Celestial Navigation Sight Reduction
Sight reduction is the complete process that converts a raw sextant reading into a plotted line of position. This guide covers every step tested on the USCG Master 100 GRT oceans endorsement: the celestial sphere and PZX triangle, GHA and LHA, sextant altitude corrections, Ho versus Hc, the intercept method, HO 229 and HO 249, noon sight, morning and evening star sights, compass error by amplitude and azimuth, running fixes, and the Nautical Almanac.
Related Celestial Navigation Guides
1. The Celestial Sphere and the PZX Navigation Triangle
All celestial sight reduction begins with two conceptual tools: the celestial sphere and the PZX triangle. Mastering these lets every formula and table make intuitive sense.
The Celestial Sphere
Imagine an infinite sphere surrounding the earth with the observer at the center. Every star, planet, sun, and moon is projected onto this sphere. The celestial equator is the earth's equator extended outward. The celestial poles are the earth's poles extended. Directly overhead is the zenith; directly below is the nadir.
- Declination (Dec) — the celestial equivalent of latitude; angular distance north or south of the celestial equator
- GHA — westward angle from the Greenwich meridian to the body's hour circle
- LHA — westward angle from the observer's meridian to the body's hour circle
- Altitude — angular height of the body above the horizon, measured 0 to 90 degrees
- Azimuth — bearing to the body measured clockwise from true north
The PZX Triangle
The PZX triangle (also called the astronomical or navigational triangle) is a spherical triangle with three vertices:
- P — the elevated celestial pole (north pole for northern hemisphere observers)
- Z — the observer's zenith (directly overhead); the side PZ equals 90 degrees minus latitude
- X — the geographic position of the celestial body; the side PX equals 90 degrees minus declination
The angle at P equals LHA. The side ZX (the zenith distance) equals 90 degrees minus the computed altitude Hc. The angle at Z is the azimuth angle Z, which converts to true azimuth Zn. Sight reduction tables solve this triangle.
The Three Inputs to Every Sight Reduction
1. Assumed Latitude (aL)
A whole degree of latitude close to your DR position. HO 229 and HO 249 require whole-degree arguments. The assumed latitude is chosen to make LHA come out to a whole number of degrees.
2. Local Hour Angle (LHA)
Computed from the body's GHA (Nautical Almanac) and the assumed longitude. LHA must be a whole number of degrees to enter the tables. Choose assumed longitude within 30 minutes of DR longitude that produces a whole-degree LHA.
3. Declination (Dec)
The body's celestial latitude, extracted directly from the Nautical Almanac daily pages. The tables use whole-degree declination; minutes require the d-correction interpolation.
2. Greenwich Hour Angle, Local Hour Angle, and Declination
Understanding how GHA, LHA, and declination relate is essential for both exam problems and practical navigation. These three numbers fully describe the geometry between the observer and the celestial body.
GHA (Greenwich Hour Angle)
GHA is the westward angular distance from the Greenwich meridian (0 degrees longitude) to the hour circle of the celestial body. It ranges from 0 to 360 degrees and increases at roughly 15 degrees per hour as the earth rotates eastward. GHA is tabulated in the Nautical Almanac for every hour of every day for the sun, moon, planets, and Aries. Stars use GHA Aries plus SHA (sidereal hour angle) to obtain GHA of the star.
GHA Extraction from the Nautical Almanac
- Turn to the daily page for the observation date
- Read the tabulated GHA for the whole hour of GMT in the body's column
- Turn to the Increments and Corrections pages (colored pages)
- In the column for minutes of GMT, read the increment for seconds
- Add the increment to the tabulated GHA to get total GHA
- Apply the v correction for moon or planet if tabulated (sometimes adds, sometimes subtracts)
LHA (Local Hour Angle)
LHA adjusts GHA for the observer's longitude. The conversion rule is:
LHA = GHA + East Longitude
LHA = GHA - West Longitude
If LHA exceeds 360, subtract 360. If LHA is negative, add 360.
For HO 229 and HO 249, LHA must be a whole number of degrees. To achieve this, use an assumed longitude within 30 minutes of the DR longitude that produces a whole-degree LHA. With west longitude: assumed longitude equals the minutes of GHA subtracted from the whole degree that makes LHA whole. The exam will provide the assumed longitude or give you the GHA and let you compute it.
Declination
Declination is the body's angular distance north or south of the celestial equator, analogous to geographic latitude. It is labeled N or S and ranges from 0 to 90 degrees. The sun's declination changes throughout the year: roughly N 23.5 degrees at the June solstice, 0 at the equinoxes, and S 23.5 degrees at the December solstice. Stars have fixed declinations; the moon and planets change slowly.
In the Nautical Almanac, declination is listed alongside GHA on each daily page. When the declination is changing, a small d value is listed at the bottom of the column. Extract d, enter the increments tables for the minutes of GMT, find the d correction column, and apply it (add if declination is increasing, subtract if decreasing).
3. Sextant Operation and Technique
The sextant measures the altitude of a celestial body above the visible horizon. Proper technique and understanding of sextant errors are tested directly on the USCG Master exam.
Key Parts of the Sextant
- Frame and arc — rigid structure with the graduated arc (scale in degrees)
- Index arm — rotates along the arc; carries the index mirror
- Index mirror — attached to index arm; rotates with it; reflects the celestial body
- Horizon mirror — half-silvered; shows the horizon directly in the clear half and the reflected body in the silvered half simultaneously
- Telescope — magnifies the field for precise alignment
- Shade glasses — reduce solar intensity for sun observations
- Drum micrometer — fine adjustment for reading to 0.1 arc minute
- Clamp — locks the index arm in position
Taking a Sun Sight
- Set index arm to the approximate altitude from a predicted value or by estimation
- Fit shade glasses appropriate for solar brightness
- Sweep the sextant toward the horizon while looking through the telescope
- Bring the sun's image down to rest on the horizon (lower limb for most observations)
- Rock the sextant side to side; the sun traces an arc — the lowest point of the arc is true altitude
- When the sun's lower limb is tangent to the horizon, call "mark" and immediately record GMT to the nearest second
- Read the sextant altitude from the arc and micrometer drum
Sextant Errors
Index Error (IE)
Index error is a built-in instrumental error caused by misalignment of the index mirror relative to the horizon mirror. To measure it, set the sextant to zero and look at the horizon; if the direct and reflected images do not align perfectly, the sextant reads the error. On the arc (positive reading): subtract from Hs. Off the arc (negative reading): add to Hs. Mnemonic: if it's on, it's off (subtract); if it's off, it's on (add).
Side Error
Side error exists when the index mirror is not perpendicular to the plane of the instrument. Check by holding the sextant horizontal and looking at a star; if the star's reflected image is to the left or right of the direct image, side error exists. It must be corrected physically by adjusting the mirror.
Perpendicularity Error
Occurs when the index mirror is not perpendicular to the frame. Check by setting the arc to about 35 degrees, looking into the index mirror, and verifying that the arc as seen directly and its reflection appear as one continuous arc.
Collimation Error
Collimation error means the telescope is not parallel to the frame. Check by observing two stars and confirming they appear at the same relative position with and without the telescope in place. This is usually a factory or technician adjustment.
4. Altitude Corrections: From Hs to Ho
Every sextant reading (Hs) requires a series of corrections before it becomes the observed altitude (Ho) used in the intercept calculation. The USCG exam frequently tests the identity of each correction, its sign, and what it corrects for.
Index Error (IE)
Apply first, before any other correction. If IE is on the arc (positive), subtract it. If IE is off the arc (negative), add it. Index error is an instrument error inherent to the sextant being used; it does not change with observation conditions. Always confirm IE at the start of a sight session by checking the horizon at zero.
Dip Correction
Dip corrects for the observer's height of eye above the water surface. The visible horizon is depressed below the geometric (true) horizon by an amount that depends on height of eye. Dip is always negative — always subtracted. The Nautical Almanac inside front cover provides a dip table; for a height of eye of 9 feet, dip is approximately 2.9 arc minutes. After applying IE and dip, the result is apparent altitude (Ha).
Refraction
The atmosphere refracts (bends) light from celestial bodies upward, making bodies appear higher than their true geometric altitude. Refraction is always a negative correction (always subtracted). It is largest at low altitudes: approximately 34 arc minutes at 0 degrees altitude, 5 arc minutes at 10 degrees, 1 arc minute at 45 degrees, and negligible above 70 degrees. The Nautical Almanac altitude correction tables include refraction combined with other corrections for convenience. Never observe bodies below 5 degrees altitude; refraction errors become large and unpredictable near the horizon.
Semi-Diameter (SD) — Sun and Moon Only
The sun and moon have measurable angular diameter. When you observe the lower limb (bottom edge) tangent to the horizon, the center of the body is actually higher by the semi-diameter. Add SD for lower limb observations; subtract SD for upper limb observations. The sun's SD is approximately 16 arc minutes year-round (slightly more in winter when earth is closer). The moon's SD varies and is tabulated daily in the Nautical Almanac. Stars and planets are point sources and have no SD correction.
Parallax in Altitude (PA) — Moon Only
Parallax in altitude is significant only for the moon, which is close enough to earth that the observer's position on the surface differs meaningfully from the earth's center (where almanac coordinates are referenced). PA is always added. The moon's horizontal parallax (HP) is tabulated in the Nautical Almanac; PA equals HP times cosine of the apparent altitude. For the sun, PA is approximately 0.1 arc minutes and is included in the Nautical Almanac combined correction. For stars and planets, PA is negligible.
Correction Summary by Body Type
Stars
IE: yes (add or subtract)
Dip: yes (always subtract)
Refraction: yes (subtract)
SD: no (point source)
PA: no (negligible)
Sun
IE: yes (add or subtract)
Dip: yes (always subtract)
Refraction: yes (subtract)
SD: yes (add lower limb; subtract upper limb)
PA: negligible, included in tables
Moon
IE: yes (add or subtract)
Dip: yes (always subtract)
Refraction: yes (subtract)
SD: yes (tabulated daily)
PA: yes (always add)
5. Ho vs. Hc and the Intercept Method (Marcq Saint-Hilaire)
The intercept method is the universal technique for converting a celestial observation into a plotted line of position. Developed by French naval officer Marcq Saint-Hilaire in 1875, it replaced the earlier methods that required knowing longitude precisely.
Ho (Observed Altitude)
Ho is the corrected sextant altitude — the altitude after applying all corrections (IE, dip, refraction, SD, PA as applicable). It represents the true angular height of the celestial body above the geometric horizon as measured from the observer's actual position. Ho is what was actually seen and measured.
Hc (Computed Altitude)
Hc is the altitude the body would have if the observer were exactly at the assumed position (AP). It is calculated mathematically from the AP's latitude, the body's declination, and the LHA — all using sight reduction tables (HO 229 or HO 249). Hc is what should have been seen at the AP. The difference between what was seen and what should have been seen at the AP drives the plot.
Step-by-Step Sight Reduction Procedure
- Record Hs and GMT. At the moment of observation, read the sextant altitude and note the exact GMT from the ship's chronometer. Accuracy of one second in time equals 0.25 miles of position error.
- Correct Hs to Ho. Apply IE, dip, and the main altitude correction from the Nautical Almanac. The result is Ho, the observed altitude.
- Extract GHA and declination. Using GMT, go to the Nautical Almanac daily pages for the body. Read the tabulated GHA for the whole hour, then add the increment for minutes and seconds from the increments pages. Read the declination. Apply v and d corrections if tabulated.
- Choose an assumed position (AP). Select a whole-degree latitude near the DR and an assumed longitude that makes LHA a whole number. For west longitude: assumed longitude minutes equal GHA minutes of arc, making LHA a whole number when subtracted.
- Compute LHA. LHA equals GHA plus east longitude, or GHA minus west longitude. Confirm it is a whole number of degrees.
- Enter HO 229 (or HO 249). Use the volume for your assumed latitude range. Find the page for LHA. Enter with assumed latitude and tabulated declination (whole degrees) to read Hc and azimuth angle Z. Apply the d correction to Hc using the declination minutes and the interpolation table.
- Convert azimuth angle Z to true azimuth Zn. Rules: If LHA is greater than 180, the body is to the west (Zn for northern hemisphere, northern declination: Zn equals 360 minus Z). If LHA is less than 180, the body is to the east (Zn equals Z). The table headings in HO 229 state the naming rules explicitly — always read the rule printed on the table page.
- Compute the intercept (a). Intercept a equals Ho minus Hc, in arc minutes (nautical miles). If positive (Ho greater than Hc), plot toward the body. If negative (Hc greater than Ho), plot away from the body.
- Plot the LOP. From the AP on the chart, draw the azimuth line toward Zn. Measure the intercept distance along this line (toward or away). Draw the LOP perpendicular to the azimuth at the intercept point.
- Repeat for a fix. Two or more LOPs from different bodies plotted simultaneously (or advanced for a running fix) intersect at the vessel's position.
Ho Mo To — The Classic Exam Mnemonic
Ho Mo To: Ho More Than Hc, plot Toward. If observed altitude Ho exceeds computed altitude Hc, the observer is closer to the geographic position of the body than the assumed position, so the intercept is toward. The reverse (Ho less than Hc) means the intercept goes Away. Some instructors use the phrase "Coast Guard Academy" as shorthand for "Computed Greater Away."
6. HO 229 vs. HO 249 Sight Reduction Tables
The USCG exam will specify which set of tables to use. Understanding their structure prevents errors in choosing volumes and reading the table pages.
HO 229 — Sight Reduction Tables for Marine Navigation
- Six volumes covering latitudes 0 to 90 degrees in 15-degree bands (Volumes 1 through 6)
- Arguments: assumed latitude (whole degrees), LHA (whole degrees), declination (whole degrees with interpolation for minutes)
- Output: Hc to 0.1 arc minute, azimuth angle Z in 0.1-degree steps, and the d value for declination interpolation
- Interpolation: a declination increment table on each spread interpolates for declination minutes
- Exam standard: the USCG Master oceans endorsement exam primarily references HO 229
- Precision: the most precise tabulated marine reduction method short of direct computation
HO 249 — Sight Reduction Tables for Air Navigation
- Three volumes: Volume I for selected stars; Volumes II and III for declinations 0 to 29 degrees
- Volume I advantage: precomputes data for 41 navigational stars, eliminating the need to separately look up SHA and compute LHA of the star
- Output: Hc to the nearest whole arc minute; azimuth to the nearest whole degree
- Speed: faster than HO 229 because interpolation is simpler and Volume I requires only LHA of Aries and latitude
- Limitation: less precise (to the nearest minute, not 0.1 minute) and Volume I only works for the listed selected stars
- Common use: offshore sailing and aviation; some USCG exam problems specify it
Reading HO 229 — Page Layout
Each page spread in HO 229 covers a specific LHA value (or range) and two assumed latitudes (one on the left page, one on the right). Within the page, columns are organized by declination from 0 to 90 degrees. The main tabulation gives Hc and Z (azimuth angle) for the intersection of the assumed latitude, LHA, and whole-degree declination. A separate column headed d gives the change in Hc per degree of declination; multiply d by the decimal minutes of declination divided by 60 to get the declination correction. Add or subtract the correction depending on whether declination is increasing or decreasing (the sign of d).
The naming convention for azimuth angle Z: each page heading states the rule, which is typically of the form "N LHA if LHA is greater than 180, S LHA if less than 180" for northern latitudes. Always read the rule on the page being used rather than memorizing a single formula that may not apply to every quadrant.
7. Noon Sight for Latitude (Local Apparent Noon)
The noon sight is the oldest and most straightforward celestial observation. It yields latitude directly without entering reduction tables, and it is tested on every USCG Master exam.
Predicting Local Apparent Noon (LAN)
LAN is the moment the sun crosses the observer's meridian. It occurs at a time that depends on the vessel's longitude and the equation of time. To predict LAN:
- From the Nautical Almanac daily page, read Mer. Pass. (meridian passage) in GMT for the date
- Apply a longitude correction: add 4 minutes per degree of west longitude; subtract 4 minutes per degree of east longitude
- The result is approximate LAN in GMT; convert to zone time for the watch
- Begin tracking the sun about 20 minutes before predicted LAN
Conducting the Noon Sight
The noon sight requires tracking the sun to its maximum altitude. Unlike timed star sights, exact GMT at meridian passage is not critical — the sun moves very slowly in altitude near transit, so a reading within 2 minutes of LAN is usually adequate.
- Set sextant to predicted altitude at LAN, using a prior computation or estimate
- Begin tracking 20 minutes early; advance the drum as altitude increases
- When the sun stops rising and begins to fall, note the maximum reading
- Record Hs (the maximum sextant altitude)
Calculating Latitude from the Noon Sight
After recording Hs at maximum altitude, apply corrections to get Ho:
- Apply IE (add or subtract)
- Apply dip (always subtract)
- Apply sun altitude correction from Nautical Almanac (refraction plus SD for lower limb)
- Result is Ho (observed altitude at meridian passage)
Then compute zenith distance: ZD equals 90 degrees minus Ho.
Latitude calculation depends on which hemisphere the sun is in relative to the observer. Find the sun's declination from the Nautical Almanac for the time of LAN:
Sun south of observer (bearing 180): L = ZD + Dec (N) or L = ZD - Dec (S)
Sun north of observer (bearing 000): L = Dec (N) - ZD or L = ZD - Dec (N)
Same name: add. Contrary name: subtract. Label result N or S based on which is larger.
8. Morning and Evening Star Sights
Twilight star sights provide the best opportunity for a multi-body fix because both stars and the horizon are simultaneously visible. The USCG exam tests star sight procedure, twilight timing, and star identification.
Types of Twilight
Civil Twilight
Sun is 0 to 6 degrees below horizon. Horizon is clearly visible; only the brightest stars and planets are visible. Good for observing Venus, Jupiter, and first-magnitude stars like Sirius or Arcturus.
Nautical Twilight
Sun is 6 to 12 degrees below horizon. This is the prime window for celestial navigation — the sea horizon is still visible and many navigational stars are bright enough to identify. The Nautical Almanac tabulates the time of nautical twilight for every day.
Astronomical Twilight
Sun is 12 to 18 degrees below horizon. All but the faintest stars are visible, but the horizon is usually too dark for reliable sextant sights.
Evening Star Sight Procedure
- Before evening twilight, compute predicted altitudes and azimuths for target stars using the DR position and HO 249 Volume I (or a star finder)
- Identify three or more stars well separated in azimuth — ideally 120 degrees apart
- As stars appear, shoot the brightest first (horizon still clearest)
- Record exact GMT for each sight
- Take three or more sights per star if time permits; average the readings
- Reduce each sight through the full procedure: IE, dip, star correction, GHA Aries plus SHA for GHA star, LHA, enter HO 229 or HO 249, compute Hc and Zn, intercept, plot LOP
- Plot all LOPs; the cocked hat (triangle) identifies the fix
Key Navigational Stars for USCG Exam
- Polaris — within 1 degree of North Pole; altitude approximates latitude
- Sirius — brightest star in the sky; Canis Major; brilliant blue-white; winter sky
- Canopus — second brightest; southern sky; Carina; useful south of equator
- Arcturus — bright orange-red; Bootes; found by arcing from the Big Dipper handle
- Vega — bright blue-white; Lyra; summer sky; one of the Summer Triangle stars
- Capella — bright yellow; Auriga; near the zenith in winter from mid-latitudes
- Rigel — blue-white; foot of Orion; southeastern sky in winter
- Betelgeuse — red giant; Orion's shoulder; unmistakable orange-red color
- Aldebaran — red-orange; Taurus; the Eye of the Bull; winter sky
- Spica — blue-white; Virgo; found by "arc to Arcturus, spike to Spica" from Big Dipper
- Antares — deep red; Scorpius; summer sky; often mistaken for Mars
- Deneb — white; Cygnus (Northern Cross); Summer Triangle; circumpolar at many US latitudes
9. Polaris Sight for Latitude
Polaris is unique among navigational stars because its altitude above the horizon directly approximates the observer's latitude in the Northern Hemisphere. It is a routine and efficient way to get latitude without solving the full PZX triangle.
Polaris Sight Procedure
- Observe Polaris during nautical twilight when both star and horizon are visible
- Apply IE and dip to get apparent altitude Ha
- Apply star altitude correction (refraction only, from inside front cover of Nautical Almanac) to get Ho
- Record GMT of the observation
- From the Nautical Almanac, find GHA Aries for the date and time
- Compute LHA Aries: GHA Aries plus east longitude (or minus west longitude)
- Enter the Polaris Tables in the back of the Nautical Almanac using LHA Aries
- Extract corrections a0, a1, and a2
- Apply the formula: Latitude equals Ho minus 1 degree plus a0 plus a1 plus a2
The Polaris Correction Formula
L = Ho - 1° + a0 + a1 + a2
a0 is the largest correction (up to about 1 degree); a1 corrects for observer latitude; a2 corrects for date. All corrections come directly from the Polaris Tables.
Polaris's angular distance from the exact celestial North Pole (currently about 0.7 degrees and slowly decreasing) is the reason for the corrections. Without the corrections, Ho equals latitude only when Polaris is exactly on the meridian. The a0, a1, and a2 corrections account for all positions of Polaris in its small circle around the pole.
10. Compass Error by Amplitude and Azimuth
USCG regulations require vessels to check compass error regularly. Two celestial methods are commonly tested: amplitude (at sunrise or sunset) and azimuth (any time a body is visible).
Compass Error by Amplitude
Amplitude is the bearing arc from east or west to the rising or setting body. It is usable only at the moment of rise or set when the body is on the visible horizon (altitude is zero, or technically about 0 degrees 34 arc minutes for refraction-on-horizon correction).
The formula: sin(Amplitude) equals sin(Declination) divided by cos(Latitude). Amplitude tables in Bowditch or HO 229 provide the solution without calculation.
Naming the amplitude bearing: prefix E (for rising) or W (for setting). Suffix N or S to match the body's declination. Example: a rising sun with N 20 degrees declination at latitude 30 N gives amplitude E 23 N, which converts to true bearing N 67 E (090 minus 23 equals 067 true, measured from north).
Compass error equals true bearing minus compass bearing of the body at the horizon. Apply variation to find deviation if needed.
Compass Error by Azimuth
Azimuth check is more flexible than amplitude because it works any time a celestial body is visible — not just at the horizon. It is the more commonly tested USCG method.
- Record the exact GMT when the bearing is taken
- Extract GHA and declination from the Nautical Almanac
- Choose assumed longitude to make LHA a whole number; compute LHA
- Enter HO 229 with assumed latitude, LHA, and declination to find azimuth angle Z
- Convert Z to true azimuth Zn using the naming convention on the table page
- Read the compass bearing of the same body at that moment
- Compass error (CE) equals Zn minus compass bearing
- Positive CE is easterly (compass reads less than true); negative is westerly
Compass Error, Variation, and Deviation
Total compass error (CE) equals the algebraic sum of variation (V) and deviation (D). Once CE is determined by celestial observation, deviation for the current heading can be calculated if variation for the area is known:
CE = V + D
D = CE - V
East errors are positive, west errors are negative. A compass reading 5 degrees less than true has 5 degrees east error.
11. Running Fix from a Single Celestial Body
When only one celestial body is available (typically the sun during daylight), a running fix allows a position to be determined by advancing an earlier LOP to the time of a later observation.
Running Fix Procedure
- Take the first sun sight; reduce it to Ho; plot the first LOP from AP1
- Note the time and record the vessel's course and speed
- Continue on course; after a suitable interval (commonly 3 to 6 hours), take the second sight
- Reduce the second sight; plot the second LOP from AP2
- Advance the first LOP: calculate the distance run between sights (speed times time in hours). Move every point on the first LOP in the direction of the vessel's course by that distance
- Label the advanced LOP with the time of the first sight and the time it was advanced to
- The intersection of the advanced first LOP and the second LOP is the running fix
- Label the fix with the time of the second sight
Classic Sun-Run-Sun Fix
Morning sun sight yields a bearing-line LOP. The vessel runs a known track. At noon, a noon sight yields a latitude LOP. The morning LOP advanced to noon crosses the noon latitude LOP for the running fix. This is the most traditional form of the running fix and is heavily tested on the USCG Master exam.
Accuracy warning: The running fix assumes the vessel followed the plotted course and speed exactly. Currents, leeway, and speed variations all degrade the fix. The longer the interval between sights, the greater the potential error. Always annotate the running fix on the chart to indicate it is a running fix, not a simultaneous fix.
12. Using the Nautical Almanac
The Nautical Almanac (published jointly by HM Nautical Almanac Office and the US Naval Observatory) is the primary reference for all celestial navigation. It provides GHA and declination for every celestial body used in navigation.
Daily Pages
Each daily page (actually two pages covering three days) contains:
- Sun column: GHA and declination for each whole hour of GMT, plus the d value (declination change per hour) and the SD (semi-diameter in arc minutes)
- Moon columns: GHA, v (GHA change correction), declination, d, HP (horizontal parallax), SD — all updated hourly
- Planet columns: GHA and declination for Venus, Mars, Jupiter, Saturn (noted at the top if visible)
- Star column: SHA and declination for the 57 selected stars (these do not change significantly from day to day; one column per three-day spread)
- Bottom of page: sunrise, sunset, twilight times; moonrise, moonset; meridian passage for sun and planets
Increments and Corrections (Colored Pages)
These pages cover the change in GHA for minutes and seconds of time beyond the whole hour. Each page covers 2 minutes of time. Within each page:
- The first column (SUN/PLANETS) gives the GHA increment for the sun and planets for each second
- The second column (ARIES) gives the increment for Aries
- The third column (MOON) gives the increment for the moon (moves slower than the sun)
- The v or d correction columns give the correction to apply for bodies with a non-standard rate of change
- These corrections are always added for v (using the tabulated v value); for d, add or subtract depending on whether declination is increasing or decreasing
Altitude Correction Tables (Inside Front Cover)
The inside front cover of the Nautical Almanac provides all the main altitude corrections:
Dip Table
Enter with height of eye in feet or meters. Read dip correction (always negative). For 9 ft height of eye, dip is approximately minus 2.9 arc minutes.
Sun Altitude Correction
Enter with apparent altitude. Provides combined refraction plus SD correction. Separate columns for lower limb (October through March and April through September account for varying SD) and upper limb.
Stars and Planets Correction
Enter with apparent altitude. Provides refraction correction only (stars are point sources). Values range from minus 34 arc minutes at 0 degrees altitude to minus 0.2 arc minutes near 90 degrees.
13. Common USCG Exam Question Patterns
Understanding the types of questions the USCG exam asks lets you drill exactly what will be tested. Celestial navigation questions on the Master 100 GRT exam follow predictable patterns.
Pattern 1: GHA and LHA Computation
The exam provides a date, GMT, and longitude. You extract GHA from the Nautical Almanac (tabulated GHA plus increments from the colored pages) and compute LHA. Common trap: forgetting to add the increment for minutes and seconds, or confusing east and west longitude signs.
Practice: extract GHA for the sun, moon, a named star, and a planet. The process differs slightly for each. Stars use GHA Aries plus SHA; the moon needs v correction; planets need v correction.
Pattern 2: Altitude Correction
Given Hs, height of eye, body name, limb observed (for sun), and IE, compute Ho. Identify each correction, its sign, and its source in the almanac. The exam tests that you know dip is always subtracted, which corrections apply to stars versus sun versus moon, and the on-the-arc / off-the-arc IE rule.
Common trap: applying SD when observing a star (no SD for stars), or applying dip with the wrong sign.
Pattern 3: Intercept and Azimuth
Given Ho, assumed latitude, LHA, and declination, enter HO 229 to find Hc and Z. Apply the d correction. Compute intercept a equals Ho minus Hc. Convert Z to Zn. State whether to plot toward or away.
Common trap: wrong azimuth naming (forgetting to use the rule on the page versus applying a rule from memory that belongs to a different quadrant).
Pattern 4: Noon Sight Latitude
Given Hs at meridian passage, IE, height of eye, and date, compute Ho and then latitude. Requires extracting declination from the almanac and applying the same-name / contrary-name rule.
Common trap: sign error on the latitude formula when declination and observer are in the same hemisphere versus opposite hemispheres.
Pattern 5: Compass Error by Amplitude or Azimuth
Amplitude: given declination and latitude, find true amplitude bearing, compare to compass bearing, state compass error. Azimuth: given LHA, declination, latitude, enter HO 229 to find Zn, compare to compass bearing, state error.
Common trap: naming errors (east vs. west error, which direction to apply correction to compass to get true).
Pattern 6: Polaris Latitude
Given Hs of Polaris, IE, height of eye, GMT, and longitude, compute Ho, find LHA Aries, enter Polaris Tables, apply a0/a1/a2, compute latitude.
Common trap: forgetting to subtract 1 degree in the formula (Ho minus 1 degree plus corrections), or using GHA Aries plus west longitude instead of minus west longitude.
Frequently Asked Questions
What is the most important thing to get right in every celestial sight reduction?
Accurate GMT. Every celestial sight is tied to a precise time because GHA — and therefore LHA and the entire geometry — depends on the earth's rotational position at the moment of observation. A one-second timing error creates a position error of roughly 0.25 nautical miles. Use a marine chronometer set to UTC and verify it against a time signal regularly. Record GMT immediately at the mark — never try to reconstruct it from memory afterward.
Can you use a calculator instead of HO 229 or HO 249 on the USCG exam?
The USCG exam is a written test; tables are provided or referenced. In practical navigation aboard a vessel, calculators and dedicated navigation software are widely used and accepted. The STCW competency framework requires understanding the principles behind sight reduction, not manual table-entry speed. However, the exam itself tests table use, so candidates must understand how to enter and read HO 229 and HO 249.
Why do you need an assumed position rather than using the DR position?
HO 229 and HO 249 require whole-degree arguments for latitude and LHA. The DR position rarely falls on whole degrees of latitude or produces a whole-degree LHA. The assumed position (AP) is a computed position near the DR that satisfies the whole-degree requirements, keeping table entry errors to zero. The AP is abandoned after the sight is plotted — it is a computational convenience, not a navigational position.
What does it mean when three star LOPs form a large cocked hat triangle?
A large cocked hat (the triangle formed by three intersecting LOPs) indicates accumulated errors. Possible causes: a timing error on one sight, a Nautical Almanac extraction error, a sextant reading error (misread arc or micrometer), or an error in GHA, LHA, or assumed position computation. Standard practice is to assume the vessel is at the corner of the triangle nearest danger. To improve the fix: re-check all computations, look for a consistent error in one body's sight, and if possible take additional sights of different stars.
What is the difference between a meridian passage and local apparent noon?
They are the same event: local apparent noon (LAN) is the moment the sun crosses the observer's meridian (meridian passage). The Nautical Almanac lists the time of meridian passage at Greenwich (Mer. Pass.) for each day. To predict LAN at another longitude, apply the 4-minute-per-degree longitude correction. The sun moves westward at 1 degree per 4 minutes, so for each degree of west longitude, add 4 minutes to the Greenwich meridian passage time; for east longitude, subtract.
Practice Celestial Navigation Questions
NailTheTest includes practice questions covering sight reduction, altitude corrections, GHA/LHA computation, compass error, noon sight, and Polaris. Each question includes a detailed explanation of the solving process.
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