Abbreviations, Definitions and Measurements (Rev 15 Dec 2025)

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. 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 27.3 days with respect to the background stars. It follows a complex west-to-east trajectory contrary to the usual east-to-west movement. Additionally, the Moon rises on average 50 minutes later each day.

The width of the Moon is roughly 1/2° and moves the width of its apparent diameter in 1 hour. This is equivalent to 30 arc-min in 60 minutes or 0.1 arc-min in 12 sec. The moon's orbit is tilted about 5.1° and it swings north and south of the ecliptic equator.

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 (NP) to the South Pole, connecting points of equal longitude.
• Ecliptic: The Sun's Celestial Highway: The ecliptic is the plane of Earth's orbit around the Sun. 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 Earth's 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.
• WMM World Magnetic Model: is used by Open CPN and Celestial Navigation to Determine Magnetic direction.
• 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 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 celestial 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. Measure Formats are Degrees(space)Minutes, decimal degrees, Degrees(space)minutes(space)seconds. The measurement is re- displayed Per OpenCPN Display option. Change Display Option and Re-display also changes.
• Estimated Hs (New Feature): Celestial Nav plugin will estimate Hs (Sextant altitude Measurement) at the sight's DR Lat & Longitude. This can be used to: validate sight measurement, preset sextant for a Future sight, use the sight as a Star Finder.
• For Lunar Distance Measurements, you need a high quality and well adjusted sextant. What is good enough for Altitude Sights might not be good enough for Lunars. Just recognize that the time accuracy is affected by the quality of your sextant and how well it is adjusted.
• Sextant Perpendicularity error: happens when the index mirror isn't perpendicular to the sextant's frame. This can be fixed by adjusting the index mirror screw.
• Sextant Side Error: Side error is when the horizon horizon mirror isn't Perfectly perpendicular to the sextant's frame. For Altitude Sights, it is like seeing a ghost image a few arc-minutes from The celestial body. For altitude sights, a little Side Error isn't much of a problem. But for Lunar Sights you want NO side error. Once you eliminate side error, you'll need to revalidate and then remove Index Error.
• Sextant Index Error: You have index error when index mirror and horizon mirror are not perfectly parallel to each other. When the index arm is set to zero minutes, and you don't see a single continuous line or see a broken line, turn the micrometer drum until the line looks continuous. Then read the index. If "On the arc" The error is positive meaning the sextant reads a higher angle than the altitude. If "Off the arc", the error is negative meaning the sextant reads a lower angle than the altitude. For Lunar Sights, you want to do as much as you can to eliminate Index Error. Index Error for Altitude sights can be tolerated if it is only a few arc minutes.
• Index Correction: The correction made by the Sextant observer when recording the Hs. The adage is if "on the arc", take it off (subtract), if "off the arc" add it on. In Celestial Navigation, Plugin identify the Index Error (Parameters) for the sight. The application handles the Index Correction calculation.
• 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 Hc and 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.

• LDo.pc: Raw Sextant Measured angular distance between Moon and Celestial Body. From edge of moon to edge of celestial body.
• Near: when the closest edge of a celestial body (Sun, Star, Planet) is brought to the nearest visible edge of the moon
• Far: when the nearest edge of the celestial body must cross the moon’s face to the far side edge of the moon.
• LDo apparent: Apparent Lunar Distance. Apparent Center of Moon to Apparent Center of Celestial Body. There is no Dip correction. Just SDs and IC added to the measurement.
• LDc Cleared: The Lunar Distance after Adding Parallax and Refraction. No Dip adjustment.
• Predicted LD Cleared: Calculated (Nautical Almanac data) Lunar Distance from Center of Moon to Center of Celestial Body from the perspective of the center of the earth. It is a formula based On GHA and Dec of the Moon and Celestial Body.
• Predicted LD Cleared: has similar meaning as Hc for altitude sights. LDc (Cleared) has similar meaning as Ho for altitude sights.
• Relative Bearing Angle: Difference between the Bearing of the Apparent Moon to the Bearing of the Apparent Celestial Body. This is not the same angle as Azimuth (Zn).

DRIPS mnemonic

• 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). HP of Sun, Moon, Planets is part of the Almanac data.
• SD = Semi-Diameter. One half of the angular width of the Sun or Moon. SD of planets is assumed to be 0 in Celestial Nav plugin.

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 your boat's Waterline, the visible horizon "dips" or appears lower than the true horizon. DIP is the angle from the true horizon to the visible distant sea 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.
• Dip Short: When celestial body is brought down to a shore line because land obstructs vision to the distant sea. To calculate Dip Short correction You need to know the Distance (in nautical miles) from your location To the shoreline in the direction of the Azimuth.
• Artificial Horizon: Bring down Celestial Body to a liquid surface (a substitute horizon) because of no useable natural horizon or shoreline. The Correction is halving the measured angle.
• Backsight: If you can't sight the celestial body because the bearing of the body is obstructed, turn 180 degrees away and bring it down to the side that is not obstructed.
• 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.i Parallax is added.
• Augmentation: Part of Parallax. A small increase in the Moon's Apparent size (SD) based on altitude overhead. Augmentation increases as Moon rises towards it's Zenith and then declines to 0 when the Moon sets.
• 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.

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.
• Terrestrial Time (TT): Used for predicting celestial body positions. Differing from UTC.
• 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. It is not impacted by Daylight savings, leap year, etc.
• 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. AP is derived from DR and is used for Calculating position to be used in table lookups such as Pub229.
• 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. Or, 2 or more COPs create 2 intersections. One of which can be a FIX.
• LOP: Line of Position is the same as COP. COP when zoomed in looks like a straight line.
• 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. Caution: Currently, OpenCPN does not support this contention. Need to Specify East or West, E or W.
• 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 anti-clockwise.
• With this release, less of a need to convert from Decimal Degrees, Degrees(space)Minutes(seconds). Cel Nav supports the OpenCPN Angle formats. And in Calculate form, shows both decimal degrees And degree and fractional minutes.
• 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 + 0.75*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).

In Celestial Equation formulas, angles are calculated in decimal degrees, They are displayed with 4 significant digits after the decimal point. Intermediate calculations are carried out to more significant digits. And where possible, the degree - minutes associated with the decimal Degrees is shown.

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