Between Theory and Observations: Tobias Mayer's Explorations of Lunar Motion, 1751-1755

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Springer Science & Business Media, Nov 11, 2009 - Mathematics - 246 pages
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In the 18th century, purely scientific interests as well as the practical necessities of navigation motivated the development of new theories and techniques to accurately describe celestial and lunar motion.

"Between Theory and Observations" presents a detailed and accurate account, not to be found elsewhere in the literature, of Tobias Mayer's important contributions to the study of lunar motion—including the creation of his famous set of lunar tables, which were the most accurate of their time.

 

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Contents

Introduction
1
12 Organization
4
13 Conventions
6
The Quest for Lunar Theory
9
22 Application to Navigation
12
23 Astronomical Prerequisites
15
The Pioneers Work
26
32 The Geographers Lunar Tables
29
68 The Preface to the kil Tables of 1753
116
69 Conclusion
118
Multisteps in Theoria Lunae
121
71 Theoria Lunaes Breakpoint
122
72 Failing Assertions
127
73 Substitution of Arguments
130
74 An Approximation Technique
133
75 The Complete Transform
136

33 New Opportunities
30
Multiple Steps
33
35 Contending for the Longitude Prize
34
36 His Later Researches
37
37 The Boards Decision and Beyond
39
A Manual to the Tables
43
42 SingleStep and Multistep Procedures
46
43 Calendar Conventions
47
44 An Example Computation
48
45 A Note on Accuracy
54
46 The Wanderings of Evection
55
Theoria Lunae
57
52 Circumstances of Composition
60
53 Through a Birds Eye
63
54 Mastering the Theory
66
55 Solved Equations
88
The Horrocks Legacy
91
61 Newton on Lunar Motion 1702
92
62 The Equations of Newtons Theory
95
63 Horrockss Variable Orbit
97
64 Old Wine in New Bottles
100
65 Lemonniers Version of NTM
104
66 Lunar Tables Probably Older?
108
67 Accuracy of Theories Compared
114
76 Conclusions
139
Hausbackene Combinationen
143
81 A Search in the Literature
144
82 A Variety of Manuscripts
150
83 A Pair of Pliers
153
84 A Role for Each Manuscript
160
85 Spreadsheets
162
86 Results
173
Further Aspects of Model Fitting
177
91 The Quality of Observations
178
92 World Temperature Distribution
181
93 On Averaging and Cancelling
182
A Case of Model Fitting
185
95 Eulers Lunar Tables of 1746
195
Concluding Observations
198
102 Further Research
204
A Summary
206
Lunar Equations Versions and Aliases
209
Spreadsheet Contents
217
Manuscript Sources
229
References
233
Index
241
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