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.