Computing a Line of Position takes these steps:
These are the terms which are used when computing observed altitude (Ho):
The Nautical Almanac contains correction tables which are used to compensate for all of these effects. Dip, horizontal parallax and refraction may also be computed with a calculator, but we'll do it with tables here.
The Nautical Almanac contains a number of Altitude Correction Tables. These incorporate combined corrections for refraction, semidiameter and horizontal parallax.
Leg 57 gives this information for the sighting of Rigil Kentaurus:
A table for computing dip error can be found just inside the front cover of the almanac. The table indicates that the dip for an eyepoint at 9 feet is 2.9 arc-minutes.
With this information, we can now fill in the first part of our worksheet:
We now use 35°09.4 as an index into the altitude correction table for stars and planets. This table gives us a value of Ro of -1.3'. We enter this in the correction line.
If we're feeling ambitious, we could also go to the temperature and pressure correction table. However, pressure and temperature are not given in the problem text, so we'll skip that step.
Our final observed altitude for Rigil Kentaurus is 35°08.1'
The purpose here is to find the object's exact geographic position. We find its declination directly from the book. We find its hour angle by adding its Sidereal Hour Angle (SHA) to the Greenwich Hour Angle of Aries.
First, we open the Almanac to 1999-03-24 and find the Greenwich Hour Angle (GHA) of Aries for 23h. The Almanac gives 166°58.3'. In plain English, this means the First Point of Aries is at 166°58.3' west longitude.
We still haven't used the minutes and seconds of the observation time. We now go to the Increments and Corrections tables in the back of the Almanac and find the page for 41 minutes past the hour. We look down the seconds column for 56 seconds and examine the Aries column to get a correction factor of 10°30.7'
Next, we look up the Sidereal Hour Angle and declination for Rigil Kentaurus. The Almanac gives 140°06.3 and S60°49.7 respectively. In plain English, this means that on this date, Rigil Kentaurus was 140°06.3 west of the First Point of Aries, at 60°49.7 south latitude. (Stars don't move very much in the sky, so the almanac only lists their positions at 3-day intervals.)
Our worksheet now looks like this:
Adding the GHA of Aries at 23h (166°58.3), the correction factor (10°30.7), and the SHA of Rigil Kentaurus (140°06.3) gives a GHA of 317°35.3. In plain English, this means that if you were to stand at 60°49.7 south latitude, 317°35.3 west longitude at exactly the specified time, you'd be standing directly underneath Rigil Kentaurus. We call this the Geographic Position (GP).
The Geographic position of Rigil Kentaurus is = 317°35.3, 60°49.7S
The v, d, and HP terms to not apply for stars.
Now here's where it gets funky. If you're using a calculator or computer, simply enter the dead reckoning position for the Assumed Position.
If you're using the sight reduction tables instead, you have to adjust for the fact that the sight reduction tables only take whole numbers. You want to round your latitude and the object's declination to the nearest whole degrees. You want to round the difference between your longitude and the star's geographic position to a whole degree.
GHA is measured in degrees west of Greenwich. Since we're in west longitudes, we'll be subtracting our longitude from the GHA. If we were in east longitudes, we'd be adding. What we do now is to pick an assumed longitude that has the same minutes value as the star's GHA. (East longitudes would require picking a reciprocal.)
Our dead-reckoning longitude was 74°44.6W. The geographic position of Rigil Kentaurus is 317°35.3. We choose 74°35.3 for our assumed position. This way, subtracting our assumed longitude from the GP of Rigil Kentaurus leaves a round number.
Our assumed position for this sight is 54°S, 74°35.3W. Mark this on the plotting sheet. Label it "AP-R.K.".
Now we go back to the tables to compute expected altitude (Hc) and azimuth (Z).
Go to the sight reduction tables and look up latitude 54°, declination same name as latitude (latitude and declination are both south). Find declination 60°, hour angle 243°
The table gives these values:
Value d is the difference, in minutes, from this declination (60°) to the next. We compute the actual correction value by simply multiplying this by the actual fraction of a degree beyond 60°.
Naturally, there is a table to do this too. We now look for the Correction Table, and enter d (46') and the minutes value of the declination (49.7', rounded = 50'). The table gives 38':
Conclusion: We are 3 nm further from the geographic position of Rigil Kentaurus, in the direction 147°, than our assumed position.
We've already marked our assumed position for Rigil Kentaurus on the chart. Now we take our plotting ruler and lay it on the center of the compass rose through the 147° line. Use the plotting ruler to transfer that angle to the "AP-R.K." mark we made.
Draw a vector from our assumed position in the direction 147°. Measure 3 nm back along that vector and draw a line perpendicular to the vector. This is our Line of Position for Rigil Kentaurus. Label it "LOP-R.K."
Next: Line of Position — Acrux