Primaries - key of Naibod
Posted: Sat Dec 15, 2012 10:55 am
Hello
Most of the recent examples of primaries on this forum have used Ptolemy's key (of course, in dealing with events in the first years of life, the key makes very little difference).
I've found, in my admittedly limited experience, that for events in later life, Naibod usually seems to give slightly closer "hits" - but sometimes Ptolemy is closer.
Naibod (16th century, though Martin says this key was probably used earlier by others) is an attempt to fine-tune the looser 1?= 1 year by taking the mean daily solar motion in RA as the key. This is often illustrated by a reasoning that if in a mean solar day, the earth turns 360?59'8" to return to solar noon, you just knock off the 360 and take 59'8" as the key. Martin, in his book presents the same thing from a slightly different point of view: in one year, the sun appears to move 360? or RA, so you divide that by the number of days in the year to get the mean daily motion.
Morin and others adopted Naibod as being more accurate than Ptolemy's key.
The problem for me is that if Naibod works for the reasons given, then the key of Brahe/Kepler (true solar RA arc -birthday) or even that of Placidus (true solar RA arc over X days) should surely work even better - but they don't, quite the contrary, at least for me.
So I wondered if it could be valid to think of another approach giving a value very close to Naibod, but much less sensitive to individual daily variations in the sun's apparent speed.
If we say that in a mean solar day, the earth has to turn 360?59'8", and then (since 1 day=1 year) divide THAT by 365.242 days, we get a daily average of 59'18", which in trun represents one year (coefficient 1.0118, close to Naibod which is 1.01456), but which is hardly modified by daily variations.
I'm not of course trying to "push" this key, I realise that it has no historical backing and I can quote no authorities and give no text references to support it, should those be requested. I would simply like to know if my reasoning for this "user key", which I'm experimenting with, is perhaps valid, or if it's completely out of order because of something I haven't thought of, and that I'm wasting my time.
Many thanks for any informed opinions.
Graham
Most of the recent examples of primaries on this forum have used Ptolemy's key (of course, in dealing with events in the first years of life, the key makes very little difference).
I've found, in my admittedly limited experience, that for events in later life, Naibod usually seems to give slightly closer "hits" - but sometimes Ptolemy is closer.
Naibod (16th century, though Martin says this key was probably used earlier by others) is an attempt to fine-tune the looser 1?= 1 year by taking the mean daily solar motion in RA as the key. This is often illustrated by a reasoning that if in a mean solar day, the earth turns 360?59'8" to return to solar noon, you just knock off the 360 and take 59'8" as the key. Martin, in his book presents the same thing from a slightly different point of view: in one year, the sun appears to move 360? or RA, so you divide that by the number of days in the year to get the mean daily motion.
Morin and others adopted Naibod as being more accurate than Ptolemy's key.
The problem for me is that if Naibod works for the reasons given, then the key of Brahe/Kepler (true solar RA arc -birthday) or even that of Placidus (true solar RA arc over X days) should surely work even better - but they don't, quite the contrary, at least for me.
So I wondered if it could be valid to think of another approach giving a value very close to Naibod, but much less sensitive to individual daily variations in the sun's apparent speed.
If we say that in a mean solar day, the earth has to turn 360?59'8", and then (since 1 day=1 year) divide THAT by 365.242 days, we get a daily average of 59'18", which in trun represents one year (coefficient 1.0118, close to Naibod which is 1.01456), but which is hardly modified by daily variations.
I'm not of course trying to "push" this key, I realise that it has no historical backing and I can quote no authorities and give no text references to support it, should those be requested. I would simply like to know if my reasoning for this "user key", which I'm experimenting with, is perhaps valid, or if it's completely out of order because of something I haven't thought of, and that I'm wasting my time.
Many thanks for any informed opinions.
Graham