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Soon after civilization befell human, we became curious about any and everything around us. We developed the field of biology because we are fascinated by the circle of life as well as its wonder; we developed the field of psychology because we are curious about how the human brain works in various ways; we developed the field of chemistry because we are just pumped to get a closer look at how elements can create an entire universe…also, astrophysics were developed.
Human beings never stop examining the outside world, the “real” outside world---the cosmos. However, in order for us to know more about the whole universe, we need to first take a better look at the closest satellite to us. In this article, we talk about the moon, more specifically, lunar eclipse.
The time difference algorithm of lunar eclipse in ancient Chinese calendar is designed to correct the time difference between the fixed expectation and the very moment of eclipse.
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The algorithm was first developed by Dayan Li. Since then, the corresponding algorithms have been designed for Qintian Calendar, Jiyuan Calendar, Gengwu Yuan Calendar and Jishi Calendar. The theoretical model proves that the algorithm of lunar eclipse time difference is necessary. The algorithm of lunar eclipse time difference designed in the ancient Chinese calendar should be independent of the lunar parallax, thus refuting Zhu Zaiyu's criticism of the algorithm of lunar eclipse time difference in the 'Era Calendar' and other calendars.
The algorithm for the difference in moon phrase as the figure represented, line NS, NM represent the ecliptic and the moon’s path.
Point M,S are the sun and the moon at a particular time. AB represent the minimum distance of the sun and moon.
When NS = a, NM = b; vm、vs represents the velocity of the moon and the sun relative to the intersection N.
If Δt represents the time length from SM to AB, draw the line BC⊥NS;
BC=NB sin (i)=2 (b-vmΔt) sin (i)
AC= (a-vsΔt) - (b-vmΔt) cos (i)
Since AB2 +BC2 + AC2 ,
AB2= (b - vm Δt)2 + (a - vs Δt)2 - 2 (b - vm Δt) (a - vsΔt) cos(i)
When the derivative of AB = 0
(a-vsΔt) (vmcos(i)-vs) + (b-vmΔt) (vscos(i)-vm) =0
Set β to be the Ecliptic latitude of the moon at a particular moment,
β =b sin(i), thus a=b cos(i), thus we could get the value of Δt
Furthermore, if we assume the sun is static – when considering the relative velocity to the moon, thus vs=0. Thus we could get a simplified equation for Δt when the connection line between the sun and the moon AB is perpendicular to NM.
The equation above is a relatively simplified equation only. For more accurate result, formulating a differential equation is necessary. Since point N is always mobile, the triangle MNS is actually moving with changing time Δt. In other words, the ecliptic latitude MS=β of the moon M is related to time Δt. Thus, when searching derivation for AB, we could not assume β as a constant: we ignore the fact only because it have neglectable changes.
Base on the previous discussion, we can safely draw the conclusion on how ancient Chinese scientists calculated lunar eclipse.
First and foremost, calculation about lunar eclipse from Ji Yuan Li and Shou Shi Li is correct. We have found out that the purpose of time difference of lunar eclipse from ancient Chinese was to revise the time difference of lunar eclipse, the difference between Dingwang and Shisheng. According to current theories of astronomy, the difference between these two can be up to 8-11 minutes, which can be neglected under a circumstance that doesn’t require rigorous calculations. However, with the promotion of accuracy calculation, calendar makers needed a more precise measurement to calculate the magnitude of eclipse. As a result, they added time difference of lunar eclipse for further consideration. Therefore, the starting point of using time difference of lunar eclipse was right.
Secondly, ancient Chinese’s calculation of time difference of lunar eclipse had no connection with lunar parallax. According to modern theories of astronomy, calculation on sun eclipse needs to consider parallax, but not in lunar’s scenario. Ancient Chinese calendar makers had clear realization about it. They design 3 difference calculation on sun eclipse. But they only made time difference calculation about lunar eclipse. This indicates that there is no relationship between time difference of lunar eclipse and lunar parallax. Therefore, we can see the ancient Chinese calculation is correct.
Moon Phrase Algorithm for Lunar Eclipse of Ancient China. (2024, Feb 17). Retrieved from https://studymoose.com/document/moon-phrase-algorithm-for-lunar-eclipse-of-ancient-china
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