意料之外

mca

被 Phonon 姐提醒，我把南北極和 22 個國內外城市的 日全食/日環食 全部抽了出來比較，結果令我意外，由公元前 1500 至 3000 年期內，

最多日全食 + 日環食 竟然在 ?  
最多日全食次數是 18，在 ?
最少日全食次數是 3，在 ?
日全食要相隔 ? 年才重覆出現 .....

http://alanchuhk.com/SolarEclipse_Worldwide.doc

AC

phonon

咁有毅力去追求答案，簡直佩服你到五體投地。

Hee! Hee! 我之前回應阿 Bill 的　message 只因不滿足於他推論，所以隨便講吓，無想過你會咁認真看待。

從你身上的確學到很多嘢。你的結果的確又幾令我覺得意外，我還以為南北兩極的日食會比較少些。

[ 本帖最後由 phonon 於 2009-8-14 00:30 編輯 ]

oldfield

excellent!

jojomamani

認真的研究精神！實在令人拜服！

philipchung

Dear MCA,
Very impressed attitude and very interesting results.
The three proposed factors that could affect the no. of occurrance of total solar eclipse are insightful.

On the proportion of A (annular) and T (Total), I'll like to add a few minor observations: Firstly, it's hard to observe a pattern of their respective occurrance. E.g. roughly in the last 1000 years, most of the solar eclipse occurred at Hangzhou were (T) while ALL the solar eclipse occurred at South pole were (A). It seems that geographical latitude is not a significant factor as evidenced from the table (which I myself was a bit surprised).

Secondly, as already pointed out by MCA, A/T ratio is larger than 1 in all cities except St. Petersburg.  (I noted that Beijing and Los Angeles had an A/T ratio equals 1). This results deserve a closer look as it may reveal something fundamental, it may also add some details of MCA's proposed factor no. (1).

Thirdly, to supplement the comments made by MCA in his para.4, i.e. 風水輪流轉, I noted from the data as shown in the Table, the av. no. of eclipse (T+A) from -1499 to 3000 AD is about 30.2 and all data fall within 1.8 standard deviation.  Though I have not done a statistical hypothesis test, I personally don't believe that most places in the world would enjoy equal chance of total solar eclipse occurrance.  The geographical location does matter.

Dennis

好有趣及心機的文章，謝謝分享﹗

mca

Dear Philip,

你也很 impressive ，從你主持的講座和會址的TAG 書量便知了  

礙於時間和篇幅，有幾點我沒有寫出來，現在正好補充一下：

1.    抽查地點其實有 ~50 處，一半在文內列出來，另一半 fast scan 後發覺不影統計的走勢所以從略。

2.   日食 A/T < 1 確有其基本道理 (fundamental)，就是 月影的平均長度永遠少於月地平均距離 (373,000：384,000 km 之比)，這時月影的尾端不能投到地面產生日全食，只有環食，即使地月系統在遠日點，月影的最大長度不過是 380,000 km，仍然少於月地平均距離。故此全球的 A 總是多於 T，後者只能等待月球走近 近地點 (356,000 km) 時才會發生。

月影長度和月地距離 (還有觀測位置) 又控制了日全食帶的寬度，它的寬度變化甚大，從 200+ 至 零 km 也可以，當食帶窄至 20 km 以下時，像原文所說的「元朗見全食、赤柱見偏食」的情況便出現了 (儘管赤柱見到的食分很接近 1.00)。

在我來看，地方性 A/T 比例參差不齊的作俑就是 “食帶寬度變化”，三千年前如是，未來一千年也會如是，所以用甚麼條件作為統計的標準要明確，例如觀測地點的實際經緯度要列明，當食帶很窄時，經緯度改變幾角分也會使 A/T 比例走樣，我仍未有時間去分別南極 (90 S) ：89 S  的 A/T 比例 (也不願重覆 NASA 已有的數據)，不過我相信上述元朗 / 赤柱例子，你所說的 1.8 sigma 已有啟示了。從另一方面想，兩極 A+T 機會偏多的原因是由於月影錐以低角度投向地面 (兩極的太陽角度不會高過 23 度)，月投影蓋過的地面面積較廣，那裡又恰好在地球的自轉軸端上，出現較多 A+T 是可以理喻的。

講開統計，社會上不時見人蓄意誇大或壓低數字 (例如上市公司年報、集會人數、商品銷量、收視率、讀者人數等)，你不能說他們不對，統計機制和結果沒有錯，問題只是他們講 D 吾講 D，段章取義以利其目的而已。

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To anyone interested, which of the following statements you feel comfortable? The same statistics but deviates 10 times by amount !

1.  On the nearside there are about 300,000 craters larger than 1 km  (Rukl’s Atlas of the Moon, 1990)

2.  Those with diameters in excess of 1 km are estimated to add up to 300,000 on the visible hemisphere of the Moon.  (Kopal’s Atlas of the Moon, 1971)

3.  There are about half a million craters with diameters greater than 1 km on the moon.  (The Moon Wikipedia)

4.   With an Earth based telescope, some 30,000 craters are visible with diameters ranging to 1 km to several hundred km.  (Kaufmann & Freedman’s Universe 5th edition, 1998)

5.   At the best Earth-based resolution of 1 km, 30,000 craters can be identified on the hemisphere of the Moon that faces the Earth  (Morrison’s The planetary System, 1996)

6.  據統計，月球表面大于 1 km 的撞擊坑總數在 33 000 個以上。
(手頭的國內書本都說 33000 個，包括教科書和歐陽自遠主篇的月球科學慨論)

Alan Chu

[ 本帖最後由 mca 於 2009-8-29 10:37 編輯 ]