04-02-2023, 08:27 PM
I got different results from my page xi Pub 249
An example of when the “short cut” method of finding your LHA in Eastern longitudes gets it wrong and why you should not rely on it.
This is taken from my copy of Pub.249 Vol II, commercial edition, page xi (see attached scan of the page which includes the pertinent part of the computation of the LHA.) I could not find a publication date in the volume but it offers correction tables from 1981 to 2016. It would no have been in my possession (purchased new from Celestaire) before about 2000.
Their Example:
1978 Jan 1 moon by bubble sextant at Greenwich Mean Time of 00h 53m 45s
DR position: 23° 42' S 113° 25' E
GHA moon for 00h 50m 00s: 300° 08'
inc for 03m 47s 0° 54'
GHA moon for 00h 53m 47s 301° 02'
AP lon (add because east ) 112° 58' (also the long. used for your plotting)
LHA 413° 60'
LHA (carry the 60') 414° 00'
subtract 360° -360°
54° 00' (the whole degree LHA needed for tables)
Here is the short cut method:
whole degrees DR longitude 113°
whole degrees LHA 301°
add 1 degree more 1°
LHA result 415°
subtract 360° - 360°
LHA by shortcut 55° <= this is the wrong answer! 54° is correct.
If you plug 55° LHA into the tables, or app, or calculator, you will get results for Hc and Z, just not the results the examiner got. If you were sitting for a test you just blew it!
Not only does the short cut method give you the wrong answer it also fails to provide you with a starting point of longitude for your plotting. So aside from being wrong it is also useless for navigation.
Now this particular example also demonstrates the requirement (for exams) to derive your AP longitude to within 30' of your DR longitude. Here is how that all goes when done rigorously:
DR long. was 113° 25' E
Starting from the GHA moon for 00h 53m 47s found earlier:
GHA moon 00h 53m 47s 301° 02'
Subtract just the minutes of GHA from 60'
60'
- 02'
58' (this is what you append to your whole degrees of DR long.)
AP long. is now: 113° 58' E
Now we check if we are within 30' of our DR longitude.
58'
- 25'
33' <= too big for Mr. Examiner!
So now we adjust the whole degrees of AP long by one degree to 112° 58' E
Check again to see if we are not within 30' of our DR.
we need 02' to get back to 113° E from 112° 58' and then we add another 25' from our own DR
02'
+ 25'
27' difference in long. which is OK for Mr. Examiner.
So the correct AP longitude to use in this example is 112° 58' E
Scroll back up to the beginning of the example to see that they used 112° 58' E as the AP longitude. This resulted in a LHA of 54° NOT 55° as would be given by thte short cut.
My advice is to forget about the short cut. It isn't that hard to do it properly and you will not only get the right answer you also get the AP longitude needed for plotting.
An example of when the “short cut” method of finding your LHA in Eastern longitudes gets it wrong and why you should not rely on it.
This is taken from my copy of Pub.249 Vol II, commercial edition, page xi (see attached scan of the page which includes the pertinent part of the computation of the LHA.) I could not find a publication date in the volume but it offers correction tables from 1981 to 2016. It would no have been in my possession (purchased new from Celestaire) before about 2000.
Their Example:
1978 Jan 1 moon by bubble sextant at Greenwich Mean Time of 00h 53m 45s
DR position: 23° 42' S 113° 25' E
GHA moon for 00h 50m 00s: 300° 08'
inc for 03m 47s 0° 54'
GHA moon for 00h 53m 47s 301° 02'
AP lon (add because east ) 112° 58' (also the long. used for your plotting)
LHA 413° 60'
LHA (carry the 60') 414° 00'
subtract 360° -360°
54° 00' (the whole degree LHA needed for tables)
Here is the short cut method:
whole degrees DR longitude 113°
whole degrees LHA 301°
add 1 degree more 1°
LHA result 415°
subtract 360° - 360°
LHA by shortcut 55° <= this is the wrong answer! 54° is correct.
If you plug 55° LHA into the tables, or app, or calculator, you will get results for Hc and Z, just not the results the examiner got. If you were sitting for a test you just blew it!
Not only does the short cut method give you the wrong answer it also fails to provide you with a starting point of longitude for your plotting. So aside from being wrong it is also useless for navigation.
Now this particular example also demonstrates the requirement (for exams) to derive your AP longitude to within 30' of your DR longitude. Here is how that all goes when done rigorously:
DR long. was 113° 25' E
Starting from the GHA moon for 00h 53m 47s found earlier:
GHA moon 00h 53m 47s 301° 02'
Subtract just the minutes of GHA from 60'
60'
- 02'
58' (this is what you append to your whole degrees of DR long.)
AP long. is now: 113° 58' E
Now we check if we are within 30' of our DR longitude.
58'
- 25'
33' <= too big for Mr. Examiner!
So now we adjust the whole degrees of AP long by one degree to 112° 58' E
Check again to see if we are not within 30' of our DR.
we need 02' to get back to 113° E from 112° 58' and then we add another 25' from our own DR
02'
+ 25'
27' difference in long. which is OK for Mr. Examiner.
So the correct AP longitude to use in this example is 112° 58' E
Scroll back up to the beginning of the example to see that they used 112° 58' E as the AP longitude. This resulted in a LHA of 54° NOT 55° as would be given by thte short cut.
My advice is to forget about the short cut. It isn't that hard to do it properly and you will not only get the right answer you also get the AP longitude needed for plotting.