Celestial navigation · Dead reckoning · GPS · Lines of position · Error accumulation
Navigate a ship using celestial observations and dead reckoning. Take sun/star sights to fix position using the intercept method. Compare accuracy of traditional navigation vs GPS, and simulate how errors accumulate in dead reckoning.
The navigator measures the altitude of celestial bodies (sun, stars, planets) with a sextant. Each measurement yields a Line of Position (LOP). The calculated altitude Hc = arcsin(sin Lat · sin Dec + cos Lat · cos Dec · cos GHA). The intercept a = Ho − Hc determines how far the LOP is from the assumed position. Two or more LOPs intersecting give a celestial fix accurate to 1–2 nautical miles.
Dead reckoning projects position forward from the last known fix using speed and heading: x' = x + v·cos(θ)·dt, y' = y + v·sin(θ)·dt. Errors accumulate with time: σ_position = σ_v · t. Without GPS, errors of tens of miles build up over days. Currents, wind, and compass deviation compound these errors further.
GPS calculates position from timing signals from 4+ satellites. Each satellite defines a sphere of possible positions; their intersection gives a 3D fix. Precision depends on satellite geometry — PDOP (Position Dilution of Precision) quantifies this. Low PDOP (<2) means good geometry and <3m accuracy. Selective availability (now off) formerly added 100m error.
Select Celestial, Dead Reckoning, or GPS mode. Set ship speed, heading and elapsed time. In Celestial mode, the simulator shows lines of position from 3 bodies intersecting at the fix. In DR mode, watch the error ellipse grow over time. Observe how DR accuracy degrades over hours without a new fix. GPS mode shows satellite geometry and PDOP.
This simulation recreates how a vessel fixes its position at sea using three methods: celestial navigation, dead reckoning and GPS. In celestial mode it draws Lines of Position from three bodies (Sun, Polaris and Venus) using the intercept method, where the calculated altitude Hc = arcsin(sin Lat · sin Dec + cos Lat · cos Dec · cos LHA) is compared with the sextant-observed altitude Ho to give the intercept a = Ho − Hc. The intersecting LOPs mark the fix.
The controls let you set ship speed (1–25 knots), heading (000–359°), elapsed time (0–72 hours) and observation error (0.1–5 arcminutes), then switch between Celestial, Dead Reckoning and GPS modes. The panel reports position error, fix accuracy, distance run and PDOP. Reliable position-fixing remains the foundation of safe maritime navigation, collision avoidance and ocean passage planning worldwide.
What does this simulation actually show?
It shows a chart-style ocean view with your ship and three ways of fixing its position. You can compare a celestial fix from sextant sights, a dead-reckoning track that drifts from the true position over time, and a high-precision GPS fix from multiple satellites.
What is the intercept method in celestial navigation?
It is a technique for plotting a Line of Position from a sextant sight. You compute the altitude a body should have from an assumed position (Hc), measure its real altitude (Ho), and the difference, called the intercept, tells you how far toward or away from the body your true position lies. Crossing two or more such lines gives a fix.
How does dead reckoning work here?
Dead reckoning projects your position forward from the last known fix using only speed and heading: x' = x + v·cosθ·dt and y' = y + v·sinθ·dt. The simulation draws both the true track and a drifting DR track, with an error ellipse that grows as elapsed time increases.
Ship Speed sets the vessel's velocity in knots, Heading sets its course in degrees, Time elapsed advances the clock up to 72 hours, and Observation Error sets the sextant uncertainty in arcminutes. Together they drive the ship's plotted position and the size of the resulting errors.
Dead reckoning has no external reference, so small uncertainties in speed and heading integrate over time. The position error scales roughly as σ ≈ σ_v · t, so after many hours the error ellipse can span tens of nautical miles. Currents, wind and compass deviation make it worse.
PDOP, or Position Dilution of Precision, measures how favourable the satellite geometry is. When satellites are well spread across the sky PDOP is low (under 2) and the fix is precise to a few metres; when they are clustered PDOP rises and accuracy degrades even with the same signal quality. This page reports a PDOP of about 1.4 in GPS mode.
A skilled navigator's celestial fix is typically accurate to one or two nautical miles, limited mainly by sextant observation error. GPS, by contrast, fixes position to within a few metres. The simulation reflects this: celestial error scales with your observation-error slider, while GPS reads under five metres.
It is a simplified, educational model. The intercept formula, dead-reckoning equations and the relationship between observation error, elapsed time and position error are genuine, but the chart is schematic and the celestial bodies, coastlines and satellite layout are illustrative rather than ephemeris-accurate.
A single sight yields only one Line of Position, which fixes you somewhere along a line, not at a point. Crossing two LOPs gives a fix, and a third body provides a check: if all three lines meet in a tight triangle the fix is trustworthy, while a large triangle warns of an observation or timing error.
Yes. GPS is the primary method, but celestial navigation remains a vital backup because it needs no electronics, satellites or external infrastructure that could fail or be jammed. Many navies and merchant fleets still train and certify officers in sextant work for exactly this reason.
Ocean passage planning, collision avoidance, landfall timing and search-and-rescue all depend on knowing your position. Modern bridges blend GPS, dead reckoning and visual or celestial checks so that a single failure cannot leave the crew lost, which is the core lesson this simulation demonstrates.