Assumed Position (AP): How to Determine and Its Practical Use in Celestial Navigation

An assumed position (AP) is a hypothetical location primarily used in Celestial navigation to calculate a ship's position based on celestial body observations. It's often determined using the Mark Stair method with site reduction tables (Table 249). This video will explain how to determine AP and use it to find a ship's line of position.

The scenario is based on a previous video about dead reckoning (DR) and estimated position (EP). At 2100 hours, a sextant altitude of the star Antares was observed. The DR position is Latitude 01°55.7' North and Longitude 103°40.0' East. This video focuses solely on AP determination and its application, not detailed celestial navigation calculations.

To determine AP: for assumed latitude, take the nearest whole degree of latitude. For example, with a DR latitude of 01°55.7' North, the assumed latitude is 02° North. For assumed longitude, calculate the Local Hour Angle (LHA) of Aries using the formula: LHA Aries = GHA Aries + easterly longitude - westerly longitude.

Given a Greenwich Hour Angle (GHA) of Aries of 168°56.2' and an easterly DR longitude, the assumed longitude is added to GHA. To make the LHA a whole number of degrees, the minutes of the assumed longitude must result in 60 minutes when added to the GHA minutes (e.g., 3.8 minutes). The assumed longitude should be the nearest to the DR longitude, which in this case is 104°03.8' East, resulting in an LHA of Aries of 273°.

If the DR longitude were westerly, the assumed longitude would be subtracted from GHA. The minutes of the assumed longitude should match the minutes of the GHA to make the LHA a whole number. Again, the assumed longitude must be the nearest to the DR longitude.

In this scenario, the assumed latitude is 02° North and the assumed longitude is 104°03.8' East. The AP is used to determine the computed altitude and true azimuth of celestial bodies using site reduction tables, specifically Table 249 (volume one for selected stars). These tables are organized by assumed latitude and LHA of Aries.

Using Table 249 for an assumed latitude of 02° North and an LHA of Aries of 273°, the computed altitude for Antares is 52°23' and the true azimuth is 219° True. The whole numbers for assumed latitude and LHA are crucial for using these tables effectively.

Plot the assumed position on the chart. Lay down the true bearing (219° True) of Antares from the assumed position. To find the Line of Position (LOP), calculate the intercept by finding the difference between the computed altitude (52°23') and the observed altitude (e.g., 52°27'). If the observed altitude is greater, the intercept is 'towards' the celestial body; if lesser, it's 'away'.

An intercept of 4 nautical miles 'towards' means measuring 4 miles from the AP along the bearing line, towards Antares. Draw a perpendicular line to this bearing, passing through the intercept point – this is the LOP. Somewhere on this LOP is the ship's actual position. If two or more celestial bodies are observed simultaneously, the intersection of their LOPs gives the ship's fixed position.