Abbreviations, Definitions and Measurements

Celestial navigation has been with us since the beginning of time. Various civilizations have used it, some like the Polynesians, with remarkable and extremely daring skills.

Celestial navigation uses coordinates for Earth and celestial objects. Earth's coordinates are latitude and longitude. Celestial objects have their own coordinates, one system being celestial longitude and latitude based on the ecliptic plane—Earth's orbit around the Sun, tilted about 23 degrees to Earth's equatorial plane. The center of the Sun is the origin of this system.

The alternative system views the universe from an Earth-centered perspective and utilizes coordinates based on the equatorial plane. The coordinates in this system are declination and Greenwich hour angle.

Sean D’Epagnier

The System

The Earth, tilted at 23.4 degrees, rotates on average every 24 hours and wobbles (called precession) as it orbits counterclockwise on the Sun's imaginary ecliptic plane. Most planets also orbit counterclockwise on the Sun's imaginary ecliptic plane, appearing to wander among stars.

The Moon orbits Earth and together they revolve around the Sun. The Moon's orbital and rotational period is approximately 28 days, following a complex west-to-east trajectory contrary to the usual east-to-west movement. Additionally, the Moon rises roughly one hour later each day.

The stars, light years away from earth, appear fixed relative to each other, but they appear to rotate like a pinwheel near the star Polaris and also appear to move westward 1 degree each night during the year. The stars are located in the sky by their sidereal hour angle (SHA) from Aries, a fictitious body used as a reference.

The objects like the Sun, Stars, planets, and the Moon are positioned on an imaginary infinite radius sphere called celestial sphere centered on the Earth. The celestial equator is the same as the Earth's equator. Polar North and South are the same as the Earth's Poles. Finally, all celestial objects like stars, planets, and the moon are projected on the celestial sphere with Latitude and Longitude coordinates, and we use these same coordinates to determine our Latitude and Longitude position on Earth.

Bob Bossert

Definitions

Celestial Definitions

• Meridians: The Lines Connecting Earth's Poles: An imaginary line on Earth's surface that runs from the North Pole to the South Pole, connecting points of equal longitude.
• Ecliptic: The Sun's Celestial Highway: The ecliptic is the plane of Earth's orbit. From our viewpoint, it maps the sun's path over the year and hosts the Zodiac signs. Kepler determined that planetary orbits around the sun were elliptical rather than circular based on observations that appeared as circles edge-on.
• Equinoctial Plane: Earth's Celestial Equator: The plane on the celestial sphere that separates the Northern part from the Southern part. It is an extension of the equatorial plane.

Measurements

• Latitude: is the measure of a location's distance north or south of the Earth's Equator, expressed in degrees. It is part of the terrestrial global coordinate system.
• Longitude: is the measurement of a location's distance east or west of the Prime Meridian, an imaginary line that runs from the North Pole to the South Pole through Greenwich, England. It is expressed in degrees, ranging from 0 degrees at the Prime Meridian to 180 degrees east and 180 degrees west. Longitude lines, also known as meridians, are vertical lines converging at the poles and help form Earth's global coordinate system.
• Altitude or elevation: The angle between a celestial body and the observer's horizontal plane. This measurement is accomplished using a sextant for sailors and a theodolite for surveyors.
• Azimuth (Zn): Angle angle measured clockwise from the North Pole to the celestial object on the horizon. It is a means to locate a celestial object relative to the observer’s assumed or DR position.
• Bearing: The horizontal angle from North to the direction you are pointing. To avoid confusion, specify whether it is TRUE north or MAGNETIC north. When the magnetic variation is West, it's added to the true bearing to determine the magnetic bearing. The opposite is true for East variation: it's subtracted.
• Nautical mile: 1852 meters or 6080 feet. It is based on a minute of Latitude. It is commonly used by sailors worldwide for measuring distance because it is so convenient to convert between nm and degrees/minutes.

GHAAST and SHA

• GHAAST: (Greenwich Hour Angle of Aries) is a reference point in celestial navigation, used primarily for stars. GHAAST = Greenwich Hour Angle of Aries at Siderial Time. Used to determine the position of the celestial meridian relative to the Greenwich meridian. Locates the position of the celestial sphere at a specific time.
• SHA: (Sidereal Hour Angle) is the angular distance from GHAAST to a celestial body's meridian. Position of celestial body relative to the vernal equinox.

  Stars maintain their relative positions with minimal movement. The Nautical Almanac lists the GHA for the "first point of Aries," the reference point for star coordinates. To calculate: GHA (star) = SHA (star) + GHA (Aries). Although ideally constant, the Earth's wobble shifts the GHA of Aries during a 26,000-year cycle. The first point of Aries marks where the Sun crosses the equatorial plane around March 21st.

• RA: Right Ascension (star’s SHA = 360 minus the star’s RA). RA is measured by astronomers in hours and minutes and increases eastward. Navigators convert it to degrees: 1 hour equals 15 degrees, 1 minute of time equals 15 arc minutes. GST (Greenwich Sidereal Time) is used instead of GHA Aries.
• GHA: (Greenwich Hour Angle) is the sum of GHAAST and SHA. The horizontal angular degrees (0 to 360 degrees) from the Greenwich meridian (0 degrees) to the celestial body, always measured in a westward direction.
• HA: Hour Angle, measure of time since celestial body observer’s meridian, angular distance westward between observer's meridian and celestial bodies meridian.
• LHA: Local Hour Angle, horizontal angular degrees (0 to 360 degrees) measured Westward from the Assumed or DR Position meridian to the celestial object. LHA = GHA (of celestial object) - Longitude West. Measured Eastward LHA = GHA + Longitude East.
• GP: Geographical Position of a heavenly body. (GHA and Dec)

• DEC: Declination- angular degrees (0 to 90 degrees) or Latitude of a celestial body above or below the celestial equator or equatorial plane for celestial objects, it is specified by North or South. Or a positive angle is North and a negative angle is South.

• MPP: Mean Position of Polaris (helps to determine latitude when north of equator), also Most Probable Position

Altitude Measurements

• Hs: Sextant measured altitude of the celestial body from the Observer’s eye to the visible horizon. Height of sextant.
• Index Error: index mirror and horizon mirror are not perfectly parallel to each other when the index arm is set to zero minutes. Measured in arc minutes. On the arc: The error is positive meaning the sextant reads a higher angle than the altitude. Off the arc, the error is negative meaning the sextant reads a lower angle than the altitude.
• Index Correction: The correction made by the Sextant observer when recording the Hs. If “on the arc”, take it off (subtract), if “off the arc” add it on. In Celestial Navigation, you identify the Index Error for the sight. And the application handles the Index Correction
• Ha: Apparent altitude: sextant measurement (Hs) adjusted for index correction (IC either plus or minus) and the observer's height of eye above sea level (DIP). Apparent Height
• Ho: Observed altitude: apparent altitude (Ha) adjusted for refraction, semi-diameter (SD), and parallax.Final corrected sextant angular measurement. Height observed.
• Hc: Computed Altitude: Math derivation of the altitude of a celestial body at your DR position. Comparable to Ho. Height computed.
• Sight Error: If your DR position is from a GPS, the difference between Hcand Ho is Sight Error.
• Intercept: is the difference between Computed Altitude (Hc) and Observed Altitude (Ho) (absolute value) in nautical. Based on 1 nautical mile is 1 arc minute.
• Away: is when the actual position (LOP) is further away from the observed celestial body than the DR/Fix position. If Hc => Ho, then the Celestial Body is Away otherwise it is Toward.

DRIPS neumonic

• Dip of the Horizon (function of eye height)
• R = Refraction (function of Ha, temperature and pressure)
• IE = Index Error of sextant
• PA = Parallax in Altitude (function of HP and Ha)
• SD = Semi-Diameter. One half of the angular width of the Sun or Moon of the body..

Additional Calculations and Measurements

• Angle and Distance Measurement: 1 Arc Minute = 1 nautical mile.
• Zn: Azimuth. Horizontal angle in degrees between True North and a celestial body.
• Height of Eye: Distance from observer's eye to sea level.
• Dip: The true horizon is perpendicular to the Earth's center at the observer's position. When your “height of eye” is above sea level, the visible horizon "dips" or appears lower than the true horizon. DIP is the angle from the true horizon to the visible horizon. DIP is calculated from tables/formulas based on “Height of Eye” and DIP includes refraction of the visible horizon. Dip is subtracted from Hs.
• Refraction: Light waves bend when traveling through the earth’s atmosphere. The body (star) we see is actually at a lower altitude. The lower the body is in altitude, the more the light waves bends. The denser the atmosphere (colder), the more light waves bend. Refraction is subtracted from the Hs.
• IC: Index Correction is the adjustment applied to a sextant reading to account for alignment errors in the instrument, ensuring accurate measurements. The correction is in arc minute
• HP or PA: Horizontal Parallax, correction for shift due to not taking Sights from the center of the earth.
• SD: Semi-diameter. Half the apparent angular diameter of a celestial body as seen from the observer on Earth. Used for corrections to the observed altitude Ho.
• Limb: For Sun and Moon measurement accuracy, the Hs is measured from the Upper Limb or the Lower Limb of the Body. Add or Subtract Semi-Diameter from Hs to adjust sextant measurement to the center of the body.
• Star Finders: Report calculated Hc altitudes and azimuths. Similar to the plugin Sights > Find button.

Time

• Delta T (ΔT): is the difference between Terrestrial Time (TT) and Universal Time (UT1), used to account for variations in Earth's rotation when calculating celestial positions. Celestial-navigation_pi adjusts DeltaT yearly to published values. If there becomes a need for additional DeltaT adjustment use Sight > Clock Error Tab.
• Julian Date and Time: Julian Date (JD) provides a standardized way to represent time in astronomical observations and calculations. It is a continuous count of days and fractions of days since noon Universal Time (UT1) on January 1, 4713 BC
• UTC (Coordinated Universal Time): is the primary time standard by which the world regulates clocks, based on atomic time and aligned with Earth's rotation.
• UT1: is Universal Time adjusted for Earth's rotation irregularities, used in celestial navigation for precise timekeeping and positional calculations.
• GMT: Greenwich Mean Time

Position

• DR: Dead Reckoning Position from Deduced Reckoning.
• AP: Assumed Position. DR Latitude and Longitude.
• COP: Circle of Position. Circle of Equal Altitude. With a single circle of position, your position is somewhere on the Circle of Position. Deduce the likelihood of being on a specific location on the Circle of Position based on DR position.
• LOP: Line of possible positions based upon a single observation of a celestial body. Line of Position is the same as COP. COP when zoomed in looks like a straight line. Line of possible positions based upon a single observation of a celestial body. Multiple LOP’s creates an intersection and Fix.
• FIX: Position of vessel determined by intersecting two or more LOP or COP taken within 20 minutes.
• R-FIX: Running Fix, two or more LOP or COP taken greater than 20 minutes apart. There is less certainty in a Running Fix

Sign conventions

• Latitude and Declination are generally specified as North or South. When not specified, positive is North, negative is South.
• Longitude is generally specified as West or East. If not specified, Negative Longitude is West. Positive Longitude is East.
• GHA, SHA, LHA, Azimuth (Zn) are positive. GHA (0 - 360) is measured Westward from Greenwich. LHA (0 - 360) is measured Westward from your DR Meridian. SHA (0 - 360) is measured Westward from GHA of Aries. Azimuth (Zn) (0 - 360) is measured from North Pole Clockwise to the Body,
• Bearings are positive clockwise, negative anticlockwise.
• To convert from arc minutes to degrees, divide by 60. For example, 45 minutes is (45/60) or 0.75 degrees.
• To convert from Decimal Degrees to Degrees and Minutes. Multiply the decimal part of the degrees by 60. For example, 25.75 degrees. Is (25 degrees + 75*60’) or 25 degrees 45’
• To convert from Degrees-minutes to Decimal Degrees. Divide the minutes by 60. For example, 25 degrees 45.5’ is 25+45.5/60 = 25.75833 degrees
• Multiplying by 60 converts degrees of latitude into minutes and nautical miles. 1 nautical mile equals 1 arc minute).

Also in these formulas, angles are in degrees, which is why 60 appears to convert degrees into minutes or nautical miles (since 1 nautical mile equals 1 minute of arc on Earth).

Good reference https://www.siranah.de/html/sail040e.htm#a2