Skip to content

Home

Jump to bottom
Mattias Holm edited this page Dec 26, 2022 · 10 revisions

Implementation of Various Astronomical Algorithms

This was initially started as a port of the C-celmek library, however it has grown in scope to attempt to implement most algorithms from Meeus as well.

In addition the library should be "swiftified".

Some Meeus algorithms were already implemented in the C-version.

These algoritms are implemented

  • VSOP87
  • ELP2000 82b
  • Goffin2000

From Meeus (second edition) we have:

  • Ch 1: Hints and Tips
    • Example 1.a: Right ascensions / hour angle conversion
    • Negative angles
  • Ch 2: About Accuracy
    • Mean geometric longitude of the Sun
    • Mean longitude of the Moon (see Ch 47)
  • Ch 3: Interpolation
    • Equation 3.3: Interpolation formula
    • Example 3.a: Interpolation
    • Example 3.b: Interpolation
    • Example 3.c: Interpolation
    • Example 3.d: Interpolation
    • Equation 3.8: Five tabular values
    • Example 3.e: Interpolation
    • Equation 3.12: Interpolation to halves
    • Example 3.f: Interpolation
    • Equation 3.13: Lagrange's interpolation formula
    • Example 3.g: Interpolation
  • Ch 4: Curve Fitting
    • Equation 4.1: Linear equation
    • Equation 4.2: Least squares
    • Example 4.a
    • Equation 4.3: Correlation coefficient
    • Example 4.b
    • Equation 4.5: Quadratic curve fitting
    • Equation 4.6: Quadratic curve fitting
    • Equation 4.7: General curve fitting
    • Example 4.c
    • Example 4.d
  • Ch 5: Iteration
    • Example 5.a
    • Example 5.b
    • Example 5.c
    • Example 5.d
  • Ch 6: Sorting Numbers
  • Ch 7: Julian Day
    • General remarks examples for tests
    • Calculation of the JD: Gregorian
    • Calculation of the JD: Julian
    • Example 7.a
    • Example 7.b
    • Example dates on p62
    • Julian day at Jan 0.0
    • Leap years: Gregorian
    • Leap years: Julian
    • MJD
    • Calendar date from the JD
    • Example 7.c
    • Example 7.d
    • Day of the week
    • Example 7.e
    • Day of the year
    • Example 7.f
    • Example 7.g
    • Month and day from day of year
  • Ch 8: Date of Easter
    • Gregorian Easter
    • Julian Easter
  • Ch 9: Jewish and Moslem Calendars
    • Example 9.a
    • Example 9.b
    • Example 9.c
  • Ch 10: Dynamical Time and Universal Time
    • Equation 10.1
    • Equation 10.2
    • Example 10.a
    • Table 10.A
    • Example 10.b
  • Ch 11: The Earth's Globe
    • p sin/cos phi prime calculation
    • Example 11.a
    • Parallel of latitude radius
    • Radius of curvature of meridian at latitude
    • Example 11.b
    • Equation 11.1
    • Equation 11.2
    • Equation 11.3
    • Higher accuracy algorithm on p85
    • Example 11.c
  • Ch 12: Sidereal Time at Greenwich
    • Equation 12.1
    • Equation 12.2
    • Equation 12.3
    • Equation 12.4
    • Example 12.a
    • Example 12.b
  • Ch 13: Transformation of Coordinates
    • Local hour angle from sidereal time and right ascension
    • Eq 13.1 and 13.2 equatorial to ecliptical
    • Eq 13.3 and 13.4 ecliptical to equatorial
    • Eq 13.5 and 13.6 local horizontal coordinates
    • Horizontal to equatorial
    • Eq 13.7 and 13.8 equatorial to galactic
    • Galactic to equatorial
    • Example 13.a
    • Example 13.b
    • Exercise on p96
  • Ch 14: The Parallactic Angle, and three other Topics
    • Equation 14.1
    • Equation 14.2
    • Equation 14.3
    • Example 14.a
    • Ecliptic and Equator
    • Diurnal path and Horizon
  • Ch 15: Rising, Transit, and Setting
    • Equation 15.1
    • Equation 15.2
    • Example 15.a
  • Ch 16: Atmospheric Refraction
    • Equation 16.1
    • Equation 16.2
    • Equation 16.3
    • Equation 16.4
    • Example 16.a
  • Ch 17: Angular Separation
    • Equation 17.1
    • Equation 17.2
    • Equation 17.3
    • Equation 17.4
    • Example 17.a
    • Exercise 1 on p110
    • Exercise 2 on p110-111
    • Equation 17.5
    • Example 17.b
    • Relative position angle
  • Ch 18: Planetary Conjunctions
    • Example 18.a
  • Ch 19: Bodies in Straight Line
    • Example 19.a
  • Ch 20: Smallest Circle containing three Celestial Bodies
    • Equation 20.1
    • Example 20.a
    • Exercise on p128
    • Example 20.b
    • Example 20.c
  • Ch 21: Precession
    • Equation 21.1
    • Example 21.a
    • Besselian and Julian Year
    • Rigorous method
    • Example 21.b
    • Using ecliptical coordinates
    • Example 21.c
    • Table 21.A
    • Old precessional elements
    • Motion in space
    • Example 21.d
  • Ch 22: Nutation and the Obliquity of the Ecliptic
    • Equation 22.1 Julian centuries from epoch J2000
    • Obliquity of the ecliptic
    • Example 22.a
  • Ch 23: Apparent Place of a Star
    • Effect of nutation
    • Effect of aberration
    • Example 23.a
    • Ron-Vondrak aberration
    • Example 23.b
  • Ch 24: Reduction of Ecliptical Elements from one Equinox to anther one
    • Example 24.a
    • Example 24.b
    • Example 24.c
  • Ch 25: Solar Coordinates
    • Eq 25.2: Geometric mean longitude of the Sun
    • Eq 25.3: Mean anomaly of the Sun
    • Eq 25.4: Earth orbit eccentricity
    • Eq 25.5: Sun radius vector
    • Example 25.a
    • Higher accuracy
    • Example 25.b
  • Ch 26: Rectangular Coordinates of the Sun
    • Reference to the mean equinox of the date
    • Example 26.a
    • Reference to the standard equinox of J2000.0
    • Reference to the mean equinox of B1950.0
    • Reference to any other mean equinox
    • Example 26.b
  • Ch 27: Equinoxes and Solstices
    • Example 27.a
  • Ch 28: Equation of Time
    • Example 28.a
    • Example 28.b
  • Ch 29: Ephemeris for Physical Observations of the Sun
    • Example 29.a
    • Example 29.b
  • Ch 30: Equation of Kepler
    • First method
    • Example 30.a
    • Second method
    • Example 30.b
    • Third method
    • Fourth method
  • Ch 31: Elements of the Planetary Orbits
    • Example 31.a
    • Table 31.A
    • Table 31.B
  • Ch 32: Positions of the Planets
    • Example 32.a
    • Example 32.b
  • Ch 33: Elliptic Motion
    • First Method
      • Eq 33.1
      • Eq 33.2
      • Eq 33.3
      • Eq 33.4
      • Eq 33.5
      • Example 33.a
    • Second Method
      • Eq 33.6
      • Eq 33.7
      • Eq 33.8
      • Eq 33.9
      • Eq 33.10
      • Eq 33.11
      • Eq 33.12
      • Eq 33.13
      • Eq 33.14
      • Example 33.b
    • Heliocentric ecliptical coordinates
    • Equation of the center
    • Velocity in an elliptic orbit
    • Length of the ellipse
  • Ch 34: Parabolic Motion
    • Eq 34.1
    • Eq 34.2
    • Eq 34.3
    • Eq 34.4
    • Eq 34.5
    • Eq 34.6
    • Example 34.a
  • Ch 35: Near-parbolic Motion
    • Eq 35.1
  • Ch 36: The Calculation of some Planetary Phenomena
    • Table 36.A
    • Eq 36.1
    • Example 36.a
    • Example 36.b
    • Example 36.c
    • Example 36.d
    • Exercises on p255
    • Table 36.B
    • Table 36.C
    • Table 36.D
  • Ch 37: Pluto
    • Eq 37.1
    • Table 37.A
    • Example 37.a
  • Ch 38: Planets in Perihelion and in Aphelion
    • Example 38.a
    • Example 38.b
    • Table 38.A
  • Ch 39: Passages through the nodes
    • Eq 39.1
    • Eq 39.2
    • Eq 39.3
    • Eq 39.4
    • Case of parabolic orbit
    • Example 39.a
    • Example 39.b
    • Example 39.c
  • Ch 40: Correction for Parallax
    • Eq 40.1
    • Eq 40.2
    • Eq 40.3
    • Eq 40.4
    • Eq 40.5
    • Eq 40.6
    • Eq 40.7
    • Example 40.a
    • Exercise on p281
    • Parallax in horizontal coordinates
    • Parallax in ecliptical coordinates
  • Ch 41: Illuminated Fraction of the Disk and Magnitude of a Planet
    • Eq 41.1
    • Eq 41.2
    • Eq 41.3
    • Eq 41.4
    • Example 41.a
    • Example 41.b
    • Magnitude of planets
    • Example 41.c
    • Example 41.d
  • Ch 42: Ephemeris for Physical Observations of Mars
    • Eq 42.1
    • Eq 42.2
    • Eq 42.3
    • Eq 42.4
    • Example 42.a
  • Ch 43: Ephemeris for Physical Observations of Jupiter
    • Main method
    • Example 43.a
    • Lower accuracy
    • Example 43.b
  • Ch 44: Positions of the Satellites of Jupiter
    • Low accuracy
    • Example 44.a
    • High accuracy
    • Example 44.b
  • Ch 45: The Ring of Saturn
    • Eq 45.1 and method
    • Example 45.a
  • Ch 46: Positions of the Satellites of Saturn
    • Table 46.A
    • Eq 46.1
    • Eq 46.2
    • Mimas
    • Enceladus
    • Tethys
    • Dione
    • Rhea
    • Titan
    • Hyperion
    • Iapetus
    • Differential light-time
    • Perspective effect
    • Example 46.a
  • Ch 47: Position of the Moon
    • Eq 47.1
    • Eq 47.2
    • Eq 47.3
    • Eq 47.4
    • Eq 47.5
    • Eq 47.6
    • Table 47.A
    • Table 47.B
    • Example 47.a
    • Eq 47.7
  • Ch 48: Illuminated Fraction of the Moon's Disk
    • Eq 48.1
    • Eq 48.2
    • Eq 48.3
    • Eq 48.4
    • Eq 48.5
    • Example 48.a
  • Ch 49: Phases of the Moon
    • Eq 49.1
    • Eq 49.2
    • Eq 49.3
    • Eq 49.4
    • Eq 49.5
    • Eq 49.6
    • Eq 49.7
    • Example 49.a
    • Example 49.b
    • Table 49.A
  • Ch 50: Perigee and Apogee of the Moon
    • Eq 50.1
    • Eq 50.2
    • Eq 50.3
    • Example 50.a
    • Table 50.A
    • Table 50.B
    • Table 50.C
  • Ch 51: Passages of the Moon through the Nodes
    • Eq 51.1
    • Example 51.a
  • Ch 52: Maximum Declinations of the Moon
    • Eq 52.1
    • Table 52.A
    • Table 52.B
    • Example 52.a
    • Example 52.b
    • Example 52.c
  • Ch 53: Ephemeris for Physical Observations of the Moon
    • Eq 53.1
    • Eq 53.2
    • Example 53.a
    • Topocentric librations
    • Selenographic position of the Sun
    • Eq 53.3
    • Eq 53.4
    • Example 53.b
    • Example 53.c
    • Table 53.A
  • Ch 54: Eclipses
    • Solar Eclipses
      • Eq 54.1
      • Eq 54.2
    • Lunar Eclipses
      • Eq 54.3
      • Eq 54.4
    • Example 54.a
    • Example 54.b
    • Example 54.c
    • Example 54.d
    • Exercise on p388
  • Ch 55: Semidiameters of the Sun, Moon and Planets
    • Sun and Planets
    • Moon
    • Asteroids
  • Ch 56: Stellar Magnitudes
    • Adding Stellar Magnitudes
    • Example 56.a
    • Example 56.b
    • Example 56.c
    • Brightness Ratio
    • Example 56.d
    • Example 56.e
    • Distance and Absolute Magnitude
  • Ch 57: Binary Stars
    • Example 57.a
    • Eccentricity of apparent orbit
    • Example 57.b
  • Ch 58: Calculation of a Planar Sundial
    • Example 58.a
    • Example 58.b
    • Example 58.c
    • Special cases

Clone this wiki locally