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by Dr. J. B. Tatum
jtatum@uvic.ca



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Max Fairbairn's Planetary Photometry

Integrals and Differential Equations

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: 365d.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.



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