搜索
查看: 7995|回復: 16

牛頓怎樣想出萬有引力理論?

 關閉 [複製鏈接]
發表於 2010-7-8 23:11:22 | 顯示全部樓層 |閱讀模式
發表於 2010-7-9 11:39:41 | 顯示全部樓層
本帖最後由 mca 於 2010-7-10 02:25 編輯

回應#1

這幾篇網文沒有把牛頓怎樣想出萬有引力理論交代消楚,他們大慨不是學天文的,作文只站在數學立場而為。

你可參考天文學史的書籍 ,例如 Cambridge University 的 Illustrated History of Astronomy 的第六章  Newton and Newtonianism --- The Dynamics of Elliptical Orbit  那幾頁, 它講得比較好。

牛頓因下跌蘋果而發現萬有引力的故事是坊間的加鹽加醋傳聞而已,在微積分蘊釀時代牛頓巳有 "引力" 慨念,從引力他想到月球的軌道運動,但未肯定引力與距離平方成反比的關係。1665~1666 瘟疫爆發時,他在母親鄉間的屋院避瘟疫,偶然見屋外跌下蘋果,他把月球軌道運動的下墜與下跌蘋果聯想起來,計了一輪數沒有頭緒 (他當時計錯了數,但思維的邏輯沒錯),於是把問題放下,一放就過了六七年,後來見到較新的天文數據,他再計算,終於醒悟使月球運動下墜的引力和使蘋果跌落地面的力同源一轍,並且肯定了引力與距離平方成反比的關係,這時他開始整理他的研究成書,並在 ~1687 年發表 "Principia"。


有時間我會另寫詳細些。


Alan
發表於 2010-7-10 01:54:26 | 顯示全部樓層
本帖最後由 mca 於 2010-7-18 12:42 編輯

(以下是我知道的故事)


牛頓怎樣發現萬有引力定律
----------------------------------
講野史,坊間往往加鹽加醋來吸引聽眾,中國有康熙遺詔被改寫為  "傳位于四子" 的傳聞,外國亦有牛頓因蘋果跌在頭上而發現萬有引力的故事,現在史學家已証明這些野史不確。

早在青年時代,牛頓已從前輩 Galileo (b 1564)、Kepler (b 1571)、Descartes (b 1596)、Huygens (b 1629)、Hooke (b 1635) 等學者領悟到太陽行星及衛星之間存着某種力量關係 *,這種關係稱為 引力 gravitation,原字出自拉丁語 gravitatem (nom. gravitas),表示「重」的意思。踏入微積分萌芽時代,牛頓更從數學上了解某些參數之間存着 "逆平方律"  (inverse square law) 的關係,例如 x = 1 / y^2,於是他開始憧想 ----- 引力與距離是否也有  "逆平方律" 的關係呢? 要知答案,自然要用事實求証,可是一時間牛頓還沒有找到事實証明。

1665 至 1666 年,英國爆發瘟疫,牛頓剛剛大學畢業,他走回 Lincolnshire 鄉間母親處避開瘟疫,某天他偶然在庭園見蘋果從樹上跌下來 **,他靈機一觸就這樣想 ----- 蘋果墜落地上的力 (重量) 與 維持月球繞地球運行之力 (引力) 是否同出一轍呢 ?  究竟這所謂 "引力" 有沒有延展性令其他行星繞太陽運轉 ?   於是他開始計算,當時他大約知道地球半徑 R = 4000 哩 (6400 km),月地距離 D = 240 000 哩 = 60 倍地球半徑,蘋果跌向地面的加速度 a = 32.2 呎/秒/秒 (980 cm/sec^2),因此在頭一秒 ( t = 1 sec) 時,蘋果已下跌了 1/2.a.t.t = 16.1 呎,如果蘋果下墜之力與月地間的引力都是同一力量,而引力又與距離平方成反比的話,那麼月球也應像蘋果在軌道切線之下跌了 16.1 呎 / 60 的平方 = 0.0537 吋,見圖一。

               


本來像圖一要証明月球下墜 0.0537 吋是很普通的算術,但不知何故,牛頓竟然計錯數 (他把地球半徑的哩數換算為錯誤的吋數,另一說他引用了欠準的地球半徑值),結果他得不到應有的 0.0537 吋,他只好把引力問題放下而轉研其他項目,就這樣一放之下便過了六七年,直至某次他聽到 Picard 發表新的地球半徑數據,於是他重新計算以前的月球/蘋果引力問題,今次他真的計得 ~ 0.0537 吋,說明了三個原理:   (一) 蘋果下墜之力與維持月球軌道運動之力是同一性質的 (universal);(二) 兩件物體之間的引力與其距離的平方成反比;(三) 地球上的引力加速度與下墜體的質量無關 (即解釋了伽利略在比蕯斜塔做的跌球實驗)。自此之後牛頓對研究更具信心,友人哈雷 (預測彗星回歸的 Halley) 又鼓勵和資助他發表研究結果,終於在 1687 年出版了影響後世的 Principia ***,1713 年出第二版,1726 年出第三版,今天還有 "網上版"。

                             


--------------------
註 *   The Oxford Guide to the History of Physics and Astronomy, page 227:
"In 1679, Newton learned of Robert Hooke's 胡克 idea that orbital or curved motion could be explained by a combination of a linear inertial component along the orbit's tangent and a continual falling inward toward the center. Newton wrote that he had never before heard of this 'hypothesis.' But he perceived a connection between Hooke's suggestion and Johannes Kepler's law of areas .....".

註 **   http://www.maths.tcd.ie/pub/Hist ... Ball/RB_Newton.html
In the year 1666 he retired again from Cambridge ... to his mother in Lincolnshire & while he was musing in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon thought he to himself & that if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a-calculating what would be the effect of that superposition... (Keesing, R.G., The History of Newton's apple tree, Contemporary Physics, 39, 377-91, 1998)

另一網頁  http://www-groups.dcs.st-and.ac.uk/~history/PrintHT/Orbits.html  這樣寫:
Fifty years after these events Newton was to record his own recollections of these events which, although interesting, do not really agree with the known historical facts!  [I preserve Newton's old English. Note that ye = the, orb = orbit, wch = which.]

"..... In the same year I began to think of gravity extending to ye orb of the Moon and (having found out how to estimate the force with wch globe revolving within a sphere presses the surface of a sphere) from Kepler's rule of the periodical times of the Planets being in sesquialternate proportion to their distances from the centres of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must reciprocally as the squares of their distances from the centres about wch they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth, and found them answer pretty nearly. All this was in the two plague years of 1665-1666....."

註 ***   http://www.laughtergenealogy.com/bin/histprof/misc/newton.html
The Principia ----- Newton concluded his first investigations on gravity and motion in 1665 and 1666. Nothing was heard of them for nearly 20 years. His original theory had been based on an inaccurate measurement of the earth's radius, and Newton realized differences between the theory and the facts. Although he later learned the true value of the earth's size, he was not led to complete his investigation or to produce a book for publication.

One day in 1684, Edmond Halley, an English astronomer, Robert Hooke, an English scientist, and Christopher Wren, the architect, were discussing what law of force produced the visible motion of the planets around the sun. They could not solve this problem. Halley went to Cambridge to ask Newton about it. He found Newton in possession of complete proof of the law of gravity. Halley persuaded Newton to publish his findings. Halley paid all the expenses, corrected the proofs, and laid aside his own work to publish Newton's discoveries. Newton's discoveries on the laws of motion and theories of gravitation were published in 1687 in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). This work, usually called Principia or Principia Mathematica, is considered one of the greatest single contributions in the history of science. It includes Newton's laws of motion and theory of gravitation. It was the first book to contain a unified system of scientific principles explaining what happens on earth and in the heavens.


其他參考:

Cambridge Illustrated History of Astronomy, Chapter 6 --- Newton and Newtonianism

On-line versions of Newton’s Principia  http://en.wikipedia.org/wiki/Phi ... incipia_Mathematica

Newton might have known gravity from a visible comet, not a falling apple !
http://www.youtube.com/watch?v=D5BQkdyAw8A&feature=related
發表於 2010-7-11 01:41:50 | 顯示全部樓層
本帖最後由 mca 於 2010-7-11 12:42 編輯

To 梅西爾

名教授 Richard Feynman 有一學界聞名的講座:The Law of Gravitation, an example of Physical Law,講義已收集在小冊子 “Richard Feynman --- The Character of Physical Law” 中,BBC 亦有現場 TV 錄影,你可在 YouTube 重看 (http://www.youtube.com/watch?v=euGp9quNqLU),video 分為 6 parts 共  1 小時,Feynman 講得幾生動,不過它是五十年前的舊製作,畫質稍遜,要細味還是看原書中的講義及插圖。

"Richard Feynman --- The Character of Physical Law"  這本小冊子在圖書館不難找到,十年前我在商務買了一本,約 HK$100。

   http://www.amazon.com/Character- ... brary/dp/0679601279  這書獲高度評價 !
 樓主| 發表於 2010-7-11 13:00:11 | 顯示全部樓層
Thanks Alan
發表於 2010-7-12 16:11:42 | 顯示全部樓層
回應 #5

這系列的 Feynman 公開講座有一種特色,他不會機械式去硬銷物理定律的數學內容 (因為所有理科教本都會教的,不須在講座中長篇大論而使局外人發悶),他要讓聽眾知道是什麼契機觸發科學家去想,前人作過甚麼努力?  研究時遇過那些困難?  研究結果對後人有什麼啓發作用 .....  這些都是講座中最重要的 "核心價值”,希望你好好明白和掌握。
 樓主| 發表於 2010-7-12 22:51:10 | 顯示全部樓層
Alan,有時我會覺得,以微積分理解牛頓力學,可能會較好。
因為牛頓有很多成果,也可以說是建基於微積分的基礎。
在不同情況,我們把微積分方程寫到另一種形式,便行了

這只是我的愚見,還望指教
發表於 2010-7-13 08:20:49 | 顯示全部樓層
梅西爾:

你的想法很對,我讀書時也這樣想,所以要先學好微積分,不過随着年紀漸長,經驗告訴我,物理不等于數學,你現在未必明白,將來會。

在 Feynman 第二次講座正好回應你的問題,第二次講 The Relation of Mathematics to Physics,其中有些說話很精警 (個人意見):

“….. Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about (in the sense of physics).  They do not even need to know what they are talking about, or, as they themselves say, whether what they say is true. I will explain that ….. (p.55 of my version of Richard Feynman – The Character of Physical Law, Chapter 2)  

….. That is a very important thing that a lot of people who come to physics by way of mathematics do not appreciate. Physics is not mathematics, and mathematics is not physics. One helps each other. But in physics you have to have an understanding of the connection of words with the real world. It is necessary at the end to translate what you have figured out into English, into the world, into the blocks of copper and glass that you are going to do experiments with. Only in that way can you find out whether the consequences are true. This is a problem which is not a problem of mathematics at all ….. (p.56)”


第二次講座亦可在 YouTube 找到:

Richard Feynman - The Relation of Mathematics & Physics, Part 1
http://www.youtube.com/watch?v=1SrHzSGn-I8

Part 2 to Part 6 are all here:
http://www.youtube.com/results?s ... ics+part+2&aq=f


當然,如果你以純數為業而不理會物理世界 (包括天文學),上面幾句話對你不適用。


Alan
 樓主| 發表於 2010-7-14 10:06:03 | 顯示全部樓層
Alan,

我會這樣認為。如果數學不是用來解決其他數學以外的問題,那麼數學可以說是真的沒有其他用處。其實用性將會大減。

以數學解決問題時,可以單純利用數學思考,但不會解決到問題。我的經驗時,不以單靠數學的思維去解決,同時也該思考一下物理情況。

謝謝你給我的兩句話。

梅西爾
發表於 2010-7-14 18:55:41 | 顯示全部樓層
牛頓著作 Principia 只是後人叫的簡稱,原名是 Philosophiae Naturalis Principia Mathematica (拉丁語),英譯 Mathematical Principles of Natural Philosophy,中譯《自然哲學的數學原理》。 從書名可知數學與自然科學 (牛頓叫哲學) 的關係,如果不把數學與自然科學掛勾,只是玩弄公式和數字,或是不懂得把數學轉化為生活意識的語言,他只是一位藝術家,不是科學家。這也說明諾貝爾物理學的頒發原則 --- 得主都與科研或其應用有關。 (個人意見)
您需要登錄後才可以回帖 登錄 | 申請討論區帳戶

本版積分規則

手機版|Archiver|香港天文學會

GMT+8, 2022-8-12 05:46 , Processed in 0.010469 second(s), 16 queries .

Powered by Discuz! X3.4

© 2001-2013 Design S!|平潭

快速回復 返回頂部 返回列表