Nautical Almanac
Wolf Ephemeris
A Modern Nautical Almanac for Practical Celestial Navigation
The Wolf Ephemeris is a privately issued nautical almanac that systematically compiles celestial position data, altitude correction tables, and related astronomical tables required for celestial navigation.
Designed for navigators, students, and astronomy enthusiasts, it brings together the principal astronomical quantities required for celestial observations and navigational computations within a single volume.
About This Publication
The Wolf Ephemeris has been developed as a modern nautical almanac for practical use in celestial navigation.
While prepared with reference to the Nautical Almanac published by the Japan Coast Guard, all numerical values and computational procedures presented in this work are generated using methods independently developed by the author.
Its purpose is to provide a reliable and practical reference that combines modern astronomical computation with a table structure suitable for real navigational use.
Key Features
01
High-Precision Astronomical Computation
Celestial positions of the Sun, Moon, planets, and navigational stars are calculated using modern astronomical models and high-precision numerical methods.
02
Relativistic Corrections
The calculations incorporate general relativistic effects, including gravitational light deflection and time delay caused by major solar-system bodies.
03
Atmospheric Modeling for Rise and Set Calculations
Sunrise, sunset, moonrise, and moonset calculations consider atmospheric conditions using meteorological parameters derived from ERA5 global reanalysis data.
04
Designed for Practical Celestial Navigation
The structure of the tables is optimized to reduce the number of calculation steps required during real navigational observations.
About This Publication
The Wolf Ephemeris was developed to provide a practical and precise nautical almanac for celestial navigation.
While traditional nautical almanacs are powerful reference works, their structure can sometimes be complex for practical use.
This publication aims to combine the reliability of modern astronomical computation with a clear layout designed for efficient navigation.
All numerical values presented in this work are generated using independently developed computational methods rather than direct reproduction of existing official publications.
Structure of the Almanac
Each page of the almanac presents the principal astronomical quantities for one day.
All times are expressed in Coordinated Universal Time (UTC).
The tabulated precision is:
E-value: 1 second
d-value: 0.1 arcminute
Although the displayed values are rounded to the published precision, all internal computations are performed at significantly higher precision.
Computational Framework
The celestial coordinates presented in this publication are computed using modern astronomical theory.
Key elements of the computational framework include:
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ΔT (Terrestrial Time − Universal Time)
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Calculations using Barycentric Dynamical Time (TDB)
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Adoption of the IAU 2006 precession–nutation model
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A modified Julian time system designed to preserve numerical precision
These methods allow extremely small variations in celestial motion to be handled with high numerical stability.
Computational Accuracy
The Wolf Ephemeris has been designed to achieve the highest level of accuracy practically attainable for navigational astronomical calculations.
Internal numerical computations are performed using high-precision arithmetic of approximately 100 decimal digits.
This minimizes rounding errors in:
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time calculations
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coordinate transformations
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correction terms
Relativistic Corrections
The celestial position calculations incorporate relativistic effects based on General Relativity, including:
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gravitational light deflection
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Shapiro light-time delay
These corrections include the gravitational fields of:
Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, and the Moon.
In addition, gravitational influences from 373 asteroids are also included in the computation.
Sunrise, Sunset, Moonrise, and Moonset
In this publication, rise and set calculations do not assume uniform standard atmospheric conditions.
Instead, air temperature and atmospheric pressure corresponding to the calculation location are incorporated.
Meteorological parameters are derived from ERA5 global reanalysis data provided by the Copernicus Climate Change Service (C3S) and interpolated for the relevant time and location.
This approach allows atmospheric refraction effects near the horizon to be represented more realistically.