普勒推算出，由于行星存在逆行，一年中可能发生三次木星合土星现象。他还算出这个现象曾在公元前7年（7BC）发生过。这就是举世闻名的“圣诞星”。以下计算你可以忽略地球的岁差。
（c）请推算公元前7年发生“圣诞星”现象时它们所在的星座。（给出标准星座名或标准星座名的三字母缩写，例如 Ursa Major 或 UMa）
（d）在公元前7年发生的三次木星合土星事件中，第二次发生时，对于地球上的观测者，太阳所在的星座是什么？（给出标准星座名或标准星座名的三字母缩写，例如 Ursa Major 或 UMa）
