NavList:

Frank, you wrote:
"But what is your purpose here? What are you trying to calculate?"

I am trying to approximate, as closely as possible with the formulas found in the N.A., what would be the *apparent* altitude of the bodies at the time of the lunar. I've been shooting from my front yard at night, so no natural horizon. I am currently experimenting with coffee and soon, motor oil as an AH. Until then, I must calculate the altitudes. The way I see it, there are basically three ways I can use the equations given on your lunars page: Use the directly calculated altitude for H_Moon OR use Hc to calculate PA & refraction and subtract those from Hc to approximate Ha OR use the method I outlined in my previous post to more closely approximate PA, refraction & Ha. Conveniently, ICE gives all of the corrections alongside the Hc. But, as you've pointed out, it's getting increasingly inaccurate, especially regarding the Moon. Besides, I wanted to try out MICA!

So, as an example, I'll use a lunar I shot on March 24th of this year (2014). Here's the raw data:

2014 Mar. 24
Moon-Venus Lunar (Near Limb)
AP: N 37° 03.3', W 076° 28.6'
Altitude: 40 ft.
Temp.: 30.5 °F
Press.: 30.30 inHg
Watch Error: 0
Index Error: 0

(Note: I ignored the temp./press. correction for this exercise.)

UTC: 11h 12m 27s
LDs: 38°01.8'

____UTC__________LDc____

11h 00m 00s.....38°29.6'
11h 12m 27s.....38°22.9'
12h 00m 00s.....37°57.0'
________________________

Now, here are my results from the three methods I mentioned above:

#1: I used LHA & Dec. to calculate Hc. I used Hc to calculate PA, subtracted PA from Hc and used the result to calculate refraction. I used Hc directly for H_Moon. (Same process for Venus, only no PA calculated as I could not find the HP in MICA.)

Moon
Hc: 34°27.3'
HP: 59.1'
PA: 48.7'
R : -1.5'
DH_Moon: 47.2'
SD: 16.1'
Aug.: 0.2'

Venus
Hc: 23°17.9'
R : -2.3'
DH_Venus: -2.3'

A: -0.094830649
B: 0.448602174
Q: 0.000124222

Corr. LD: 38°23.6' Error: 0.7'
Interpolated Time: 11h 11m 03s Error: -1m 24s
Error in Longitude: 21.0'
---------------------------------------------

#2: Same as the first example, only I subtracted PA and refraction from Hc to approximate Ha. All values not listed remained the same. I used Ha for H_Moon. (Again, same for Venus, no PA.)

Moon
Ha: 33°40.1'

Venus
Ha: 23°20.2'

A: -0.075459348
B: 0.427897849
Q: 0.000124635

Corr. LD: 38°22.6' Error: -0.3'
Interpolated Time: 11h 12m 47s Error: 20s
Error in Longitude: 5.0'
-----------------------------------------

#3: I used the method I described in my previous post to more closely approximate Ha. Again, all values not listed remained the same as in #1. Note the different PA & DH values. I'd also like to point out that these values most closely match those computed by your online calculator.

Moon
PA: 49.2'
DH_Moon: 47.7'
Ha: 33°39.6'

Venus
Ha: 23°20.2'

A: -0.075267894
B: 0.427685138
Q: 0.000127294

Corr. LD: 38°22.7' Error: -0.2'
Interpolated Time: 11h 12m 42s Error: 15s
Error in Longitude: 3.8'
-----------------------------------------

So, although this lunar does not quite fit into your description of "short distance lunars (less than 20°)", it also does little (or nothing) to disprove the assertion that, "an error of +/-6 minutes of arc in the altitude of the Sun or other body will not lead to an error greater than a tenth of a minute in the cleared distance." (Even though the difference here was only 0.5'.)

You also wrote:
"I'm not sure what you're getting at here. What are you doing with the observed time? If I interpret that phrase 'however little' literally, then I would say 'yes'. A small change leads to a small change. But is it significant?"

I must admit, I'm not sure what you mean by asking what I'm doing with the time. I use the calculated distances on the hours before and after the lunar to determine the change in distance per minute. Then, I use the corrected distance to interpolate the minutes and seconds at which the lunar was shot. I then compare this to what I know to be the actual time. Beyond that, I'm not doing anything with it. As to whether or not such a small difference is significant: I think that's subjective. At sea, probably not...but it matters to me.

As a side note: a quick check seemed to indicate that my results would have been very similar if I had just used the corrections from the N.A., with or without using my method. Also, although ICE gives a GHA that is -0.1' different than MICA, all of the corrections match those I calculated using my method (#3).

Now, I'm ready for everyone to tell me where I screwed up! Lol. :)

Regards,
Sean C.
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