Intercept Method - Summary

Summary

The intercept method is based on the following principle. 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 observer has already estimated his position by dead reckoning and calculated the distance from the estimated position to the body's GP; the difference between the "measured" and calculated distances is called the intercept.

The diagram on the right shows why the zenith distance of a celestial body is equal to the angular distance of its GP from the observer's position. 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). The angle at the centre of the earth that the ray of light passing through the body's GP makes with the line running from the observer's zenith is the same as the zenith distance. This is because they are corresponding angles. In practice it is not necessary to use zenith distances, which are 90° minus altitude, as the calculations can be done using observed altitude and calculated altitude.

Taking a sight using the intercept method consists of the following process:

• Observe the altitude above the horizon Ho of a celestial body and note the time of the observation.
• Assume a certain geographical position (lat., lon.), it does not matter which one so long as it is within, say, 50 NM of the actual position (or even 100 NM would not introduce too much error). Compute the altitude Hc and azimuth Zn with which an observer situated at that assumed position would observe the body.
• If the actual observed altitude Ho is smaller than the computed altitude Hc this means the observer is farther away from the body than the observer at the assumed position, and viceversa. For each minute of arc the distance is one NM and the difference between Hc and Ho expressed in minutes of arc (which equal NM) is termed the "intercept". The navigator now has computed the intercept and azimuth of the body.
• On the chart he marks the assumed position AP and draws a line in the direction of the azimuth Zn. He then measures the intercept distance along this azimuth line, towards the body if Ho>Hc and away from it if HoLOP at the moment of the observation.
• The reason that the chosen AP is not important (within limits) is that if a position closer to the body is chosen then Hc will be greater but the distance will be measured from the new AP which is closer to the body and the end resulting LOP will be the same.