perezozo ® 19-Апр-2018 02:46

Astronavigation: A Method for Determining Exact Position by the Stars


Year: 2017
Language: english
Author: Kurt Anton Zischka
Genre: Reference book
Publisher: Springer
Edition: 1st
ISBN: 3319479938
Format: PDF
Quality: Scanned pages + text layer
Pages count: 340
Description: This book acts as a manual for the ancient methods of navigating by the stars, which continue to provide the sailor or pilot with a timeless means of determining location. Despite the prevalence of GPS, a comprehensive set of formulae that can be evaluated on any inexpensive scientific calculator in the event of a catastrophic software or systems failure is a vital failsafe. It also serves as a living link to centuries of explorers from centuries past.
Beginning with the basics of positional astronomy, this guide moves on to the more complex math necessary to understand the ephemerides, tables showing the future positions of the stars and planets. These astronomical almanacs were the satellite navigation of their day. The objective of this book is twofold: to provide the reader with a concise, comprehensible manual on positional astronomy as it applies to astro-navigation and to furnish the concise algorithms for finding the position of the Sun and various navigational stars at any given instant.
In a world where too many mariners and aeronauts rely solely on technology and are vulnerable to solar flares, electrical issues, and the like, this knowledge can be a life-saving backup, not to mention a fascinating study in its own rights. Included is an exact mathematical way to determine your position in the air or on the sea far more quickly and accurately than by using the old celestial navigational method, without even needing to know or understand the underlying mathematics. There is even a section that teaches how to measure the azimuth of a star using an analog wrist watch so if a sextant gets damaged, locating position is still possible. This book offers mathematicians and adventurers a way to determine position when the skies go dark.
The U.S. Navy has recently realized that their electronic navigation systems are vulnerable to cyberattack, and as a result has instructed the Naval Academy to begin teaching celestial navigation again.
About the Author
Kurt Anton Zischka received a Dr. of Science Degree at the Technische Hochschule in Darmstad. He went on to teach at the University of Saskatchewan and at the University of Windsor, Ontario, in the subject of Applied Mathematics and Mathematical Physics. He held a Visiting Appointment as a Professor at the University in Karlsruhe, Germany, and also had an appointment at the D.I. of F.R. in Bombay (Mumbai), India. Later, he worked for two years at a University in West Africa. He is also an avid sailor.

Contents

Contents
Part I
Analytical Approach to Navigation
1 Terrestrial Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 On the Design of Conformal-Mercator and Non-conformal
Charts and Plotting Sheets . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Rhumb-Line or Loxodrome Navigation . . . . . . . . . . . . . . . .
1.3 Approximations of Loxodromes by Straight Lines
on the Plotting Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Applications and Numerical Examples . . . . . . . . . . . . . . . . .
1.5 Gnomonic or Great-Circle Navigation . . . . . . . . . . . . . . . . .
1.6 Numerical Examples and More Chart Projections . . . . . . . . .
2 Astro-navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Lines of Position, Position Fix, Navigational Triangle
and Fix by Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Celestial Sphere, Equatorial and Horizon System
of Coordinates, Navigational Triangle and the Ecliptic
Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Conclusions and Numerical Examples . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . .
2.5 Conclusions and Numerical Examples . . . . . . . . . . . . . . . . . . . . .
2.6 An Exact Method Based on Cartesian Coordinates
and Vector Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Numerical Examples and Conclusions . . . . . . . . . . . . . . . . . . . . .
2.8 On Approximate Solutions for Finding the Position at Sea
or Air by Employing Two or More Altitude Observations . . . . . .
2.9 An Approximate Method Based on Matrices and the Least
Square Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Sumner’s Line of Assumed Position Method as Scientific
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contents
2.11 Numerical Example and Logarithmic Algorithm . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . .
2.13 On the Effect of a Change in Time on the Altitude
and Azimuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14 How to Determine Latitude at Sea or Air
Without the Use of a Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 To Find Latitude by Observing Polaris When Exact UTC
and Longitude or an Approximation Is Available . . . . . . . . . . . . .
2.17 The Most Probable Position When Only One LOP
and DRP Are Known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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 . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.19 On the Identification of Stars and Planets . . . . . . . . . . . . . . . . . . .
2.20 How to Navigate Without a Sextant . . . . . . . . . . . . . . . . . . . . . . .
2.21 On Finding Time and Longitude at Sea, the Equation
of Computed Time (ECT), and Being Completely Lost . . . . . . . .
3 Methods for Reducing Measured Altitude to Apparent Altitude . . . .
3.1 Navigational Refraction that Includes Astronomical Refraction
for Low Altitude Observations . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 The Dip of the Horizon as a Function of Temperature
and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Planetary Parallax and Semi-diameter of the Sun and Moon . . . .
3.4 Time and Timekeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 On the Minimization Procedure for the Random Errors
in Determining Altitude and Time . . . . . . . . . . . . . . . . . . . . . . . .
4 Some of the Instruments and Mathematics Used
by the Navigator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Some of the Formulae and Mathematics Used
by the Navigator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Some of the Instruments Used by the Navigator . . . . . . . . . . . . . .
Part II
Formulae and Algorithms of Positional Astronomy
5 Elements of Astronomy as Used in Navigation . . . . . . . . . . . . . . . . . .
5.1 Some Basic Concepts Describing the Motion of the Earth
Around the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An Approximation to the Time of Transit of Aries at Greenwich
and the Greenwich Hour Angle GHA of ♈ . . . . . . . . . . . . . . . . .
The Right Ascension of RA of the Mean Sun, Mean Longitude,
Mean Anomaly, Longitude of Perigee, Longitude of Epoch
and Kepler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Equation of the Center, Equation of Time and True
Longitude of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Examples and Other Concepts of Time . . . . . . . . . . . .
An Approximate Method for Finding the Eccentricity,
the Longitude of the Perigee and the Epoch . . . . . . . . . . . . . . . . .
Some Improved Formulae for the Equation of Time
and Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Qualitative Description: The Relevant Astronomical Phenomena . . .
6.1 On the Change of the Elements of the Orbit with Time . . . . . . . .
6.2 The Concept of the Julian Date (JD) and Time Expressed
by Julian Centuries (T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 The Elements of Our Orbit as a Function
of the Time T Expressed by Polynomials . . . . . . . . . . . . . . . . . . .
6.4 Qualitative Aspects of Precession and Nutation . . . . . . . . . . . . . .
6.5 The Concept of Proper Motion for Stars . . . . . . . . . . . . . . . . . . . .
6.6 Aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Annual Stellar Parallax, Definitions of Mean, True and
Apparent Place of a Celestial Object . . . . . . . . . . . . . . . . . . . . . .
7 Quantitative Treatise of Those Phenomena . . . . . . . . . . . . . . . . . . . . .
7.1 Effects of Precession on the RA and the Approximate Method
of Declination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Rotational Transformations and Rigorous Formulae
for Precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Approximate Formulae for the RA ʘ and Declination d
as the Result of Two Rotations Only . . . . . . . . . . . . . . . . . . . . . .
7.4 Effects of Nutation on the RA and Declination . . . . . . . . . . . . . .
7.5 Effects of Proper Motion on the RA and Declination d . . . . . . . .
7.6 Effects of Aberration on the RA and Declination d . . . . . . . . . . .
7.7 Effects of Annual Parallax on the RA and Declination d . . . . . . .
7.8 Calculating the Apparent RA and Declination d,
and the Equation of the Equinox . . . . . . . . . . . . . . . . . . . . . . . . .
8 Ephemerides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1 Low Accuracy Ephemeris for the Sun, a Numerical Example . . .
8.2 Intermediate Accuracy Ephemeris for the Sun . . . . . . . . . . . . . . .
8.3 Low Accuracy Ephemeris for the Stars . . . . . . . . . . . . . . . . . . . . .
8.4 Intermediate Accuracy Ephemeris for the Stars . . . . . . . . . . . . . .
Compressed Low Accuracy Ephemeris for the Sun
and Stars for the Years 2014± . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Earth Viewed as a Gyro . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A: Condensed Catalogue for the 57 Navigational Stars
and Polaris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix B: Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix C: Star Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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