Physics - Celestial Mechanics Updates

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2023 January 16

Chapter 2: Section 2.3: Additional material, on the circumference of an ellipse, added to the end of the section.

2023 January 14

Chapter 9: Section 9.5: Additional material on the period and mean speed in an elliptic orbit added to the end of the section.

2022 December 27

Chapter 4: Correction to equation 4.3.11.
Chapter 5: Significant rearranging and rewriting.

2022 March 27

Chapter 1: Section 1.16: Correction to equation 1.16.30.
Chapter 9: Section 9.7: Additional remarks on quadrant selection.

2021 September 17

Chapter 2: Section 2.4: Extensive additions.

2020 July 12

Chapter 9: Section 9.5: Corrections to equations 9.5.25 and 9.5.26.

2020 June 9

Chapter 1: Section 1.13: Correction to equation 1.13.
Chapter 1: Section 1.7: Correction to equation 1.7.5.

2020 May 16

Chapter 3: Section 3.2: Page 5: Solution to problem 6 corrected.

2020 April 17

Chapter 9: Section 9.9: Addition made to figure IX.9.
Chapter 9: Section 9.9: Numbers changed below equation 9.9.9.
Chapter 9: Section 9.11: Paragraph 2: Reference to equation 2.13.6.changed to 2.3.16.
Chapter 9: Section 9.11: Paragraph 3: P/2 changed to 2/P.

2020 March 10

Chapter 6: Section 6.5: Page 10: Line 8: “north to south” corrected to “south to north”.
Chapter 6: Section 6.7: Page 18: Line 7: (C - A)/A corrected to (C - A)/C.

2020 February 13

Chapter 3: Section 3.3: three lines from bottom of page 8: c -a changed to a - c.
Chapter 4: Section 4.2: Solutions to example at bottom of page 6 corrected.
Chapter 5: Section 5.8: Formula on last line of page 32 corrected.
Chapter 5: Section 5.9: A “r” inserted in some of the equations.
Chapter 6: Section 6.3: near end of page 6: 12 hours changed to 6 hours.
Chapter 6: Section 6.5: Reference to figure IV.4 in penultimate paragraph changed to VI.4.
Chapter 8: Section 8.2: E and W on figure VIII.2 interchanged.
Chapter 9: Section 9.5: Three lines above Eqn. 9.5.33. corrected.
Chapter 9: Section 9.7: Equation 9.7.17 corrected.
Chapter 9: Section 9.8: Equation 9.8.5 corrected.
Chapter 10: Section 10.9: Sentence below equation 10.9.21 modified. A prime removed from zeta in the following sentence.
Chapter 10: Section 10.9: A missing “E” in equation10.9.76 corrected.
Chapter 10: Section 10.10: Line 3: “three” changed to “six”.
Chapter 10: Section 10.10: Equation 10.10.5: “Y” changed to “Z”.
Chapter 10: Section 10.11: “r“ inserted in first term of integrand in equation 10.11.14.
Chapter 10: Section 10.11: “1/r” removed from integrand in equation 10.11.17.
Chapter 11: Labelling of figures changed after figure XI.3.
Chapter 13: Section 13.15: Middle of page 27: Subscript 3 changed to 2.
Chapter 14: Section 14.1: New equation 14.3.7 inserted, and subsequent equations renumbered.
Chapter 17: Section 17.3: Line 5 beneath figure XVII.2: Reference to “Section 6.3 of Chapter 4” changed to “Section 6.4 of Chapter 6”.

2020 January 7

Chapter 2: Section 2.3: A short exercise added below figure II.10.
Chapter 2: Section 2.3: Equation 2.3.17e corrected.
Chapter 2: Section 2.3: A paragraph on similar and confocal ellipses added.

2019 December 6

Chapter 10: Section 10.3: Opening paragraph modified to include retrograde orbits.

2019 August 27

Chapter 5: Subsection 5.4.8: additional derivation of the zero field inside a spherical shell.

2019 March 10

Chapter 3: Section 3.8: Formulas for tangents of multiple angles supplied.
Chapter 10: Section 10.9: Equation 10.9.16 corrected (k on RHS, not j).

2018 December 13

Chapter 15 (Special Perturbations) added.
Chapter 16: Section 16.1: Two lines under equation 16.1.15: reference to equation 16.1.19 corrected to 16.1.9.

2018 November 18

Chapter 3: Section 3.5: A third method is given for finding the poles.
Chapter 17: Section 17.4: A link is given to an alternative method for finding the auxiliary ellipse.

2018 September 8

Chapter 10: Section 10.9: Under equation 10.9.62, the numerical value of the Gaussian constant updated.

2018 July 22

Chapter 9: Figures IX.8 and IX.9 repaired.

2018 March 21

Chapter 9: Section 9.5: “Feynmann” corrected to “Feynman”.
Chapter 9: Section 9.8: Opening paragraph updated to include mention of the interstellar object Oumuamua.

2018 February 16

Chapter 8: Fifth paragraph: Two sentences added concerning the 2012 IAU redefinition of the AU.

2017 November 16

Chapter 4: Section 4.2: Subscript corrected in equation 4.2.40
Chapter 4: Section 4.7: Two lines below equation 4.7.3: “vertex” changed to “axis”

2017 October 24

Chapter 2: Section 2.3: Equation 2.3.17b corrected.
Chapter 2: Line beneath equation 2.3.33: Word “formulae” corrected to “formula”.
Chapter 3: Section 3.4: Font changes on left hand side of equation 3.4.16.
Chapter 3: Section 3.6: Equation 3.6.2: A prime removed from x on the RHS.

2016 November 3

Chapter 3: Section 3.7: Below equation 3.7.1: Reference to figure III.12 corrected to figure III.21.
Chapter 3: Section 3.7: Below equation 3.7.2: Reference to figure III.13 corrected to figure III.22.

2016 July 22

Chapter 3: Section 3.5: Solution to second example expanded.
Chapter 17: Section 17.1: Additions made to figures XVII.1 and XVII.4.
Chapter 17: Section 17.4: Change in font for some of the symbols, and explanation thereof.
Chapter 17: Section 17.4: Page 9: Correction to definition of k.
Chapter 17: Section 17.4: Page 12: Calculation re-done.

2016 July 13

Chapter 9: Section 9.9: Additional material in solution to the numerical example.

2016 July 12

Chapter 4: Section 4.2: The part on distance from a point to a plane re-written. Shortened and with improved notation and fonts.

2016 July 8

Chapter 9: Section 9.9: Example: Phrase “in case you are wondering” was repeated. One of them now removed.
Chapter 9: Section 9.9: Figure IX.9 overlapped text. Now corrected.
Thanks to Esmat Bekir for spotting these errors.

2016 July 7

Chapter 9: Section 9.5: Above equation 9.5.17: Reference to equations 9.4.16 or 9.4.17 corrected to 9.5.15 or 9.5.16.
Chapter 9: Section 9.5: Below equation 9.5.34: Extraneous phrase “Chapter 9” removed.
Chapter 9: Section 9.5: Five lines above the Figure: b/a corrected to a/b.
Chapter 9: Section 9.6: Bottom of page 16: Reference to equation 9.5.4 corrected to 9.6.4.
Chapter 9: Section 9.7: Above equation 9.7.5: Reference to equation 9.6.10b corrected to 9.7.10b.
Chapter 9: Section 9.7: First line of page 20: Extraneous word “and” removed.
Thanks to Ben Jose for spotting these errors.

2016 June 25

Chapter 6: Section 6.4: line 6: 2000 changed to 2002.
Chapter 6: Section 6.7: line 8: “and” changed to “an”.
Thanks to Esmat Bekir for spotting these errors.

2016 June 20

Chapter 10: Section 10.7: p.8: Q changed to R in expression for Y
Chapter 10: Section 10.8: 3 lines from bottom: e changed to E
Chapter 10: Section 10.9: Equation 10.9.13: η changed to ε.
Chapter 10: Section 10.9: Above equation 10.9.22: 10.7.1 changed to 10.7.10.
Chapter 10: Section 10.9: Equation 10.9.24: η changed to Y.
Chapter 10: Section 10.9: Equation 10.9.25: ζ changed to Z.
Chapter 10: Section 10.9: Equation 10.9.29: η changed to ε.
Chapter 10: Section 10.9: New equation 10.9.36b added.
Chapter 10: Section 10.9: Clarification made beneath equation 10.9.60.
Chapter 10: Section 10.9: Above equation 10.9.63. Reference to Section 9.70 changed to 9.7.
Thanks to Benjamin Jose for spotting these errors.

2016 June 17

Chapter 1: In line beneath equation 1.16.28, “interpolated” changed to “interpolate”.

2016 May 6

Misprints discovered by Esmat Bekir.
- Chapter 1: Section 1.7: Line 5 of calculation: Coefficient of x 2 corrected from 5 to -5.
- Chapter 3: Section 3.2: Equation 3.2.3: cos C corrected to sin C.
- Chapter 3: Section 3.5: Equation 3.5.10: minus sign corrected to =.
- Chapter 4: Section 4.8: Row 3: Column 1: 1 corrected to -1.
- Chapter 5: Subsection 5.8.2: Page 31: line 2: Reference to equation 5.4.1 corrected to 5.4.4.
- Chapter 5: Subsection 5.8.6: Corrections to Equation 5.8.15 and to the equation at the top of page 33.
- Chapter 5: Section 5.12: In text following equation 5.12.3: Missing subscript to C corrected.
Appendix B: Addition of alternative solution to Problem 3, submitted by Pal Achintya of India

2016 April 20

Chapter 1: Section 1.7: Correction to the last line of calculation on Page 24.

2016 March 28

Chapter 17: Section 17.4: A couple of sentences added on the solution of equation 9.6.4.

2016 March 8

Chapter 2: Corrections to equations 2.3.17b, 2.3.17e.
Chapter 17: Correction to equation 17.4.8.

2016 January 20

Chapter 1: Section 1.13: Two spelling mistakes corrected in first sentence following figure I.6D.
Chapter 1. Section 1.13: Grammatical mistake corrected in fifth line below equation 1.14.6.
Thanks to Richard Sharpe for both corrections.

2016 January 18

Chapter 1. Section 1.8. Missing equality sign inserted in equation 1.8.16. Thanks to Richard Sharpe.

2016 January 11

Chapter 1: Section 1.11: Line 5: Expression for polynomial corrected.

2016 January 5

Chapter 3: Section 3.2: Page 5: Correction to Solution 3. Thanks to Richard Sharpe.

2015 March 25

Chapter 1: Section 1.2: Page 6: A change to the first integral in the middle of page 6.

2015 March 24

Chapter 1: Solution to equations 1.9.3 and 1.9.4 re-written for greater clarity.
Appendix B (Solutions to Miscellaneous Problems) added.

2015 February 9

Appendix A (Miscellaneous Problems) added.

2015 February 5

Chapter 1: Section 1.2: Additional example of an integral with an infinite upper limit.

2015 February 2

Chapter 2: Section 2.5: Additional material on the hyperbola - its equation referred to the asymptotes.

2014 December 7

Chapter 13: Section 13.7: In the line immediately below equation 13.7.3, the solar symbol appended as a subscript to x has been changed to a lower-case “o”.

2014 December 4

Chapter 2: Section 2.2: Last line of the paragraph on The Conjugate Hyperbola: Correction to equation relating the eccentricities of a hyperbola and its conjugate.
Chapter 2: Section 2.7: Much new material at the end of the section.

2014 November 20

Chapter 2: Section 2.7: New material concerning tangents to a conic section, including new equations 2.7.18 − 2.7.21.

2014 October 7

Chapter 7: Page 4: Line 12: The word "the" at the beginning has been replaced with the word "to".
Chapter 7: Page 5: Line 5: A closing parenthesis has been inserted after UT.

2014 July 6

Chapter 16: Correction to left hand side of equation 16.1.1. Thanks to Christian Nitschelm, University of Antofagasta, Chile.

2014 May 4

Chapter 9: Section 9.7: Subsection "Method 4" (between equations 9.7.15 and 9.7.17) changed to "Method 3".

2013 December 7

Chapter 11: Penultimate line of chapter: "and" corrected to "any".

2013 November 3

Chapter 2: Section 2.4: In figure II.25, the symbol b has been moved to indicate an obtuse angle. Thanks to Tomer Shenar of Potsdam.

2013 October 22

Chapter 5: Subsection 5.4.7 has been expanded to include a point inside the cylinder. A small repair has been effected to figure V.8.

2013 July 6

Chapter 1: Section 1.2: Page 6: In the third integral, the 2 has been moved to inside the square root.
Chapter 2: Section 2.2: Angle in figure II.1 changed from alpha to theta.

2013 June 1

Chapter 2: Section 2.6: Page 50: hbar is 3867358. Determinant is aabar+hhbar+ggbar.

2013 March 25

Chapter 2: Section 2.4: Following equation 2.4.11, the coordinates of F are (q, 0).

2013 January 31

Chapter 13: Extensive revisions throughout the chapter.

2013 January 10

Chapter 1: Section 1.9: Following equation 1.9.4, approximate solution is x = 3.35.
Chapter 2: Section 2.3: Equations 2.3.17d-g added.
Chapter 9: Section 9.7: A fourth method added for solving for u.

2013 January 9

Chapter 1: Section 1.2: A sentence added at the bottom of page 7.

2012 October 2

Chapter 13: Section 13.4: The new definition of the Astronomical Unit approved by the International Astronomical Union in 2012 has been inserted into this Section.

2012 July 10

Chapter 9: Section 9.5: Page 5: In line under equation 9.5.6, "us" changed to "is".
Chapter 9: Section 9.9: Page 24: Reference to figure IX.4 changed to IX.8. Three equations relabelled.
Chapter 9: Section 9.9: Page 25: Figure IX.9 repaired. Explanation of 29.7846917 in example added.
Chapter 10: Section 10.7: K added to figure X.2.
Chapter 13: Section 13.13: Page 23: Line 2: "out" changed to "our".

2012 June 11

Chapter 3: Section 3.5: Some corrections to answers to problems 10-21. New material concerning uniqueness of solutions added.

2012 April 22

Chapter 1: Section 1.7: Correction to right hand side of equation 1.7.3.

2012 March 12

Chapter 2: Section 2.3: Two labels added to figure II.11. 2011 November 9

Chapter 8: Section 8.4: Correction to formulas at the bottom of page 6.

2011 October 20

Chapter 8: Section 8.4: Correction to formulas at the bottom of page 6. Thanks to Juan Irias.

2011 September 4

Chapter 2: Section 2.8: Page 49: First line corrected to read "the value of λ that..." Equation γ = 0 is 3x + 2y - 19 = 0.
Chapter 5: Section 5.5: Page 21: Reference to figureV.16 changed to V.17.
Chapter 5: Section 5.5: Page 25: Reference to figure V.20 changed to V.21. Angle between δA and g is θ + 90°. Equation 5.6.4 corrected accordingly.
Chapter 6: Section 6.5: Page 10: South pole of the ecliptic is in Dorado, not Mensa.
Thank you to Cristian Roner and Juan Irias.

2011 July 30

Chapter 3: Section 3.5: Correction to the penultimate line of the paragraph on Method ii on page 17. Thank you to Robert Sutton of San Antonio, Texas.

2011 July 23

Chapter 2: Section 2.8: Correction to the equation for the conic section at the top of page 50.
Chapter 17: Section 17.4: Corrections to equations 17.4.2 to 17.4.5.
Chapter 17: Section 17.4: Correction to sentence immediately preceding figure VII.3.
Chapter 17: Section 17.4: Correction on page 8 to the slope of the line FC.
Chapter 17: Section 17.4: Correction on pge 12 to the equation to the auxiliary ellipse.
Thank you to Robert Sutton of San Antonio, Texas, for all of these.

2011 July 2

Chapter 3: Section 3.5: Correction to equations preceeding and following Figure III.17. Thanks to Juan Irias.

2011 April 29

Chapter 5: Section 5.6: Broken figure V.19 repaired.

2009 December 25

Chapter 1: Section 1.2: Small addition to paragraph on page 6.
Chapter 8: Section 8.1: "do" corrected to "to" in paragraph 3.

2008 October 15

Chapter 16: Section 16.5: Equation 16.5.1 corrected.
Chapter 16: Section 16.6: Equation 16.6.27, and expression four lines below equation 16.6.27 corrected.
Chapter 16: Section 16.7: Eleven drawings of the equipotential surface added.

2008 September 4

Chapter 12 (CCD Astrometry) added.

2008 July 14

Chapter 1: Section 1.15: In example 4, changed x = tan θ to y = tan θ.
Chapter 1: Section 1.16: "The theorem given by equation 1.14.1" has been corrected to "The theorem given by equation 1.16.1".
Chapter 1: Section 1.16: An alternative, simpler, derivation of equation 1.16.14 has been added.
Chapter 4: Section 4.2: Corrections to equations 4.2.34-40, and two spelling mistakes in that section.
Chapter 4: Section 4.4: Correction to first sentence.
Chapter 4: Section 4.5: Correction to sentence preceding equation 4.5.3.
Thanks to Esmat Bekir for finding these.

2007 November 18

Chapter 5: Section 5.7: "a" corrected to "at" in last paragraph of page 25.

2007 February 24

Chapter 9: Section 9.5: Font change in equation 9.5.37.

2007 January 7

Chapter 9: Section 9.5: Correction to line following equation 9.5.4.

2006 September 5

Chapter 3: Section 3.5: Corrections to solutions of Problem 12 and Example 2. Thanks to Abdulla Suleman.
Chapter 6: Section 6.4: Calculation of LST corrected. Thanks to Camille Milot

2006 February 6

Chapter 10: Section 10.7: Definition of heliocentric ecliptic coordinates re-written. Grazie, Fabrizio.
Chapter 13: Section 13.5: Definition of heliocentric ecliptic coordinates re-written. Grazie, Fabrizio.

2006 January 16

Chapter 9: Section 9.5: Corrections to equation 9.5.12 and in line above equation 9.5.23 - thank you again, Fabrizio.
Chapter 9: Section 9.5: Additional material at end, thanks to Bob Rimmer.

2006 January 8

Chapter 2: Section 2.3: Correction to equations 2.3.12. Thanks to Bob Rimmer.
Chapter 9: Section 9.5: Extra factor M added to several equations. Thanks to Fabrizio Panaioli.

2005 February 17

Chapter 1: Extensive changes and additions.

2004 October 25

Chapter 5: Section 5.11: Additional Legendre polynomials added.
Chapter 6: Section 6.7: Addition of equations 6.7.10 - 6.7.12.

2004 March 26

Chapter 6: Section 6.8: Line 3: "notation" corrected to "nutation".
Chapter 6: Section 6.9: Paragraph 1: Last line: 365^d.24219 (Thanks to R. Shapp.)
Chapter 17: Changes to figure XVII.1 and equations 17.5.3,4,5,6. (Thanks to E. C. Downey.)

2004 March 8

Chapter 18 (Spectroscopic Binary Stars) added.

2004 February 2

Chapter 3: Section 3.5: Correction to Example 2.
Chapter 6: Section 6.9: Spelling mistake ("ecliptic") corrected.
Chapter 11: Correction to equation 11.2.2.

2003 September 22

Chapter 2: Section 2.7: Cofactors given explicitly.
Chapter 3: Clarification in paragraph below equation 3.7.5.
Chapter 17 (Visual Binary Stars) added.

2003 September 2

Chapter 2: Section 2.3: "Auxiliary circle" defined.

2003 July 22

Chapter 14 (General Perturbation Theory) added.

2003 July 4

Chapter 10: Section 10.11 (Hamiltonian Formulation of the Equations of Motion) added.
Chapter 16: "27.64" above figure XVI.6 corrected to "27/64".

2003 June 16

Chapter 5: Section 5.13 (Pressure at the Centre of a Uniform Sphere) added.

2003 May 30

Chapter 16: Figures XVI.8 and XVI.9a added.

2003 May 16

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

2003 May 8

Chapter 13: Misprint to equation 13.15.12 corrected.

2003 April 24

Chapter 1: Corrections to equations 1.9.23, 24, 25.
Chapter 13: Section 13.13: Hint given for solution of g₃

2003 April 16

Chapter 1: Section 9: Corrections to equations 1.9.7 and 1.9.16.
Chapter 13: Section 13.9: Correction on line 4.

2003 April 11

Chaptrer 9: Section 11 (Mean Distance in an Elliptic Orbit) added.

2003 March 21

Chapter 13: Section 7: Equation 13.7.7 corrected, numerical example recalculated.

2003 March 6

Chapter 13 (Calculation of Orbital Elements) added.

2003 March 4

Chapter 1: section 11 (Frequently-needed Numerical Procedures) added.

2002 December 20

All chapters paginated.

2002 November 23

Chapter 11 (Photographic Astrometry) added.
Chapter 3: Cosmetic change to the five properties of an orthogonal matrix in section 3.5.
Chapter 10: Clarification in calculation of n following equation 10.7.1. Numerical correction for alpha following equation 10.7.16.

2002 November 4

Chapter 10 (Computation of an Ephemeris) added.

2002 November 1

Chapter 2: Small addition to (v, E) relation in section 2.3.
Chapter 9: Additional exercise in section 9.6 for solution of Kepler's equation. "Ellipse" corrected to "hyperbola" following equation 9.9.4.

2002 September 20

Chapter 1: Additional material in section 2 (Numerical Integration).
Chapter 7: Updated with addition of Terrestrial Time (TT).

2002 September 12

Chapter 1: Misprint in equation 1.5.6 corrected.
Chapter 2: FIgures 9, 10, 13 redrawn.

2002 August 6

Chapter 9 (Two Body Problem in Two Dimensions) added.

2002 July 30

Chapters 1 and 5: a very few small cosmetic changes.

2002 July 19

Chapter 8 (Planetary Motions) added.
Chapter 5: two sections 5.11 (Legendre Polynomials) and 5.12 (Gravitational Potential of any Massive Body) added, plus minor font improvements.

2002 July 12

Chapter 5 (Gravitational Field and Potential) added.
Updates page began.