Intercept method
In either case, the lines of position, if taken at different times, must be advanced or retired to correct for the movement of the ship during the interval between observations.
If observations are taken at short intervals, a few minutes at most, the corrected lines of position by convention yield a "fix".
If the lines of position must be advanced or retired by an hour or more, convention dictates that the result is referred to as a "running fix".
The actual distance from the observer to the geographical position (GP) of a celestial body (that is, the point where it is directly overhead) is "measured" using a sextant.
The rays of light from a celestial body are assumed to be parallel (unless the observer is looking at the moon, which is too close for such a simplification).
Given the three magnitudes: local hour angle (LHA), observed body's declination (dec), and assumed latitude (lat), the altitude Hc and azimuth Zn must be computed.
The relevant formula for Zn is When using such tables or a computer or scientific calculator, the navigation triangle is solved directly, so any assumed position can be used.
When using precomputed sight reduction tables, selection of the assumed position is one of the trickier steps for the fledgling navigator to master.
Sight reduction tables provide solutions for navigation triangles of integral degree values.
229, the assumed position must be selected to yield integer degree values for LHA (local hour angle) and latitude.
Professional navigators are divided in usage between sight reduction tables on the one hand, and handheld computers or scientific calculators on the other.
An experienced navigator can reduce a sight from start to finish in about five minutes using nautical tables or a scientific calculator.
Navigators use the memory aid "computed greater away" to determine whether the observer is farther from the body's geographic position (measure intercept from Hc away from the azimuth).
If the Hc is less than Ho, then the observer is closer to the body's geographic position, and intercept is measured from the AP toward the azimuth direction.
Best practise is to then advance or retire the assumed positions to correct for vessel motion during the interval between sights.
Until the age of satellite navigation ships usually took sights at dawn, during the forenoon, at noon (meridian transit of the Sun) and dusk.
