Investigation of inequalities in the motion of the moon produced by the action of the planets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Washington, DC
Carnegie Inst. of Washington
1907
|
| Schriftenreihe: | Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication
72 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 160 S. Ill. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010525668 | ||
| 003 | DE-604 | ||
| 005 | 19951222 | ||
| 007 | t | ||
| 008 | 951213s1907 a||| |||| 00||| eng d | ||
| 035 | |a (OCoLC)2422002 | ||
| 035 | |a (DE-599)BVBBV010525668 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T |a DE-29 |a DE-11 | ||
| 050 | 0 | |a QB392 | |
| 082 | 0 | |a 521.62 |b N435i | |
| 100 | 1 | |a Newcomb, Simon |d 1835-1909 |e Verfasser |0 (DE-588)119174472 |4 aut | |
| 245 | 1 | 0 | |a Investigation of inequalities in the motion of the moon produced by the action of the planets |c by Simon Newcomb |
| 264 | 1 | |a Washington, DC |b Carnegie Inst. of Washington |c 1907 | |
| 300 | |a 160 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication |v 72 | |
| 650 | 4 | |a Lunar theory | |
| 650 | 4 | |a Perturbation | |
| 830 | 0 | |a Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication |v 72 |w (DE-604)BV035415500 |9 72 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007015213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007015213 | ||
Datensatz im Suchindex
| _version_ | 1804124992506429440 |
|---|---|
| adam_text | INVESTI
I1
MOflO
j!
Ti l
| i|1
f T
GATld tff
N OFilHE MOON PRODUCED BY
E AC TION QF iTHE PLANETS
PUBLISHED BY
IS
INEQUALITIES IN THE
:i!;
N
S:
BY
!i
ON 1 ME
ASSISTED
M
IFRANK E
WCOMB
BY ;
ROSS
v i
INSTITUTION OF WASHINGTON
CONTENTS
INTRODUCTION I
PART I DEVELOPMENT OF THE THEORY 3
CHAPTER I Fundamental Differential Equations 5
1 Notation ; 5
2 Dimensions of Quantities in Terms of Time, Length, and Mass 6
3 Fundamental Differential Equations „ 6
4 Transformation to the Moving Ecliptic 6
5 Preliminary Form of the Potential Function 8
6 Reduction of the Terms of the Potential Function for the Indirect Action 9
7 Reduction of It, the Potential of Direct Action 10
8 Completed Form of the Fundamental Equations 11
CHAPTER II Development and Integration of the Differential Equations for the Variation of the
Elements 13
9 Fundamental Variables 13
10 Canonical Form of the Differential Equations 14
11 Transformation of the Canonical Elements 14
12 Form of the Partial Derivatives 15
13 Numerical Values of the Fundamental Quantities ,15
14 Formation of the Transformed Differential Equations 16
15 Elimination of the Time in Certain Cases 19
CHAPTER III Definitive Form of the Differential Variations of the Elements 21
16 General View of the Problem 21
17 Reduction of the Equations for the Direct Action 21
18 Notation of the Planetary Factors 23
19 Notation of the Lunar Factors 23
20 Numerical Form of the Fundamental Coefficients 24
21 Fundamental Differential Equations for the Direct Action 26
22 Reduction of the Equations for «, e, and y to Numbers 26
23 Reduction of the Equations for I, T, and 8 to Numbers : 26
24 Development of the Indirect Action 28
25 Abbreviated Coefficients for the Indirect Action 30
26 Integration-of the General Equations 31
27 Inequalities of I, n, and 0 JL 32
28 Treatment of the Non-periodic Terms in R ••••••• 33
29 Adjustment of the Arbitrary Constants 35
30 Opposite Secular Effects of the Direct and Indirect Action of a Planet near the SunJ 35
PART II DEVELOPMENT OF THE PLANETARY COEFFICIENTS , 37
CHAPTER IV Coefficients for the Direct Action L L1 y i 39
31 Remarks; on the Method of Development by Mechanical Quadratures i 11 39
32 Action of Venus, Systems of Coordinates 1JJ! 41
33 Action of Venus, Fundamental Data for the ^coefficients v 42
34 Explanation of Tables of ^-coefficients for Venus: ; v ! 44
35 Mechanical Development in a Double Periodic^Series 46
: ill [
IV CONTENTS
PART II DEVELOPMENT OF THE PLANETARY COEFFICIENTS — Continued
CHAPTER IV Coefficients for the Direct Action — Continued
36 Numerical Coefficients for the Hansenian Term of Long Period 46
Table I Sun s Geocentric Coordinates in the Mean Orbit of 1800, Referred to Mean
Sun as Direction of Axis of X I 47
II Computation of Rectangular Coordinates of Venus in the Elliptic Orbit of
1800, Referred to Solar Perigee of Axis of X i 48
III Mutual Periodic Perturbations of Venus and the Earth ! 49-52
IVo Perturbations of the G-coordinate X of Venus S 53
IVA Perturbations of the G-coordinate Y of Venus 54
V Rectangular G-coordinates X and Y of Venus, Referred, in Each System, to an
Axis of X Passing through the Mean Sun 55-58
VI G-coordinate Z of Venus i 59-60
VII Values of A, B, C, and D for the Action of Venus on the Moon 61-66 •
VIII Development of A, B, C, and D for Venus in Periodic Series 67-68
IX Computation of the Coefficients for the Hansenian Venus-term ofLong
Period ; ; 69
X Coefficient of cos 18Z and sin 18L for A, B, C, and D in Each of 12
Systems !| 70
XI Numerical Coefficients for the Hansenian Term J 70
37• Coefficients E and F for Venus 1 71
Table XII Special Values of E and Ffor the Action of Venus J 71
38 Method of Computing ^-coefficients for Mars 1 71
Table XIII Computation of Heliocentric Coordinates of Mars i ! 73
XIV G-coordinates of Mars Reduced to the Different Systems 74~75
XV Special Values of A, B, C, and D for Mars J 75_78
XVI Mars; Direct Action ; Development of ^-coefficients I78-79
39 Computation of the ^4-coefficients for the Direct, Action of Jupiter ; 80
Table XVII Ecliptic Coordinates of Jupiter for the 12 Points of Division So
XVIII Jupiter; Direct Action ; Values of the -^-coefficients : 81
XIX Jupiter ; Direct Action ; Development of the ^-coefficients 81
40 Direct Action of Saturn : !} 82
41 Coefficients for Direct Action of Mercury : i 83
42 K-coefficients for Venus, Mars, and Jupiter J 83
Table 1 XX K-coefficients for Direct Action of Venus I; 84
XXI K-coefficients for Direct Action of Mars i 84
XXII K-coefficients for Direct Action of Jupiter 85
CHAPTER V Planetary Coefficients for the Indirect Action 87
43 Classification of Terms : 87
44 Secular Terms Arising from the Variation of the Eccentricity of the Earth s Orbit 87
45 Terms Independent of the Mean Longitude of the Disturbing Planet 89
46 Periodic Perturbations of the Point G Containing the Mean Longitude of the Disturbing
Planet ; 91
Table XXIII Action of Venus on the Earth1 92
XXIV Action of Mars on the Earth; : 93
XXV Action of Jupiter on the Earth 93
XXVI Action of Saturn on the Eaftli 94
XXVII Planetary Coefficients for the, Indirect Action of Venus 94
XXVIII Planetary Coefficients for the Indirect Action of Mars : 95
XXIX Planetary Coefficients for the Indirect Action of Jupiter 95
XXX Planetary Coefficients for the Indirect Action of Saturn 96
XXXI G coefficients for Venus ; 96
XXXIIG-coefficient sforMars 97
XXXIII G-coefficients for Jupiter ! 97
XXXIV G-coefficients for Saturn 97
CONTENTS V
PART III FUNCTIONS OF THE COORDINATES OF THE MOON 99
CHAPTER VI Formation of the Lunar Coefficients 101
47 Remarks on the Available Theories 101
48 Reduction of Coordinates to the Radius Vector of the Mean Sun as X-axis 102
49 Formation of the Squares and Products of the Coordinates 103
50 Method of Forming the Z -derivatives 104
51 Formation of the ^-derivatives from Delaunay s Theory 105
52 Derivatives from Brown s Theory 107
53 Tables of the Functions and Derivatives of the Moon s Coordinates 108
Table XXXV Functions of the Latitude and their Derivatives 109
XXXVI Functions of the Radius Vector and Latitude 109
XXXVII Functions of the Longitude and their Derivatives 110
XXXVIII Coordinates Referred to Mean Moon and their Derivatives no
XXXIX Functions of Coordinates Referred to Mean Moon in
XL Functions of Coordinates Referred to Mean Sun 112
PART IV DERIVATION OF RESULTS 3~
CHAPTER VII Constant and Secular Terms 115
54 Planetary Factors for the Direct Action 115
55 Lunar Factors 116
56 Secular Motions of7, TT, and 8 117
57 Terms Arising from the Secular Variation of the Earth s Eccentricity 118
58 Secular Variation of the Periodic Terms in General 120
59 Secular Variation of Special Terms 120
60 Comparison of the two Methods of Determining the Secular Variations 122
61 Adjustment of the Arbitrary Constants 124
62 Remarks on the Corrections Resulting from the Adjustment 125
63 Secular Variation of e 126
CHAPTER VIII Special Periodic Inequalities 127
64 Reduction to the Moving Ecliptic 127
Table XLIa Coefficients for forming/* — qy 130
XLIi Coefficients for f 131
65 Inequalities Arising from the Coefficients E and F- 133
Table XLII E and F for the Action of Venus 135
66 Action of Mars and Jupiter 137
67 Combination of Terms Depending on the Longitude of the Moon s Node 137
68 Special Computation of the Hansenian Venus-term of Long Period 138
69 The Radau Terms of Long Period 141
CHAPTER IX Periodic Inequalities in General 143
70 Values of the Planetary K -coefficients, Combining Direct and Indirect Action 143
Table XLIH Action of Venus 144
XLIV Action of Mars 14S
XLV Action of Jupiter 145
XLVI _Action of Saturn —h 145
71 Numerical Values of the Lunar Coefficients 146
Table XLVII Data for a-coefficients 146
XLVIII Lunar a-coefficients for a, e, and y 147
XLIX Lunar / -coefficients for I, tt, and 8 147
72 Formation of the Coefficients Expressing the Inequalities of the Elements 148
73 Motions of the Arguments and Factors of Integration 150
74 Terms with Purely Lunar Arguments 150
75 Elemental Inequalities I 151
76 Reduction to Inequalities of True Longitude; Results ; 154
77 Elemental Inequalities which have not been Reduced to Inequalities of the Longitude 159
78 Remarks on the Possibility of Unknown Terms of Long Period 159
|
| any_adam_object | 1 |
| author | Newcomb, Simon 1835-1909 |
| author_GND | (DE-588)119174472 |
| author_facet | Newcomb, Simon 1835-1909 |
| author_role | aut |
| author_sort | Newcomb, Simon 1835-1909 |
| author_variant | s n sn |
| building | Verbundindex |
| bvnumber | BV010525668 |
| callnumber-first | Q - Science |
| callnumber-label | QB392 |
| callnumber-raw | QB392 |
| callnumber-search | QB392 |
| callnumber-sort | QB 3392 |
| callnumber-subject | QB - Astronomy |
| ctrlnum | (OCoLC)2422002 (DE-599)BVBBV010525668 |
| dewey-full | 521.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 521 - Celestial mechanics |
| dewey-raw | 521.62 |
| dewey-search | 521.62 |
| dewey-sort | 3521.62 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01367nam a2200325 cb4500</leader><controlfield tag="001">BV010525668</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19951222 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">951213s1907 a||| |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)2422002</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010525668</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QB392</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">521.62</subfield><subfield code="b">N435i</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Newcomb, Simon</subfield><subfield code="d">1835-1909</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119174472</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Investigation of inequalities in the motion of the moon produced by the action of the planets</subfield><subfield code="c">by Simon Newcomb</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Washington, DC</subfield><subfield code="b">Carnegie Inst. of Washington</subfield><subfield code="c">1907</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">160 S.</subfield><subfield code="b">Ill.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication</subfield><subfield code="v">72</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lunar theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Perturbation</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication</subfield><subfield code="v">72</subfield><subfield code="w">(DE-604)BV035415500</subfield><subfield code="9">72</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007015213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007015213</subfield></datafield></record></collection> |
| id | DE-604.BV010525668 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:28Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007015213 |
| oclc_num | 2422002 |
| open_access_boolean | |
| owner | DE-29T DE-29 DE-11 |
| owner_facet | DE-29T DE-29 DE-11 |
| physical | 160 S. Ill. |
| publishDate | 1907 |
| publishDateSearch | 1907 |
| publishDateSort | 1907 |
| publisher | Carnegie Inst. of Washington |
| record_format | marc |
| series | Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication |
| series2 | Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication |
| spelling | Newcomb, Simon 1835-1909 Verfasser (DE-588)119174472 aut Investigation of inequalities in the motion of the moon produced by the action of the planets by Simon Newcomb Washington, DC Carnegie Inst. of Washington 1907 160 S. Ill. txt rdacontent n rdamedia nc rdacarrier Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication 72 Lunar theory Perturbation Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication 72 (DE-604)BV035415500 72 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007015213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Newcomb, Simon 1835-1909 Investigation of inequalities in the motion of the moon produced by the action of the planets Carnegie Institution <Washington, DC>: Carnegie Institution of Washington publication Lunar theory Perturbation |
| title | Investigation of inequalities in the motion of the moon produced by the action of the planets |
| title_auth | Investigation of inequalities in the motion of the moon produced by the action of the planets |
| title_exact_search | Investigation of inequalities in the motion of the moon produced by the action of the planets |
| title_full | Investigation of inequalities in the motion of the moon produced by the action of the planets by Simon Newcomb |
| title_fullStr | Investigation of inequalities in the motion of the moon produced by the action of the planets by Simon Newcomb |
| title_full_unstemmed | Investigation of inequalities in the motion of the moon produced by the action of the planets by Simon Newcomb |
| title_short | Investigation of inequalities in the motion of the moon produced by the action of the planets |
| title_sort | investigation of inequalities in the motion of the moon produced by the action of the planets |
| topic | Lunar theory Perturbation |
| topic_facet | Lunar theory Perturbation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007015213&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415500 |
| work_keys_str_mv | AT newcombsimon investigationofinequalitiesinthemotionofthemoonproducedbytheactionoftheplanets |