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Part I Analytical Approach to Navigation |
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3 | (26) |
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1.1 On the Design of Conformal-Mercator and Non-conformal Charts and Plotting Sheets |
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3 | (4) |
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1.2 Rhumb-Line or Loxodrome Navigation |
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7 | (4) |
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1.3 Approximations of Loxodromes by Straight Lines on the Plotting Sheet |
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11 | (3) |
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1.4 Applications and Numerical Examples |
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14 | (6) |
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1.5 Gnomonic or Great-Circle Navigation |
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20 | (4) |
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1.6 Numerical Examples and More Chart Projections |
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24 | (5) |
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29 | (144) |
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2.1 Lines of Position, Position Fix, Navigational Triangle and Fix by Computation |
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29 | (5) |
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2.2 Celestial Sphere, Equatorial and Horizon System of Coordinates, Navigational Triangle and the Ecliptic Coordinate System |
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34 | (8) |
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2.3 Conclusions and Numerical Examples |
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42 | (2) |
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2.4 The Use of the Exact Equations for Finding the Position at Sea or Air by Employing Two or More Altitude Measurements Together with the Corresponding Measurements of Time |
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44 | (15) |
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2.5 Conclusions and Numerical Examples |
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59 | (4) |
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2.6 An Exact Method Based on Cartesian Coordinates and Vector Representations |
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63 | (10) |
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2.7 Numerical Examples and Conclusions |
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73 | (4) |
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2.8 On Approximate Solutions for Finding the Position at Sea or Air by Employing Two or More Altitude Observations |
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77 | (14) |
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2.9 An Approximate Method Based on Matrices and the Least Square Approximation |
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91 | (3) |
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2.10 Sumner's Line of Assumed Position Method as Scientific Method |
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94 | (3) |
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2.11 Numerical Example and Logarithmic Algorithm |
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97 | (6) |
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2.12 How an Approximate Position at Sea or Air Can Be Found if an Approximate Value for the Azimuth or the Parallactic Angle Is Known in Addition to One Altitude |
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103 | (7) |
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2.13 On the Effect of a Change in Time on the Altitude and Azimuth |
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110 | (2) |
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2.14 How to Determine Latitude at Sea or Air Without the Use of a Clock |
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112 | (4) |
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2.15 On Calculating the Interval Between Meridian Passage and Maximum Altitude and Finding Approximate Longitude and Latitude of a Moving Vessel, and Longitude by Equal Altitudes |
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116 | (9) |
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2.16 To Find Latitude by Observing Polaris When Exact UTC and Longitude or an Approximation Is Available |
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125 | (3) |
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2.17 The Most Probable Position When Only One LOP and DRP Are Known |
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128 | (5) |
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2.18 How to Calculate the Time of Rising and Setting of Celestial Objects and How to Use the Measured Time of These Phenomena to Find Longitude |
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133 | (6) |
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2.19 On the Identification of Stars and Planets |
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139 | (8) |
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2.20 How to Navigate Without a Sextant |
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147 | (2) |
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2.21 On Finding Time and Longitude at Sea, the Equation of Computed Time (ECT), and Being Completely Lost |
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149 | (24) |
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3 Methods for Reducing Measured Altitude to Apparent Altitude |
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173 | (36) |
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3.1 Navigational Refraction that Includes Astronomical Refraction for Low Altitude Observations |
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173 | (12) |
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3.2 The Dip of the Horizon as a Function of Temperature and Pressure |
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185 | (6) |
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3.3 Planetary Parallax and Semi-diameter of the Sun and Moon |
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191 | (5) |
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196 | (4) |
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3.5 On the Minimization Procedure for the Random Errors in Determining Altitude and Time |
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200 | (9) |
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4 Some of the Instruments and Mathematics Used by the Navigator |
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209 | (32) |
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4.1 Some of the Formulae and Mathematics Used by the Navigator |
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209 | (21) |
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4.2 Some of the Instruments Used by the Navigator |
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230 | (11) |
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Part II Formulae and Algorithms of Positional Astronomy |
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5 Elements of Astronomy as Used in Navigation |
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241 | (18) |
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5.1 Some Basic Concepts Describing the Motion of the Earth Around the Sun |
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241 | (3) |
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5.2 An Approximation to the Time of Transit of Aries at Greenwich and the Greenwich Hour Angle GHA of V |
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244 | (1) |
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5.3 The Right Ascension of RA of the Mean Sun, Mean Longitude, Mean Anomaly, Longitude of Perigee, Longitude of Epoch and Kepler's Equation |
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245 | (3) |
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5.4 The Equation of the Center, Equation of Time and True Longitude of the Sun |
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248 | (2) |
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5.5 Numerical Examples and Other Concepts of Time |
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250 | (3) |
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5.6 An Approximate Method for Finding the Eccentricity, the Longitude of the Perigee and the Epoch |
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253 | (4) |
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5.7 Some Improved Formulae for the Equation of Time and Center |
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257 | (2) |
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6 Qualitative Description: The Relevant Astronomical Phenomena |
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259 | (16) |
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6.1 On the Change of the Elements of the Orbit with Time |
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259 | (1) |
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6.2 The Concept of the Julian Date (JD) and Time Expressed by Julian Centuries (T) |
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260 | (5) |
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6.3 The Elements of Our Orbit as a Function of the Time T Expressed by Polynomials |
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265 | (1) |
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6.4 Qualitative Aspects of Precession and Nutation |
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266 | (2) |
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6.5 The Concept of Proper Motion for Stars |
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268 | (1) |
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269 | (2) |
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6.7 Annual Stellar Parallax, Definitions of Mean, True and Apparent Place of a Celestial Object |
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271 | (4) |
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7 Quantitative Treatise of Those Phenomena |
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275 | (20) |
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7.1 Effects of Precession on the RA and the Approximate Method of Declination |
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275 | (2) |
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7.2 Rotational Transformations and Rigorous Formulae for Precession |
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277 | (3) |
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7.3 Approximate Formulae for the RA O and Declination δ as the Result of Two Rotations Only |
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280 | (2) |
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7.4 Effects of Nutation on the RA and Declination |
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282 | (3) |
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7.5 Effects of Proper Motion on the RA and Declination δ |
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285 | (2) |
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7.6 Effects of Aberration on the RA and Declination δ |
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287 | (3) |
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7.7 Effects of Annual Parallax on the RA and Declination δ |
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290 | (1) |
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7.8 Calculating the Apparent RA and Declination δ, and the Equation of the Equinox |
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291 | (4) |
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295 | (20) |
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8.1 Low Accuracy Ephemeris for the Sun, a Numerical Example |
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295 | (2) |
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8.2 Intermediate Accuracy Ephemeris for the Sun |
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297 | (3) |
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8.3 Low Accuracy Ephemeris for the Stars |
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300 | (3) |
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8.4 Intermediate Accuracy Ephemeris for the Stars |
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303 | (3) |
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8.5 Compressed Low Accuracy Ephemeris for the Sun and Stars for the Years 2014± |
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306 | (2) |
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8.6 The Earth Viewed as a Gyro |
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308 | (7) |
Appendix A Condensed Catalogue for the 57 Navigational Stars and Polaris |
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315 | (2) |
Appendix B Greek Alphabet |
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317 | (2) |
Appendix C Star Charts |
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319 | (2) |
References |
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321 | (4) |
Index |
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325 | |