# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Home brewed lunar distances**

**From:**Frank Reed CT

**Date:**2004 Apr 5, 22:44 EDT

I wrote earlier:

"Predicting lunars is every bit as easy as calculating altitudes. Having pre-calculated distances in an almanac saves maybe five minutes of table work, but that's all."

And Herbert P asked:

"Come on, Frank, aren't you exaggerating here just a tiny bit?"

Sure, but just a tiny bit. I could have put all sorts of qualifiers and caveats in my message (as is 'de rigueur' on this list) but I didn't bother <g>.

And Herbert P wrote:

"The problem of generating the lunar distance is identical to the great

circle sailing problem. Those of us who work with Pub. No. 229 can have

a look at pp. xx - xxii to see what is involved."

HO 229 is probably the worst set of tables to use for this problem, but it can be done.

And wrote:

"Your typical sight reduction table is ill suited to solve distances > 90

deg, creating cases and headaches."

Yes, that's important, but even if you ignore distances greater than 90 degrees, that still leaves you with an ability to calculate geocentric lunar distances (of the sort that used to be published in the Almanacs 100-200 years ago) in a very wide range of cases without any difficulty. It's JUST an altitude calculation. If you have the skill to calculate how high a star is (and this is the essential function of all modern sight reduction tables) then you can calculate a lunar distance by imagining yourself at the location where the Moon is directly overhead and then calculating the altitude of the other body as seen from that location. The required lunar distance is 90 - the calculated altitude.

Of a 'typical sight reduction table' you wrote:

"It is designed to work for integer values of LHA only, creating the need for either double entry numerical interpolation, or graphical interpolation."

First, not all sight reduction tables suffer from this problem. One of the reasons many people still have a fondness for HO 211 is because you can calculate directly from the DR with whatever odd minutes of arc it may have in each coordinate instead of producing a unique AP (such that the LHA is integral) for each sight. It's cleaner on the plotting sheet and for many people it's conceptually simpler. You can calculate a geocentric lunar distance using HO 211 in about 3 minutes. Try it... Well... ok, not on the FIRST try. As with any sight reduction technique, if you're out of practice, it takes ten times longer. If you've never used HO 211, consider learning it. The tables are very compact and much more reasonable to cart around as a backup on a small vessel than the fat tables like 229.

Second, you don't need to do interpolation (except by inspection). For HO 211, the tables have entries for every 0.5 minute of arc. If that's satisfactory for your lunars, you don't need to interpolate at all. If you want 0.1 minute, you can eyeball the interpolation easily (I included this process in the time estimate above). As for HO 229 or similar tables, you do an ordinary plot. Mark the AP (with its integral LHA) and the DR (really the GP of the Moon) and read off the distance the same way you would with any altitude sight. So with 229 that might all take four or five minutes per lunar. Still not a big investment of time.

And you wrote:

"Also, the Almanac data is not really meant to be used in this way. The GHA sun is adjusted to work with the interpolation table in the back of the almanac without a v-correction. (Frankly, I don't see why they are doing this.) Maximum deviation is 0.15' of arc. Not much, but it all adds up."

Although that's worth remembering, it's a side issue to this specific discussion. After all, ANY method for computing a lunar distance would have to face this issue at some point unless you generate your own ephemeri data. And of course, you're talking about a small quantity. If someone wanted to mess around with lunars three or four decades ago, getting such high accuracy would not likely be the main issue. As always with lunars, the answer to any question about the tools and techniques you should use is "it depends". It all depends on what your goal is. And each person playing with lunars will have a slightly different goal.

Myself, I wouldn't even think of calculating geocentric lunar distances TODAY with sight reduction tables except as a demo --a proof of concept. There's just no point. But it's worth knowing that you COULD do this a few decades ago, and a few enthusiasts did just that. If they had had something like the Internet to get together and compare notes, as people do on this list, I suspect the interest in modern lunars would have started a long time ago.

Frank E. Reed

[ ] Mystic, Connecticut

[X] Chicago, Illinois

"Predicting lunars is every bit as easy as calculating altitudes. Having pre-calculated distances in an almanac saves maybe five minutes of table work, but that's all."

And Herbert P asked:

"Come on, Frank, aren't you exaggerating here just a tiny bit?"

Sure, but just a tiny bit. I could have put all sorts of qualifiers and caveats in my message (as is 'de rigueur' on this list) but I didn't bother <g>.

And Herbert P wrote:

"The problem of generating the lunar distance is identical to the great

circle sailing problem. Those of us who work with Pub. No. 229 can have

a look at pp. xx - xxii to see what is involved."

HO 229 is probably the worst set of tables to use for this problem, but it can be done.

And wrote:

"Your typical sight reduction table is ill suited to solve distances > 90

deg, creating cases and headaches."

Yes, that's important, but even if you ignore distances greater than 90 degrees, that still leaves you with an ability to calculate geocentric lunar distances (of the sort that used to be published in the Almanacs 100-200 years ago) in a very wide range of cases without any difficulty. It's JUST an altitude calculation. If you have the skill to calculate how high a star is (and this is the essential function of all modern sight reduction tables) then you can calculate a lunar distance by imagining yourself at the location where the Moon is directly overhead and then calculating the altitude of the other body as seen from that location. The required lunar distance is 90 - the calculated altitude.

Of a 'typical sight reduction table' you wrote:

"It is designed to work for integer values of LHA only, creating the need for either double entry numerical interpolation, or graphical interpolation."

First, not all sight reduction tables suffer from this problem. One of the reasons many people still have a fondness for HO 211 is because you can calculate directly from the DR with whatever odd minutes of arc it may have in each coordinate instead of producing a unique AP (such that the LHA is integral) for each sight. It's cleaner on the plotting sheet and for many people it's conceptually simpler. You can calculate a geocentric lunar distance using HO 211 in about 3 minutes. Try it... Well... ok, not on the FIRST try. As with any sight reduction technique, if you're out of practice, it takes ten times longer. If you've never used HO 211, consider learning it. The tables are very compact and much more reasonable to cart around as a backup on a small vessel than the fat tables like 229.

Second, you don't need to do interpolation (except by inspection). For HO 211, the tables have entries for every 0.5 minute of arc. If that's satisfactory for your lunars, you don't need to interpolate at all. If you want 0.1 minute, you can eyeball the interpolation easily (I included this process in the time estimate above). As for HO 229 or similar tables, you do an ordinary plot. Mark the AP (with its integral LHA) and the DR (really the GP of the Moon) and read off the distance the same way you would with any altitude sight. So with 229 that might all take four or five minutes per lunar. Still not a big investment of time.

And you wrote:

"Also, the Almanac data is not really meant to be used in this way. The GHA sun is adjusted to work with the interpolation table in the back of the almanac without a v-correction. (Frankly, I don't see why they are doing this.) Maximum deviation is 0.15' of arc. Not much, but it all adds up."

Although that's worth remembering, it's a side issue to this specific discussion. After all, ANY method for computing a lunar distance would have to face this issue at some point unless you generate your own ephemeri data. And of course, you're talking about a small quantity. If someone wanted to mess around with lunars three or four decades ago, getting such high accuracy would not likely be the main issue. As always with lunars, the answer to any question about the tools and techniques you should use is "it depends". It all depends on what your goal is. And each person playing with lunars will have a slightly different goal.

Myself, I wouldn't even think of calculating geocentric lunar distances TODAY with sight reduction tables except as a demo --a proof of concept. There's just no point. But it's worth knowing that you COULD do this a few decades ago, and a few enthusiasts did just that. If they had had something like the Internet to get together and compare notes, as people do on this list, I suspect the interest in modern lunars would have started a long time ago.

Frank E. Reed

[ ] Mystic, Connecticut

[X] Chicago, Illinois