Master the sextant, Nautical Almanac, HO 229 and HO 249 sight reduction, the intercept method, noon sights, star identification, and compass error by celestial observation. Everything tested on the USCG celestial navigation exam -- with full worked examples.
GPS has transformed navigation -- but the USCG still tests celestial for good reason. Ocean passages require the ability to navigate when electronics fail. Here is what you need to know.
USCG Master licenses with ocean or offshore endorsements require demonstrated celestial navigation competency. The STCW convention (Standards of Training, Certification and Watchkeeping) mandates celestial navigation for officers on ocean-going vessels. Near-coastal OUPV and near-coastal 100-ton Master licenses do not require celestial -- but ocean-endorsed Master 100, 200, 500, and 1600 GT all include celestial navigation questions.
GPS can fail from equipment malfunction, signal jamming, spoofing, or solar weather events. On an ocean passage, a celestial fix is the definitive backup. Professional mariners use celestial observations to verify GPS accuracy -- a noon sight or three-star fix that agrees with GPS to within a few miles confirms the electronics are working correctly. The USCG takes this seriously because lives depend on it.
Celestial observation is the gold standard for determining compass error. Taking the azimuth of the sun at known time and comparing it to the compass bearing gives total compass error (deviation plus variation). This cannot be done accurately with GPS alone. A compass with undetected 10-degree error on an ocean passage compounds into dangerous positional errors. The amplitude method at sunrise or sunset is the simplest celestial compass check.
The USCG celestial exam covers these categories. Each question type requires a specific skill set. Know where to spend your study time.
ZT to UT, zone description, date change, chronometer error. All sight reduction starts here.
Reading Almanac daily pages, applying increments and corrections (yellow pages), v and d corrections.
Choosing assumed latitude and longitude to produce whole-degree LHA. The gate to table entry.
Same/contrary name, d-correction interpolation, azimuth angle conversion to Zn.
IE, dip, main correction table. Sun lower vs. upper limb. Moon parallax and HP.
Computing intercept, HoMoTo rule, drawing the LOP perpendicular to azimuth on a plotting sheet.
Predicting LAN time, meridian altitude procedure, latitude computation -- no tables required.
Recognizing Polaris, first-magnitude stars, using star finder (2102-D), SHA and GHA Aries.
Correcting Polaris altitude for a0, a1, a2 corrections from the Almanac to find latitude.
Computing Zn from tables, comparing to compass bearing, stating error as E or W.
Amplitude formula, true bearing at sunrise/sunset, compass error from observed bearing.
Advancing an LOP, cocked hat resolution, error triangle analysis.
Celestial navigation is built on a geometric model: the celestial sphere. Every body -- sun, moon, planets, stars -- is projected onto this imaginary sphere centered on the Earth. Mastering this vocabulary is the foundation of everything else.
The projection of Earth's geographic equator outward onto the celestial sphere. Divides the sphere into northern and southern celestial hemispheres. Declination is measured north or south from this line.
Bodies on the celestial equator have zero declination. The sun crosses the celestial equator at the equinoxes.
The apparent annual path of the sun against the background stars, tilted 23.5 degrees relative to the celestial equator. All planets and the moon follow paths near the ecliptic.
The ecliptic crosses the celestial equator at the vernal equinox (Aries, symbol Ram) and autumnal equinox. Maximum solar declination is plus or minus 23.5 degrees.
A great circle on the celestial sphere passing through both celestial poles and through a celestial body. Analogous to a meridian on Earth. GHA and SHA are measured along the celestial equator between hour circles.
The Greenwich Hour Circle passes through the vernal equinox. All hour angles are measured westward from a reference hour circle.
Angular distance of a body north or south of the celestial equator, measured along the body's hour circle. Ranges from 0 to 90 degrees, labeled N or S. The celestial equivalent of latitude.
Declination is extracted from the Nautical Almanac daily pages. Same-name declination (same as latitude) means the body is on the same side of the equator as the observer.
Angular distance measured westward from the Greenwich meridian to the body's hour circle, from 0 to 360 degrees. Changes continuously as the Earth rotates. Listed in the Almanac for each whole hour of UT.
GHA plus east longitude (or minus west longitude) gives LHA. LHA must be a whole degree when using HO 229 or 249 -- this determines the assumed longitude.
For stars only: the angular distance measured westward from the vernal equinox (Aries) to the star's hour circle. SHA does not change from year to year (stars are essentially fixed). GHA of star equals GHA Aries plus SHA of star.
SHA is listed in the Nautical Almanac star tables. Add SHA to GHA Aries (for the time of observation) to get the star's GHA.
Angular distance measured westward from the observer's meridian to the body's hour circle. LHA equals GHA plus east longitude, or GHA minus west longitude. Entry argument for sight reduction tables.
LHA must be a whole degree for table entry. Adjust assumed longitude to achieve a whole-degree LHA. If LHA is greater than 360, subtract 360.
The sextant measures the angle between a celestial body and the visible horizon with arc-minute precision. Understanding its parts and adjustments is tested on the USCG exam.
The graduated curved scale, typically marked from minus 5 to plus 120 degrees. The main scale for reading altitude in whole degrees.
Off the arc means a negative reading (arc error check only). On the arc means positive altitude.
A fully silvered mirror mounted on the index arm, pivoting with the arm. Reflects the image of the celestial body toward the horizon glass.
Must be perpendicular to the frame. Error (side error) is checked by viewing the horizon while rotating the drum.
A half-silvered mirror fixed to the frame. The silvered half reflects the body image; the clear half allows a direct view of the horizon. Both images are superimposed.
The horizon glass must be perpendicular to the frame and parallel to the index mirror when IE equals zero.
Magnifies the view for precise alignment of the body's image on the horizon. A 4x40 telescope is common for star sights; 7x35 or lower magnification for rough seas.
Use lowest practical magnification in rough conditions -- a wider field of view makes it easier to find and hold the body.
Tinted glass filters in front of the index mirror and horizon glass. Multiple densities available. Essential for sun and moon sights to prevent eye damage and reduce glare.
For sun lower limb, use index shades. For bright horizon, also use horizon shades. Never view the sun without shades.
The fine adjustment scale, typically reading arc minutes and tenths (0.1') using a micrometer drum, or arc minutes and fractions using a vernier scale.
Read the whole degrees from the arc first, then add the micrometer drum reading for minutes and tenths.
Clamp fixes the index arm at a rough setting; the tangent screw provides fine adjustment for precise altitude measurement.
Rough altitude pre-set: clamp near expected altitude, then fine-tune with the tangent screw while rocking the sextant.
Set arc to about 35 degrees. Hold sextant horizontally and look into the index mirror. The arc and its reflection should form a straight, unbroken line. If not, adjust the index mirror's perpendicularity screw.
Set sextant to zero. Look at the horizon. If the direct and reflected images are side by side (not aligned), side error exists. Adjust the side error screw on the horizon glass until both images are in the same plane.
Set sextant to zero. View the horizon. If the direct and reflected horizons are not aligned (one above the other), rock the drum until they align -- the reading is the index error. Memory: On the arc, subtract (off it goes). Off the arc, add (on it goes).
Non-uniform thickness in the shade glasses causes the light path to deviate. Tested by comparing sights with and without shades. Cannot be adjusted in the field -- send to manufacturer.
Error in the arc graduation itself. Detected by comparing against a known standard or by comparing multiple arc positions. A certificate of error from the manufacturer lists corrections for each degree of arc.
The pivot point of the index arm is not exactly at the center of the arc radius. Varies across the arc -- most significant near 0 and 120 degrees. Included in the manufacturer's certificate.
The sextant altitude (hs) must be corrected for several systematic errors before it becomes the Observed Altitude (Ho) used in the intercept calculation. Apply corrections in strict order.
| Correction | Symbol | Source | Sign | Applies To | Note |
|---|---|---|---|---|---|
| Index Error (IE) | IE | Read off the arc: subtract. Off the arc: add. (On subtract, Off add) | Depends on position of IE | All bodies | Determined by observer before each sight session. Check both the horizon and the star. |
| Dip | D | Nautical Almanac inside front cover, dip table. Argument: height of eye in feet or meters. | Always subtract | All bodies (not when using artificial horizon) | Higher eye height means greater dip correction. Dip accounts for the visible horizon being below the true horizon. |
| Refraction | R | Built into the altitude correction tables in the Almanac. Always present. | Always subtract (apparent altitude is too high due to refraction bending light toward Earth) | All bodies | Largest for low altitude bodies (below 10 degrees). USCG exam often warns: avoid sights below 10 degrees altitude. |
| Semi-Diameter (SD) | SD | Listed on daily pages of the Nautical Almanac. Varies slightly with Earth-sun distance. | Add for lower limb; subtract for upper limb | Sun and Moon only | We shoot the lower limb (bottom edge) of the sun and add SD to get the sun's center altitude. |
| Augmentation (Moon) | Aug | Included in the moon altitude correction table in the Almanac. | Small addition for moon at high altitude | Moon only | The moon is close enough that its semi-diameter appears slightly larger when it is higher in the sky. |
| Parallax in Altitude (HP) | HP | Moon HP listed on daily pages. Correction from inside cover moon correction table. | Always add | Moon (significant). Sun (tiny -- included in tables). | Parallax is the difference between the geocentric and topocentric positions. Very significant for the moon due to its proximity. |
The USCG exam frequently tests whether candidates apply corrections in the correct order. The sequence is always: (1) IE applied to hs, (2) Dip applied to get apparent altitude (Ha), (3) Main correction table entry with Ha to get Ho. For the moon, additional HP correction is applied. Never skip dip -- it is always subtracted from hs before entering the main correction table.
The Nautical Almanac, published annually by the U.S. Naval Observatory and H.M. Nautical Almanac Office, tabulates the positions of celestial bodies for every hour of the year in Universal Time.
The daily pages cover three days per spread and list, for each hour of UT:
The yellow pages tabulate the additional GHA for minutes and seconds of UT between the hourly tabulations:
The Nautical Almanac lists the 57 selected navigational stars with their SHA and declination for each month of the year. SHA changes very slowly (fractions of an arc minute per year due to precession). To find a star's GHA: GHA star equals GHA Aries (for the UT of sight, from daily pages plus increment) plus SHA of the star. If the result exceeds 360 degrees, subtract 360.
The Star Finder (Pub. No. 2102-D) is a circular star chart with a transparent overlay for each 10-degree latitude band. Set GHA Aries on the base plate, then overlay the correct latitude template. Stars appearing above the horizon overlay are visible at that time and latitude. The star finder gives approximate altitude and azimuth for planning and identifying stars during twilight -- the brief window when both stars and the horizon are visible for sextant work.
Sight reduction is the process of converting a sextant observation into a Line of Position (LOP). Every celestial navigation problem on the USCG exam follows this sequence.
Note the sextant altitude (hs) in degrees, minutes, and tenths. Record the exact time (UTC/UT) to the nearest second. Record the DR position at the time of sight.
Apply altitude corrections in order: (1) IE, (2) Dip (get apparent altitude Ha), (3) main correction table (refraction + SD for sun). Result is Observed Altitude (Ho).
From the daily pages, extract GHA and declination for the whole hour of UT. From the increments and corrections (yellow pages), find the additional GHA for the minutes and seconds of UT. Add to get total GHA.
Choose an assumed latitude (whole degree nearest DR latitude). Choose an assumed longitude that makes LHA a whole number of degrees. LHA equals GHA minus assumed west longitude (or plus assumed east longitude).
Enter with assumed latitude (whole degree), LHA (whole degree), and declination (degrees). Read tabulated Hc and azimuth angle (Z). Apply d-correction for declination minutes using interpolation table.
In HO 229, the azimuth angle Z must be converted to true azimuth Zn using the rules: LHA greater than 180 degrees (Zn equals Z); LHA less than 180 degrees (Zn equals 360 minus Z) for northern latitude. For southern latitude the rules are reversed.
Intercept a equals Ho minus Hc, expressed in nautical miles (1 minute of arc equals 1 nautical mile). If Ho greater than Hc, the intercept is toward (T). If Ho less than Hc, the intercept is away (A).
From the assumed position, draw a line in the direction of Zn (toward or away). Measure the intercept distance along that line. At that point, draw a perpendicular line -- that is the Line of Position (LOP).
Both publications solve the navigational triangle. The USCG exam specifies which to use. Know the differences.
Both publications solve the same spherical triangle formed by three points on the celestial sphere: the celestial pole (P), the observer's zenith (Z), and the celestial body (X). The three sides of this triangle are the co-latitude (90 degrees minus latitude), the polar distance (90 degrees minus declination), and the co-altitude (90 degrees minus altitude). The three angles include the azimuth angle at the zenith. Given assumed latitude, LHA, and declination (the three inputs), the tables solve for Hc and azimuth angle Z. This is why all three arguments must be whole degrees -- the tables are pre-computed at integer values.
The noon sight is the simplest and most traditional celestial observation. At Local Apparent Noon (LAN), the sun crosses the observer's meridian and reaches its highest point in the sky. No tables, no LHA, no assumed position required -- just the corrected altitude and the Almanac declination.
LAN time in UT equals 12h 00m plus the Equation of Time (from Almanac daily pages, bottom) plus or minus the longitude correction (longitude in degrees divided by 15 equals hours; multiply minutes of longitude by 4 to get time correction in minutes). For a vessel moving east, LAN arrives earlier; moving west, later. Apply the DR longitude correction to get the approximate LAN time 30 minutes before noon to begin watching the sun.
Begin observing about 15 minutes before predicted LAN. Watch the sun's altitude increase slowly, then hang (appear stationary) as it transits, then begin to decrease. Record the maximum altitude -- the moment it stops rising. This is the meridian altitude. The sun need not be exactly south (or north) -- it is the altitude maximum that defines LAN. Apply all altitude corrections (IE, dip, main correction) to get Ho.
Zenith distance equals 90 degrees minus Ho. The zenith distance is always named opposite to the direction the sun is from the observer (sun to south of observer means ZD is named N). Latitude equals Zenith Distance plus Declination (same name) or Zenith Distance minus Declination (contrary name). The name of the answer equals the name of the larger value when contrary.
The USCG exam tests identification of navigational stars and the use of Polaris for latitude. Twilight -- the brief period when both stars and the horizon are visible -- is the prime time for star sights.
Practically at the north celestial pole. Located by following the pointer stars of the Big Dipper outward about 5 times their separation.
Latitude from altitude: Ho of Polaris approximately equals latitude (corrections from p, q tables in Almanac give exact latitude). Extremely valuable for latitude without a full sight reduction.
USCG exam: latitude from Polaris sight. Polaris corrections (a0, a1, a2) are in the Almanac. Polaris azimuth is within 2 degrees of true north -- useful for compass check.
One of the brightest stars in the northern sky. Part of the Summer Triangle with Deneb and Altair. High declination: plus 38.8 degrees N.
Good first magnitude star for evening sights in summer/fall. High declination makes it excellent for observers in mid-northern latitudes.
One of the 57 navigational stars. Know it as bright northern star in summer. SHA approximately 080 degrees.
Brilliant orange-yellow giant, brightest star in the northern celestial hemisphere. Follow the arc of the Big Dipper handle to Arcturus.
First choice for evening star sights in spring and early summer. Declination: plus 19.2 degrees N -- favorable for mid-latitude observers.
Second brightest star visible from most of the northern hemisphere. SHA approximately 146 degrees.
Brightest star in the night sky. Low southern declination (minus 16.7 degrees). Visible in winter evenings; rises in the southeast for northern observers.
Excellent for winter star sights. Easy to identify by its brightness. Often visible near the horizon for observers in the northern hemisphere.
Brightest navigational star. Winter star -- available January through March for northern hemisphere observers. SHA approximately 259 degrees.
The point on the celestial equator where the ecliptic crosses moving northward. The reference point for measuring SHA and GHA Aries.
GHA Aries is the basis for all star GHA computations. GHA star equals GHA Aries plus SHA star. Aries' position changes with the precession of equinoxes over centuries.
Aries is not a visible star -- it is a reference point (symbol of a Ram). GHA Aries is listed in the Almanac and increases approximately 15 degrees per hour as Earth rotates.
Polaris is approximately 0.75 degrees from the true north celestial pole, meaning its altitude is almost (but not exactly) equal to the observer's latitude. The Nautical Almanac Polaris tables (inside the back of the almanac) provide three small corrections -- a0, a1, and a2 -- that account for Polaris's offset from the pole. These corrections depend on LHA Aries, latitude band, and month.
Where Ho is the fully corrected observed altitude of Polaris.
a0 depends on LHA Aries (look up in Almanac Polaris table, column for minutes of LHA Aries).
a1 depends on the latitude band (use the row for your approximate latitude).
a2 depends on the month of the year.
The result is latitude North (Polaris is only visible from the northern hemisphere above about 5 degrees N latitude).
Two celestial methods for determining compass error appear on the USCG exam: the azimuth method (any time of day) and the amplitude method (at sunrise or sunset only). Both compare a computed true bearing to the observed compass bearing.
The azimuth of the sun (or any body) can be computed at any time of day using sight reduction tables. Take a compass bearing of the sun with a pelorus or azimuth ring. Simultaneously reduce a sight to get the true azimuth Zn. Total compass error equals Zn (true) minus compass bearing.
Amplitude is used at the instant of sunrise or sunset, when the sun's center is on the celestial horizon (approximately one sun diameter above the visible horizon, corrected for refraction). The amplitude formula gives the angular distance from East/West toward North/South.
All celestial navigation computations begin with time. Converting from Zone Time to Universal Time correctly is the gateway to every other calculation. Time errors cause position errors: 4 seconds of time equals approximately 1 nautical mile at the equator.
The international time standard used in celestial navigation. Based on the Greenwich meridian. Formerly called Greenwich Mean Time (GMT). The Nautical Almanac tabulates all data in UT.
All sight reduction begins with UT. Convert local time to UT before extracting Almanac data.
Ship in ZD plus 5 (Eastern Standard Time zone): ZT 0900 plus 5h equals UT 1400.
The local standard time kept aboard ship. Based on the time zone the ship is operating in. Zone Description (ZD) is the number of hours to add to ZT to get UT.
For west longitudes: ZD is positive (add ZD to ZT for UT). For east longitudes: ZD is negative (subtract ZD from ZT for UT).
ZT 22h 30m in ZD plus 5: UT equals 22h 30m plus 5h equals 27h 30m. Subtract 24h: UT 03h 30m next day.
The number of whole hours difference between Zone Time and Universal Time. Equals the longitude divided by 15, rounded to the nearest whole number.
West longitude zones have positive ZD (add to ZT for UT). East longitude zones have negative ZD (subtract from ZT for UT).
Ship at 082 degrees W longitude: 82 divided by 15 equals 5.47, rounds to 5. ZD equals plus 5 (Central Standard Time area).
The difference between the chronometer or watch time and the correct UT. If the watch is fast, subtract the error. If slow, add it.
Chronometer error is applied to the chronometer reading to get correct UT. Fast minus. Slow plus.
Chronometer reads 14h 22m 18s. Chronometer error: 2m 14s slow. Correct UT equals 14h 22m 18s plus 0h 02m 14s equals 14h 24m 32s.
Work through these problems in order. Each builds on skills from earlier problems. The USCG exam gives similar problem types with different numbers.
Find the Observed Altitude (Ho).
The USCG exam provides altitude correction tables. Know the order: IE, then dip (gives Ha), then main correction table. Always identify lower or upper limb before looking up correction.
Find total GHA and assumed longitude that gives whole-degree LHA. State the LHA.
The trick: set assumed longitude minutes equal to GHA minutes so they cancel out, giving a whole-degree LHA. Assumed latitude is the whole degree nearest DR latitude.
Find the intercept distance, direction, and describe how to plot the LOP.
HoMoTo: Ho More, Toward. A 1-minute difference equals 1 nautical mile. The LOP extends in both directions from the intercept point, perpendicular to the azimuth.
Find the observer's latitude.
Rules: same name (N-N or S-S) -- add ZD and declination. Contrary name -- subtract smaller from larger, name of the larger. The noon sight requires no assumed position, no tables, and no LHA.
Find the true amplitude, true bearing of the sun at sunrise, and the compass error.
Amplitude is always measured from East (at sunrise) or West (at sunset) toward North or South. If declination is N at sunrise, the bearing is north of east, meaning less than 090 degrees true. If declination S at sunrise, bearing is south of east, greater than 090 degrees true.
Find the Universal Time (UT) and the UT date.
Zone Description is the number of whole hours you add to Zone Time to get UT (for west longitudes). Zone Description for a given longitude: ZD equals longitude divided by 15, rounded to the nearest whole number. West longitudes have positive ZD -- add to ZT to get UT. If UT exceeds 24h, subtract 24h and advance the date by one day.
A single celestial LOP tells you only that you are somewhere on that line. Combining multiple LOPs -- from different bodies or by advancing an earlier LOP -- gives a fix with a defined position.
When only one body is available, take two sights separated by time (at least 30 minutes for good angle change). After the second sight is plotted, advance the first LOP by the vessel's run (distance and direction traveled between sights). The intersection of the advanced LOP with the second LOP is the running fix. The running fix is only as accurate as the course and speed used to advance the LOP.
Move every point on the LOP by the vessel's run vector (same distance, same direction). The advanced LOP is parallel to the original and labeled with both times.
The ideal celestial fix uses three bodies (typically stars at twilight) with azimuths approximately 120 degrees apart (for best geometry). Three LOPs plotted from three simultaneous (or nearly simultaneous) sights form a triangle -- the cocked hat. The observer's position lies within or near the cocked hat.
Choose stars with altitudes between 20 and 65 degrees (low altitude increases refraction error; high altitude reduces azimuth angle spread). Plan star sights before twilight using the star finder -- you have only about 20 minutes of useful twilight.
Three perfectly determined LOPs meet at a single point. In practice they form a triangle (cocked hat) due to errors in observation, timing, and computation. Assume the position is at the center of the cocked hat unless there is a navigational hazard within the triangle -- in that case, assume the worst-case vertex (closest to the danger) for safety.
A small cocked hat (under 2 nm on each side) indicates good observation technique. A large cocked hat suggests timing error, IE error, or plotting error -- recheck your work before accepting the fix.
4 seconds of time error equals 1 nautical mile of position error at the equator. On the USCG exam, read and apply time very carefully. Always convert ZT to UT before extracting Almanac data. Check for date change when adding ZD pushes the UT past midnight.
The USCG exam provides blank sight reduction worksheets. Use them. Work top to bottom: time conversion, GHA extraction, assumed position, LHA, table entry, intercept. Do not skip steps or work from memory -- errors cascade.
If the observed altitude (Ho) is greater than the computed altitude (Hc), the intercept is toward the body's geographic position. If Ho is less, plot away. This mnemonic is tested directly: which direction do you plot an intercept of plus 8.4 miles?
The azimuth angle Z from HO 229 must be converted to true azimuth Zn. The rule depends on whether LHA is greater or less than 180 degrees and on which hemisphere you are in. Write the conversion formula at the top of your worksheet and apply it every time.
Refraction error is largest below 10 degrees altitude and becomes unpredictable below 5 degrees. The USCG exam may present a sight with a very low body and ask whether the correction is reliable. The answer: unreliable below 10 degrees. Plan sights between 15 and 65 degrees for best accuracy.
You have about 20 minutes of useful twilight (nautical or civil, depending on latitude and season). Use the star finder beforehand to identify which stars will be available, their approximate altitudes and azimuths, and set your sextant to those altitudes before twilight begins. Pre-plotting is essential.
The moon requires additional corrections: HP (horizontal parallax from the daily pages) and augmentation. The moon altitude correction table has separate columns for upper and lower limb. The moon's orbit is irregular, requiring both v and d corrections from the increments pages. Take extra care on moon sight problems.
In HO 229, same name (declination and latitude on same side of equator) and contrary name have different pages. Opening the wrong page gives a completely wrong Hc. Check this every single time. Same name: Sun is on same side of equator as you. Contrary name: opposite sides.
Common questions from candidates preparing for the USCG celestial navigation exam.
Celestial navigation is required for USCG Master licenses with an ocean or offshore endorsement. The OUPV (six-pack) license for near-coastal or inland routes does not require celestial. Master 100-ton near-coastal, Master 200-ton, and all ocean-endorsed Master licenses include celestial navigation questions on the USCG written exam. Topics include sextant use, sight reduction with HO 229 or HO 249, Nautical Almanac use, the intercept method, noon sight, star identification, and compass error by celestial observation.
The intercept method (Marcq St-Hilaire method) compares the computed altitude (Hc) from sight reduction tables with the observed altitude (Ho) from the sextant. The difference (Ho minus Hc) is the intercept distance in nautical miles. If Ho is greater than Hc, the intercept is plotted toward the celestial body's geographic position (GP) — remembered as 'Coast Guard Towards' or HoMoTo (Ho More Toward). If Ho is less than Hc, it is plotted away. The intercept is plotted from the assumed position along the azimuth bearing, and a line of position (LOP) is drawn perpendicular to the azimuth at that point.
Index error (IE) is the difference in reading when a sextant is set to zero and the horizon is observed — the horizon should appear as a single unbroken line through the index mirror and horizon glass. If the horizon appears as two offset lines, index error exists. IE is measured in arc minutes. If the horizon is on when the arc reads below zero (off the arc), it is subtracted from the sextant reading. If it reads above zero (on the arc), it is added — remembered as 'on the arc, off it goes; off the arc, on it goes.' The corrected reading is used to find the apparent altitude, then additional corrections for dip, refraction, and semi-diameter are applied.
Greenwich Hour Angle (GHA) is the angular distance of a celestial body measured westward from the Greenwich meridian (0 degrees longitude) to the body's meridian, expressed in degrees from 0 to 360. GHA is tabulated for the sun, moon, planets, and Aries in the Nautical Almanac for each hour of Greenwich Mean Time. To find GHA for a time between whole hours, you add the increments and corrections from the yellow pages for the minutes and seconds of GMT. GHA combined with the observer's assumed longitude gives the Local Hour Angle (LHA), which is the key entry argument for sight reduction tables along with declination and assumed latitude.
At Local Apparent Noon (LAN), the sun crosses the observer's meridian and reaches its maximum altitude. At that moment, latitude equals the sun's declination plus or minus 90 degrees minus the observed meridian altitude (corrected for index error, dip, and semi-diameter). The formula is: Latitude equals 90 minus Hc plus declination (if declination and observer are same name) or 90 minus Hc minus declination (contrary name). In practice: (1) track the sun's altitude as it rises toward noon, (2) note the maximum altitude when it stops rising, (3) apply altitude corrections to get Ho, (4) subtract Ho from 90 degrees to get the zenith distance, (5) apply declination (same name add, contrary name subtract). No assumed position, LHA, or tables are needed — just the Almanac declination and a corrected sextant altitude.
HO 229 (Sight Reduction Tables for Marine Navigation) and HO 249 (Sight Reduction Tables for Air Navigation) both solve the navigational triangle, but differ in precision and use. HO 229 gives altitude to the nearest tenth of an arc minute and azimuth to the nearest tenth of a degree — it is the more precise publication and the standard for marine use on USCG exams. HO 249 Volume 1 gives selected star altitudes pre-computed for a given epoch, making star sights faster but less precise. HO 249 Volumes 2 and 3 cover the sun, moon, and planets to the nearest arc minute. The USCG exam typically specifies which publication to use. Both require the same three arguments: assumed latitude (whole degree), Local Hour Angle (whole degree), and declination.
Compass error by celestial azimuth is found by comparing the true azimuth of the sun (computed from the Nautical Almanac and sight reduction tables) with the compass bearing of the sun observed with a pelorus or azimuth circle. The true azimuth (Zn) is computed from the sight reduction tables using LHA, declination, and latitude. The difference between true azimuth and compass bearing gives the total compass error (deviation plus variation). If the true azimuth is greater than the compass bearing, the error is East (add to compass to get true). If less, the error is West. Separating variation from deviation requires knowing the local variation from the chart.
The amplitude method gives compass error using the bearing of the sun at the moment of sunrise or sunset, when the sun's center is on the celestial horizon. Amplitude is the angular distance from East or West to the body's true bearing, expressed as a bearing from East or West toward North or South (e.g., E 23.4 N means 23.4 degrees north of due east). Amplitude is computed from the formula: sin(Amplitude) equals sin(declination) divided by cos(latitude). The true bearing of the sun at sunrise is 90 minus Amplitude (if declination is north) and at sunset is 270 plus Amplitude. Compare this true bearing to the compass bearing to find total error. The amplitude method is faster than the full intercept method but only applies at sunrise and sunset.
Parallel rulers, dividers, chart scales, plotting bearings and ranges, and triangular fixes. Foundation skills that support celestial plotting.
Interactive celestial navigation practice questions for the USCG exam. Time conversions, GHA extraction, intercept problems, noon sight, and compass error -- timed and scored.
Complete navigation study guide covering dead reckoning, tides, currents, chart reading, compass variation and deviation, and electronic navigation. Full USCG exam coverage.
NailTheTest gives you hundreds of USCG-style celestial navigation practice questions with step-by-step solutions, timed exams, and progress tracking. Your ocean endorsement starts here.