Latitude and Longitude Basics
The Coordinate System Beneath Every Celestial Fix
The Geographic Coordinate System
The Earth is divided into a grid of latitude (north-south position) and longitude (east-west position). Latitude is measured from the equator (0°) to the poles (90° N or 90° S). Longitude is measured from the prime meridian at Greenwich, England (0°) eastward and westward to 180°.
Positions are expressed in degrees (°), minutes ('), and seconds ('') of arc. One degree contains 60 minutes; one minute contains 60 seconds. For practical navigation at sea, seconds are rarely needed — positions are typically stated to the nearest tenth of a minute (0.1'), which represents about 185 meters at the equator. Some older texts use decimal degrees (e.g., 41.3756° N), but nautical charts and almanacs almost universally use degrees and minutes.
The key relationship to memorize: one minute of latitude equals one nautical mile. This is actually how the nautical mile is defined — it is 1/60th of a degree of latitude, approximately 1,852 meters. This holds true everywhere on Earth for latitude. Longitude is different — one minute of longitude equals one nautical mile only at the equator, and shrinks toward zero at the poles.
Lines of equal latitude are called parallels because they run parallel to each other around the globe. Lines of equal longitude are called meridians — they all converge at the poles and cross the equator at right angles.
When writing a position, always state latitude first, then longitude, and always include the hemisphere (N/S for latitude, E/W for longitude). 'My position is 36° 42.3' N, 075° 18.7' W' is unambiguous. Dropping the hemisphere letter is a navigational error waiting to happen.
One minute of latitude is equal to what distance?
What is the name of the reference meridian from which longitude is measured?
How Latitude is Measured
Latitude has always been the easier coordinate to determine at sea. The geometry is elegant: the altitude of Polaris (the North Star) above the horizon equals your latitude north to within about 1°, because Polaris sits almost exactly above the Earth's north pole. A small correction from the almanac's Polaris tables (the a0, a1, a2 corrections) refines this to within a few tenths of a minute of arc — accurate enough for offshore navigation.
The Sun also gives latitude directly at Local Apparent Noon (LAN) — the moment the Sun crosses your meridian and reaches its maximum altitude for the day. At that moment, a simple formula applies: Latitude = 90° − (corrected noon altitude) + Declination, with the sign of Declination depending on whether you're on the same side of the equator as the Sun. The noon sight was the daily latitude fix for centuries of ocean navigation.
The reason latitude is easy is that it depends only on the altitude of a body — how high above the horizon it is — not on the time. Altitude measurement doesn't require a chronometer. As long as you can measure the angle between a body and the horizon with a sextant, you can find latitude. It was longitude that required the clock.
Any body at upper transit (crossing your meridian at its highest point) gives a direct latitude calculation if you know the body's declination from the almanac. The Sun at noon is merely the most convenient example.
Use Polaris for a quick latitude check anytime it's visible and the horizon is clear. You don't need to work a full sight reduction — just apply the Polaris corrections from the back of the almanac to your corrected altitude. It takes less than two minutes and gives you latitude to within a mile.
Why does the altitude of Polaris directly indicate an observer's latitude?
Why does finding latitude NOT require an accurate chronometer?
How Longitude is Measured
Longitude is measured in degrees east or west of the prime meridian, from 0° at Greenwich to 180° at the International Date Line. Because meridians converge toward the poles, the actual distance represented by one degree of longitude varies with latitude — it's about 60 nautical miles at the equator, 52 nm at 30°, 30 nm at 60°, and zero at the poles. The formula is: miles per degree of longitude = 60 × cos(latitude).
The critical link between longitude and time is the same rotation rate used in the previous lesson: the Earth rotates 15° per hour, or 1° per 4 minutes, or 1 minute of arc per 4 seconds of time. This means that if you know the exact time at Greenwich when a celestial body is directly overhead (on your meridian), you can calculate how far east or west of Greenwich your meridian lies — that's your longitude.
This is why John Harrison's chronometer was revolutionary. For the first time, a ship could carry Greenwich time accurately on a long voyage. Knowing GMT at the moment of a celestial observation allowed longitude to be computed rather than estimated. Before reliable chronometers, longitude error of 5° or more (300+ nautical miles) was common on transoceanic passages.
In sight reduction, longitude enters through the concept of Local Hour Angle (LHA): LHA = GHA − West longitude (or GHA + East longitude). LHA is the angle between the observer's meridian and the body's meridian, measured westward. It tells the sight reduction tables how the body is positioned relative to the observer.
To quickly estimate how many nautical miles one degree of longitude represents at your current latitude, multiply 60 by the cosine of your latitude. At 45° N, cos(45°) ≈ 0.707, so one degree of longitude ≈ 42.4 nautical miles. This is useful for estimating how much a longitude error affects your plotted position.
West longitude is subtracted from GHA to get LHA; east longitude is added. Getting this backward produces an LHA that is 360° off from correct, placing your assumed position on the opposite side of the Earth. Always double-check your LHA is a reasonable value (0° to 360°) before entering the sight reduction tables.
At latitude 60° N, approximately how many nautical miles does one degree of longitude represent?
How is Local Hour Angle (LHA) calculated for a position west of Greenwich?
Applying Coordinates in Celestial Navigation — DR Position and Assumed Position
When working a celestial sight, you don't need to know your exact position — in fact, you can't, because that's what you're trying to find. Instead, you start with a Dead Reckoning (DR) position: your best estimate of position based on your last known fix, course steered, and speed made good. The DR position advances continuously as you sail, and it's what you use to set up sight reduction.
Sight reduction tables (HO 229, HO 249, or equivalent) require the assumed position (AP) — a position with a whole-degree latitude and a longitude chosen to make the LHA come out to a whole degree. The AP is typically taken close to the DR position but adjusted to the nearest whole values. The tables are sensitive to the AP, but the resulting intercept (a-value) compensates for the difference between the AP and your actual position, so the final plotted line of position is accurate regardless of the exact AP chosen.
The assumed position is not a guess at your position — it's a mathematical convenience that makes the tables work. Once you compute the calculated altitude (Hc) and azimuth (Zn) at the AP, you compare Hc to your observed altitude (Ho). The difference — the intercept — tells you how many nautical miles toward or away from the body you are from the AP. Plot the intercept from the AP along the azimuth, draw a line of position perpendicular to the azimuth, and you're done.
Two or more lines of position from different bodies crossed on the chart give a celestial fix — your position. The accuracy depends on the angles between LOPs (aim for 60–120° between bearings), the quality of your sextant sights, and the accuracy of your time.
A good DR position makes sight reduction faster and easier, but even a poor DR position (within 30–40 miles) won't ruin a celestial fix — the intercept method is inherently self-correcting. The assumed position simply needs to be in the same general area; the math handles the rest.
Why is an assumed position (AP) used in sight reduction tables rather than the DR position directly?
Summary
Latitude is measured north/south from the equator (0°) to the poles (90°); one minute of latitude equals exactly one nautical mile.
Longitude is measured east/west from the prime meridian at Greenwich (0° to 180°); one degree of longitude equals 60 × cos(latitude) nautical miles.
Latitude can be determined from altitude measurements alone — no accurate clock needed; longitude requires knowing precise GMT.
Local Hour Angle (LHA) links longitude to the almanac's GHA: LHA = GHA − west longitude, or GHA + east longitude.
The assumed position (AP) is a mathematical convenience near the DR position chosen so that latitude and LHA are whole degrees for table entry.
Two or more crossed lines of position from different bodies produce a celestial fix; aim for 60–120° angular separation between LOPs for best accuracy.
Key Terms
- Latitude
- Angular distance north or south of the equator, measured from 0° at the equator to 90° at the poles. One minute of latitude = one nautical mile.
- Longitude
- Angular distance east or west of the prime meridian at Greenwich, measured from 0° to 180°. Distance per degree varies with latitude.
- Parallel
- A circle of constant latitude, running east-west around the globe parallel to the equator.
- Meridian
- A circle of constant longitude, running north-south through both poles and crossing the equator at right angles.
- Dead Reckoning (DR) position
- An estimated position based on last known fix, course steered, and distance run. Used as the starting point for sight reduction.
- Assumed Position (AP)
- A position near the DR position chosen with whole-degree latitude and a longitude that makes LHA a whole number, enabling use of standard sight reduction tables.
- Local Hour Angle (LHA)
- The angle between the observer's meridian and the body's meridian, measured westward from 0° to 360°. Calculated as GHA minus west longitude (or plus east longitude).
- Local Apparent Noon (LAN)
- The moment when the Sun transits the observer's meridian — its highest altitude of the day. A noon sight at LAN gives latitude directly.
- Line of Position (LOP)
- A line on the chart along which the observer must be located, derived from a single celestial sight. Two or more LOPs crossed give a fix.