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Solving Kepler's Equation

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Solving Kepler's EquationBy Colwell. Product Information: 6. 00" by 9. 00", 202 pages, hardbound, published 1993. The sole subject of Solving Kepler's Equation work is Kepler's Equation (KE) M = E e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval [0,p]and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list

By Colwell.

Product Information: 6.00" by 9.00", 202 pages, hardbound, published 1993.

The sole subject of Solving Kepler's Equation work is Kepler's Equation (KE) M = E - e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval [0,p]and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list of them that the problem has enticed a wide variety of scientists to comment on or involve themselves in its solution.

It is surely not unique in science for a specific problem to be given so much attention over so long a period—particularly if it resists solution, if its partial solutions are inadequate or unsatisfactory, or if it is recharged with new interpretations and new applications. Still, it is curious that the Kepler problem should have continued to be this interesting to so many for so long. Admittedly it is a problem central to celestial mechanics, but it is a technical little problem for which a number of satisfactory solutions are long known. With the advent of calculators and computers, there is no impediment to achieving quick solutions of great accuracy. The problem has neither the broad appeal of an Olbers Paradox, nor the depth and intractability of a many-body problem.

In common with almost any scientific problem which achieves a certain longevity and whose literature exceeds a certain critical mass, the Kepler problem has acquired an undeniable luster and allure for the modern practitioner. Any new technique for the treatment of transcendental equations should be applied to this illustrious test case; any new insight, however slight, lets its conceiver join an eminent list of contributors.

The Kepler problem has been “on the scene” in Western civilization science for over three centuries. To gather its story is to view this science through a narrow-band filter, and our goal is to make the picture at one wavelength instructive and interesting.

The idea to gather all the work on the Kepler problem is not new. Early work was surveyed in Melander,1767, Detmoldt,1798 and Brinkley,1803, and much of the recent work was described in Danby,1983, Burkhardt,1983 and Gooding,1985. In addition, various partial bibliographies have appeared which contain extensive references to the Kepler problem. Perhaps the most cited has been Radau,1900; others are Struve,1860, Houzeau,1882, Herglotz,1910, and Wood,1950.

Our concern will be almost exclusively for the elliptic case of Kepler's problem. What coverage we attempt of the hyperbolic case will appear in Chapter 8 when we look at universal forms of KE, and the parabolic case, e = 1, will be considered in Chapter 5, where treatments for high eccentricity (e near 1) cases are gathered. Related to KE and the Kepler problem is the subject of Lambert's theorem and the Lambert orbital problem. Except for a few bibliography entries, we won't describe this area at all, even though it has an extensive literature and independent interest. The references [Gooding,1988,1990] are to be recommended for a look at the subject.

In the language of the mathematician, there exists a unique solution of the Kepler problem, but there are many methods to describe or approximate it. It isn't feasible to say how many there are: the meaning of ""solution"" depends too much on the solver's motivations. In our classification of references bearing on KE which appear in the Bibliography, we have made seven primary categories and five secondary categories of methods of solution. These have been adequate to describe almost all our references.

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SKU: 2419139437

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TMB
Fort Morgan, US
★★★★★ 5
OBSESSED!!!!!
Format: Paperback, Format: Paperback
I gave it 5 stars because it deserves the flowers. I do wish the paper was a little better quality. I think it would help make the pictures pop more. Regardless, this book is worth every penny. I haven't found anything else like it. The book is clear, concise, and isn't bogged down with too many details - just the facts m'am. It's a perfect starting reference to send someone down 101 different rabbit holes. I hope someday he puts out a hardback version on thick, slick paper with beautiful, glossy photographs. That would be lovely. For now, this will more than suffice. You get just enough about each artifact to get you going. From there, you can decide how to use your favorite search engine.
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Reviewed in the United States on November 5, 2025
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allison
Draper, US
★★★★★ 5
A great reference for Biblical factual archeology
Format: Paperback
I just received this book and I am so excited. It is a great tool and reference for Biblical studies. Each artifact has a great photograph next to the quick eye catching dates, discovery, period, keywords and Biblical passage. Then a brief but to the point description. It is simple and effective. Very easy to refer when reading your Bible or if you are just interested in archeology. Each artifact is about 2 pages and nothing more which is perfect for references. What a great book!
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Reviewed in the United States on March 1, 2025
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sandyrouse
Bozeman, US
★★★★★ 5
Excellent and in-depth archeologic finds that authenticate Bible history.
Format: Paperback
Archeology is proving much of the Bible's history as true. This book really delves into various sites and provides a lot of detail. My type of reading.
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Reviewed in the United States on February 21, 2026
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Angie Criss
Dallas, US
★★★★★ 5
Great information and pictures
Format: Paperback
Great information on Biblical sites, beautiful pictures, and a pretty book as well. I gave several of these to my family for Christmas. Everyone seemed to love them. The only thing I will caution you about is that the book is small.
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Reviewed in the United States on January 22, 2026
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Mareadas
Grantham, US
★★★★★ 4
Knowledgeable and delectable book.
Format: Paperback
This book shows an excellent archaeological evidence of the Bible accuracy of places, names, events, etc. and proving for the Christians that the Bible is a historical document as well as the inspired inerrant word of God. The majority of the book is interesting and delectable, I mean, the pages where the author presents archaeological facts such as the artifacts and their correlation with people, places times, events and practices recorded in the Bible. But I do not like when the author make personal assumptions and do not present any proof of that. He says: it probably be…. it may be… Here I show three cases of this conjectures;: 1.The author seems to affirm that the triumphal entry of Jesus into Jerusalem, or at least, the name of this event, was derived from the Roman triumph celebration. He says (page 231), regarding to the Roman Empire and the life of Jesus: “By the time of Jesus, the requirements and meaning of a triumphal entry had shifted slightly from its earlier roots associating it with a conquering hero, as it became even more significant and representative of kingship and divinity”. He continues to say: “In ancient Roman culture, a triumphant victor, known as vir triumphalis (“man of triumph”) would enter the city in a celebration parade wearing the laurel wreath and a purple garment, which identified him with the royal and the divine, while riding in a chariot pulled by four horses, alluding to Sol the sun god”.  But if we compare the Roman triumph celebration with the entry of Jesus into Jerusalem described in the Bible, it is not derived from the Roman culture but is the exact fulfillment of the prophesy of Zechariah 9:9. I do not see any correlation between the two celebration; Jesus did not ride a horse but a donkey to signify peace, meekness and humility. It was not a pompous entrance of a conquering hero or king wearing a expensive garment and royal crown. 2.Even though, it is not possible to identify the location of the tomb of Jesus with absolute certainty; the author states (page 199) that the tomb of Jesus is located at the Church of the Holy Sepulchre possible based on “the restoration work to the edicule and an arcosolium tomb from the Roman period found in the church of the Holy Sepulchre”. The author also affirms without giving any proof that: “Christians in Jerusalem then passed down a continuous memory of the location of the tomb (of Jesus) from the time of the burial and resurrection in AD33 until construction of the Church of the Holy Sepulchre was started in about AD326”. But where are the records of that time? The author probably based his statement on Eusebius who lived in the 3rd and 4th centuries AD. According to the history , the Church of the Holy Sepulchre was built by the Roman Emperor Constantine around 326 AD, when her mother the Queen Helena, wanted to replace the pagan temples with Christian churches; she met the Bishop Macarious of Jerusalem who determined the location where Jesus had been buried at the place where was a temple to the Greek goddess Venus. At the beginning of the construction of the church, a rock-cut tomb was found there and an edicule was built to protect the site. But later the edicule was destroyed and rebuild. More tombs has been found under this church. How to be sure or verify that this rock-cut tomb was the one where Jesus was buried? 3.The author is biased with respect to the Masoretic Text, he make a statement but does not support it with any evidence in this regard. Writing about the Dead Sea Scrolls (Page 173) he states: “And certain passages in the Masoretic text seem to have been intentionally modified to match ideas and theology of medieval Judaism.” it is a bad accusation.
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Reviewed in the United States on April 23, 2021

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