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天體力學研習班

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發表於 2008-5-25 15:18:21 | 顯示全部樓層 |閱讀模式
理論天文組現計劃於今年6月中開始進行「天體力學研習班」,小組每兩星期聚會一次,對天體力學有興趣的朋友,歡迎參加。是次研習班,會以J George W. Collins 的 " The Foundations of Celestial Mechanics " 一書作為研習基礎,課程深度相約於大學一、二年班的天文課程,整個研習班共有9個單元 (課程內容請見 Table of contents)。各位朋友可於以下網址下載講議內容:  
http://ads.harvard.edu/books/1989fcm..book/

日 期:        由6月23日開始,每隔星期一
時 間:        7:00 p.m. – 8:30 p.m.
地 點:        香港天文學會辦事處
(九龍牛頭角創業街36號 華基中心610 室 )
費 用:        每次聚會港幣十元
(作學會辦事處日常運作開支,如水電費等。)
參加辦法:        請以電郵 [email protected] 或 [email protected]

注:
由於本組的聚會有可能因天雨關係或講者臨時有要事未能出席而要更改聚會日期,建議有興趣的朋友先登記入理論天文組的電郵組,以取最新的活動消息。


本組是天文學會學術部轄下的小組,無論是學會之會員或非會員都歡迎加入。小組約每兩星期聚會一次,討論的題目廣泛,主要利用一些與天體物理有關的參考書和論文作為研習題目,如恆星演化、廣義相對論、黑洞、優雅的宇宙等。為了讓組員對所討論之題目更深入了解,本組鼓勵組員自行分配題目並輪流負責介紹所定下的討論題目。


Table of content

Chapter 1: Introduction and Mathematics Review …………………………….. 1
1.1 The Nature of Celestial Mechanics……………………………….. 1
1.2 Scalars, Vectors, Tensors, Matrices and Their Products…………. 2
a. Scalars. ……………………………………………………… 2
b. Vectors ……………………………………...…………………3
c. Tensors and Matrices…………………………………………. 4
1.3 Commutatively, Associativity, and Distributivity….……………….8
1.4 Operators……………………………………...………………….... 8
a. Common Del Operators……………………………………...13
Chapter l Exercises……………………………………………………..14

Chapter 2: Coordinate Systems and Coordinate Transformations………………15
2.1 Orthogonal Coordinate Systems…………………………………….16
2.2 Astronomical Coordinate Systems…………………………………..17
a. The Right Ascension –Declination Coordinate System………17
b. Ecliptic Coordinates…………………………………………..19
c. Alt-Azimuth Coordinate System……………………………...19
2.3 Geographic Coordinate Systems…………………………………….20
a. The Astronomical Coordinate System……………………….. 20
b. The Geodetic Coordinate System……………………………..20
c. The Geocentric Coordinate System…………………………...21
2.4 Coordinate Transformations…………………………………………21
2.5 The Eulerian Angles…………………………………………………27
2.6 The Astronomical Triangle…………………………………………..28
2.7 Time………………………………………………………………….34
Chapter 2 Exercises………………………………………………………38

Chapter 3: The Basics of Classical Mechanics…………………………………..39
3.1 Newton's Laws and the Conservation of Momentum and Energy….. 39
3.2 Virtual Work, D'Alembert's Principle, and Lagrange's Equations of
Motion. ……………………………………………………………...42
3.3 The Hamiltonian…………………………...………………………...47
Chapter 3 :Exercises …………………………………………………….50
v
Chapter 4: Potential Theory……………………………………………………...51
4.1 The Scalar Potential Field and the Gravitational Field………………52
4.2 Poisson's and Laplace's Equations…………………………………...53
4.3 Multipole Expansion of the Potential………………………………..56
Chapter 4 :Exercises……………………………………………………..60

Chapter 5: Motion under the Influence of a Central Force……………………... 61
5.1 Symmetry, Conservation Laws, the Lagrangian, and
Hamiltonian for Central Forces……………………………………...62
5.2 The Areal Velocity and Kepler's Second Law………………………64
5.3 The Solution of the Equations of Motion……………………………65
5.4 The Orbit Equation and Its Solution for the Gravitational Force……68
Chapter 5 :Exercises……………………………………………………..70

Chapter 6: The Two Body Problem……………………………………………...71
6.1 The Basic Properties of Rigid Bodies………………………………..71
a. The Center of Mass and the Center of Gravity………………..72
b. The Angular Momentum and Kinetic Energy about the
Center of Mass………………………………………………..73
c. The Principal Axis Transformation……………………………74
6.2 The Solution of the Classical Two Body Problem…………………...76
a. The Equations of Motion……………………………………...76
b. Location of the Two Bodies in Space and Time………………78
c. The Solution of Kepler's Equation…………………………….84
6.3 The Orientation of the Orbit and the Orbital Elements………………85
6.4 The Location of the Object in the Sky……………………………….88
Chapter 6 :Exercises……………………………………………………..91

Chapter 7: The Determination of Orbits from Observation……………………...93
7.1 Newtonian Initial Conditions………………………………………...94
7.2 Determination of Orbital Parameters from Angular Positions Alone. 97
a. The Geometrical Method of Kepler…………………………...98
b. The Method of Laplace………………………………………100
c. The Method of Gauss………………………………………...103
7.3 Degeneracy and Indeterminacy of the Orbital Elements…………...107
Chapter 7 : Exercises…………………………………………………...109
vi
Chapter 8: The Dynamics Of More Than Two Bodies…………………………111
8.1 The Restricted Three Body Problem………………………………..111
a. Jacobi's Integral of the Motion……………………………….113
b. Zero Velocity Surfaces………………………………………115
c. The Lagrange Points and Equilibrium……………………….117
8.2 The N-Body Problem……………………………………………….119
a. The Virial Theorem…………………………………………..121
b. The Ergodic Theorem………………………………………..123
c ..Liouvi lle ' s Theorem……………………………………….124
8.3 Chaotic Dynamics in Celestial Mechanics…………………………125
Chapter 8 : Exercises…………………………………………………...128

Chapter 9: Perturbation Theory and Celestial Mechanics……………………...129
9.1 The Basic Approach to the Perturbed Two Body Problem………...130
9.2 The Cartesian Formulation, Lagrangian Brackets, and Specific
Formulae……………………………………………………………133
Chapter 9 : Exercises…………………………………………………...140

[ 本帖最後由 hildawfsung 於 2008-6-8 01:24 編輯 ]
發表於 2008-5-30 01:27:44 | 顯示全部樓層
一個有趣提問:
我在網上搜尋 "天體運動" ,得到兩組資料,一為天文學的天體運行,一為人文學的裸體行為。以往有無為此而提議改名,例如改為 天體運行學 ?
發表於 2008-5-30 01:48:45 | 顯示全部樓層
 樓主| 發表於 2008-5-30 07:34:43 | 顯示全部樓層

回復 3# 的帖子

多謝你的意見, 就叫 "天體力學" 啦!
 樓主| 發表於 2008-6-15 20:03:35 | 顯示全部樓層

reminder: 天體力學研習班

各位朋友,

如果你對天體力學有興趣 , 而又準備出席由6月23日開始的研習班, 請記得到以下 網站下載 lecture notes.

http://ads.harvard.edu/books/1989fcm..book/

Best regards,

Hilda
 樓主| 發表於 2008-6-25 01:01:40 | 顯示全部樓層

理論天文組聚會 (7-7-2008)

各位朋友,

自第一次聚會之後, 本組決定採用另一本參考書 (數學意味不太重的) - Celestial Mechanics, by Dr. J. B. Tatum, 有興趣的朋友, 可到以下網址下載:

http://orca.phys.uvic.ca/~tatum/celmechs.html

下次聚會是:

日 期: 由7月7日開始,每隔星期一

時 間: 7:00 p.m. – 8:30 p.m.

地 點: 香港天文學會辦事處 (九龍牛頭角創業街36號 華基中心610 室 )

費 用: 每次聚會港幣十元 (作學會辦事處日常運作開支,如水電費等。)

參加辦法: 請以電郵 [email protected] 或 [email protected]


Table of content

Part I. Mathematical Preambles

Chapter 1.    Numerical Methods

1.1 Introduction
1.2 Numerical Integration
1.3 Quadratic Equations
1.4 The Solution of f(x) = 0
1.5 The Solution of Polynomial Equations
1.6 Failure of the Newton-Raphson Method
1.7 Simultaneous Linear Equations, N = n
1.8 Simultaneous Linear Equations, N < n
1.9 Nonlinear Simultaneous Equations
1.10 Besselian Interpolation
1.11 Fitting a Polynomial to a Set of Points. Lagrange Polynomials. Lagrange Interpolation.
1.12 Fitting a Least Squares Straight Line to a Set of Observational Points
1.13 Fitting a Least Squares Polynomial to a Set of Observational Points
1.14 Legendre Polynomials
1.15 Gaussian Quadrature - the Algorithm
1.16 Gaussian Quadrature - Derivation
1.17 Frequently-needed Numerical Procedures


Chapter 2.    Conic Sections

2.1 Introduction
2.2 The Straight Line
2.3 The Ellipse
2.4 The Parabola
2.5 The Hyperbola
2.6 Conic Sections
2.7 The General Conic Section
2.8 Fitting a Conic Section Through Five Points
2.9 Fitting a Conic Section Through n Points


Chapter 3.    Plane and Spherical Trigonomtry

3.1 Introduction
3.2 Plane Triangles
3.3 Cylindrical and Spherical Coordinates
3.4 Velocity and Acceleration Components
3.5 Spherical Triangles
3.6 Rotation of Axes, Two Dimensions
3.7 Rotation of Axes, Three Dimensions. Eulerian Angles
3.8 Trigonometrical Formulas


Chapter 4.    Coordinate Geometry in Three Dimensions

4.1 Introduction
4.2 Planes and Straight Lines
4.3 The Ellipsoid
4.4 The Paraboloid
4.5 The Hyperboloid
4.6 The Cylinder
4.7 The Cone
4.8 The General Second Degree Equation in Three Dimensions
4.9 Matrices


Chapter 5.    Gravitational Field and Potential

5.1 Introduction
5.2 Gravitational Field
5.3 Newton?s Law of Gravitation
5.4 The Gravitational Fields of Various Bodies
5.4.1 Field of a Point Mass
5.4.2 Field on the Axis of a Ring
5.4.3 Plane discs
5.4.4 Infinite Plane Laminas
5.4.5 Hollow Hemisphere
5.4.6 Rods
5.4.7 Solid Cylinder
5.4.8 Hollow Spherical Shell
5.4.9 Solid Sphere
5.4.10 Bubble Inside a Uniform Solid Sphere

5.5 Gauss?s Theorem
5.6 Calculating Surface Integrals
5.7 Potential
5.8 The Gravitational Potentials Near Various Bodies
5.8.1 Potential Near a Point Mass
5.8.2 Potential on the Axis of a Ring
5.8.3 Plane Discs
5.8.4 Infinite Plane Lamina
5.8.5 Hollow Hemisphere
5.8.6 Rods
5.8.7 Solid Cylinder
5.4.8 Hollow Spherical Shell
5.8.9 Solid Sphere

5.9 Work Required to Assemble a Uniform Sphere
5.10 Nabla, Gradient and Divergence
5.11 Legendre Polynomials
5.12 Gravitational Potential of any Massive Body
5.13 Pressure at the Centre of a Uniform Sphere


Part II. Celestial Mechanics

Chapter 6.    The Celestial Sphere

6.1 Introduction
6.2 Altazimuth Coordinates
6.3 Equatorial Coordinates
6.4 Conversion Between Equatorial and Altazimuth Coordinates
6.5 Ecliptic Coordinates
6.6 The Mean Sun
6.7 Precession
6.8 Nutation
6.9 The Length of the Year


Chapter 7.    Time

Chapter 8.    Planetary Motions

8.1 Introduction

8.2 Opposition, Conjunction and Quadrature

8.3 Sidereal and Synodic Periods

8.4 Direct and Retrograde Motion, and Stationary Points



Chapter 9.    The Two Body Problem in Two Dimensions

9.1 Introduction
9.2 Kepler?s Laws
9.3 Kepler?s Second Law from Conservation of Angular Momentum
9.4 Some Functions of the Masses
9.5 Kepler?s First and Third Laws from Newton?s Law of Gravitation
9.6 Position in an Elliptic Orbit
9.7 Position in a Parabolic Orbit
9.8 Position in a Hyperbolic Orbit
9.9 Orbital Elements and Velocity Vector
9.10 Osculating Elements
9.11 Mean Distance in an Elliptic Orbit


Chapter 10.    Computation of an Ephemeris

10.1 Introduction
10.2 Elements of an Elliptic Orbit
10.3 Some Additional Angles
10.4 Elements of a Circular or Near-circular Orbit
10.5 Elements of a Parabolic Orbit
10.6 Elements of a Hyperbolic Orbit
10.7 Calculating the Position of a Comet or Asteroid
10.8 Quadrant Problems
10.9 Computing an Ephemeris
10.10 Orbital Elements and Velocity Vector
10.11 Hamiltonian Formulation of the Equations of Motion


Chapter 11.    Photographic Astrometry

11.1 Introduction
11.2 Standard Coordinates and Plate Constants
11.3 Refinements and Corrections
11.3.1 Parallaxes of the Comparison Stars
11.3.2 Proper Motions of the Comparison Stars
11.3.3 Refraction
11.3.4 Aberration of light
11.3.5 Optical Distortion
11.3.6 Errors, Mistakes and Blunders



Chapter 12.    CCD Astrometry

     (In preparation)

Chapter 13.    Calculation of Orbital Elements

13.1 Introduction
13.2 Triangles
13.3 Sectors
13.4 Kepler?s Second Law
13.5 Coordinates
13.6 Example
13.7 Geocentric and Heliocentric Distances - First Attempt
13.8 Improved Triangle Ratios
13.9 Iterating
13.10 Higher-order Approximation
13.11 Light-time Correction
13.12 Sector-Triangle Ratio
13.13 Resuming the Numerical Example


Chapter 14.    General Perturbation Theory

14.1 Introduction
14.2 Contact Transformations and General Perturbation Theory
14.3 The Poisson Brackets for the Orbital Elements
14.4 Lagrange?s Planetary Equations
14.5 Motion Around an Oblate Symmetric Top


Chapter 16.    Equivalent Potential and the Restricted Three-Body Problem

16.1 Introduction
16.2 Motion Under a Central Force
16.3 Inverse Square Attractive Force
16.4 Hooke?s Law
16.5 Inverse Fourth Power Force
16.6 The Collinear Lagrangian Points
16.7 The Equilateral Lagrangian Points


Chapter 17.    Visual Binary Stars

17.1 Introduction
17.2 Determination of the Apparent Orbit
17.3 The Elements of the True Orbit
17.4 Determination of the Elements of the True Orbit
17.5 Construction of an Ephemeris


Chapter 18.    Spectroscopic Binary Stars

18.1 Introduction
18.2 The Velocity Curve from the Elements
18.3 Preliminary Elements from the Velocity Curve
18.4 Masses
18.5 Refinement of the Orbital Elements
18.6 Finding the Period
18.7 Measuring the Radial Velocity

[ 本帖最後由 hildawfsung 於 2008-6-25 01:03 編輯 ]
 樓主| 發表於 2008-7-7 09:31:01 | 顯示全部樓層
Dear all,

This message remind you the coming TAG meeting will be 7th July, 08.

Date: 7th July, 2008 (Monday)
Time: 7:00 p.m.
Venue: HKAS office

Thanks your notice.

Best regards,

Hilda
 樓主| 發表於 2008-7-21 00:08:37 | 顯示全部樓層

天體力學研習班 (21th July, 08, Monday)

Dear all,

This message remind you the coming TAG meeting will be 21th July, 08.

Date: 21th July, 2008 (Monday)
Time: 7:00 p.m.
Venue: HKAS office

Here are the labor division of the topics whom will responsible for leading the group to discuss.   

Chapter 3 - Heung

Chapter 4  - Leung Chun Sing

Chapter 5 - Ray

Chapter 6 - Wong Chi Yuen

Chapter 7,8 - Eddie

Chapter 10 - Pang Lok Sing


Thanks your notice.

Best regards,

Hilda
 樓主| 發表於 2008-7-21 23:14:57 | 顯示全部樓層

天體力學研習班 (4th Aug, 08, Monday)

This message reminds you the coming TAG meeting will be dated on 4th Aug, 08. Leung Chun Sing and Ray will present their parts in the coming meeting.

Date: 4th Aug, 2008 (Monday)
Time: 7:00 p.m.
Venue: HKAS office

Here are the labor division of the topics whom will responsible for leading the group to discuss.   

Chapter 3 - Heung
Chapter 4  - Leung Chun Sing
Chapter 5 - Ray
Chapter 6 - Wong Chi Yuen
Chapter 7,8 - Eddie
Chapter 10 - Pang Lok Sing
 樓主| 發表於 2008-8-5 03:20:38 | 顯示全部樓層
This message reminds you the coming TAG meeting will be dated on 18th Aug, 08. Ray will present his parts in the coming meeting.

Date: 18th Aug, 2008 (Monday)
Time: 7:00 p.m.
Venue: HKAS office

Here are the labor division of the topics whom will responsible for leading the group to discuss.   

Chapter 3 - Heung
Chapter 4  - Leung Chun Sing
Chapter 5 - Ray
Chapter 6 - Wong Chi Yuen
Chapter 7,8 - Eddie
Chapter 10 - Pang Lok Sing
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