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Re: Moon Venus Lunar - Interpretation of results
From: Sean C
Date: 2020 Jan 30, 19:36 -0800

Jim,

You wrote:

"If 1 arc min = 4 secs of time, then 16x4 = 64 seconds.  Which would make GMT 64 seconds earlier than 2210, or 22h08m56s.  Is this correct?"

No. The error in your *measurement* was 16'. Under the circumstances, this would cause an error in time of 32 minutes and 3 seconds - giving a "measured time" of 21:37:57. That is an error of 1,923 seconds. Divide that by four and you get 480.75 arc minutes or 8°00.8'. Sometimes I wish Frank's app would show you the "measured time" directly. But if you want to calculate it yourself, you can do it like this:

Take the error in longitude in minutes (in this case 8° · 60  = 480 + 00.8' = 480.8') and multiply by 4 (480.8 · 4 = 1923.2). That is the error in seconds of time. You can divide that by 60 to get the decimal minutes (1923.2 / 60 = 32.0533...) and multiply the mantissa by 60 to get the seconds - or you can divide the error in seconds by 3600 to get decimal hours and, if you're using a calculator that can dislay in DMS format, get the minutes and seconds directly.

BTW, I worked your lunar using Frank's "easy lunars" method (and some additional fomulas from the Nautical Almanac). The results are below and I included all of the calculations so you could see exactly what is going on. The results don't exactly match Frank's app, but then the app is probably much more accurate. Also, as Frank mentioned, using an "AP" that is not exact can have some effect on the results - and since I used an astronomy program to get the altitudes, that may have something to do with it. And as Frank wrote on his "easy lunars" page: that method is "prone to error when the lunar distance itself is below 15 degrees". Your lunar is very near that threshold.

Don't be discouraged, though! Keep at it and you will certainly get better. I have shot many lunars and mine are still far from perfect. (I have had the odd "lucky shot", though.) :)

Regards,

Sean C.

----------------------------------------------------------------------------------------

2020 Jan. 29 Venus Lunar (Near Limb)

43°00.0'N, 71°00.0'W
IC:-2.3' / 35°F / 29.95inHg*

Measured LD @ 2210 UT: 15°20.8'

Apparent Altitudes**:
Moon: 38°57.7'
Venus: 30°10.7'

Moon HP: 54.1'

Moon SD:
0.2724 · 54.1' = 14.7'

Moon SD Aug.:
0.3' · sin(38°57.7') = 0.2'

Pre-cleared LD:
15°20.8' - 2.3' + 14.7' + 0.2' = 15°33.4'

Moon Refraction:
-0.0167° / tan(38°57.7' + 7.32° / (38°57.7' + 4.32°)) = -1.2'

Moon PA:
54.1' · cos(38°57.7') = 42.1'

DH Moon:
42.1' - 1.2' = 40.9'

Venus Refraction:
-0.0167° / tan(30°10.7' + 7.32° / (30°10.7' + 4.32°)) = -1.7'

DH Venus: -1.7'

A:
(sin(30°10.7') - cos(15°33.4') · sin(38°57.7')) / (cos(38°57.7') · sin(15°33.4')) = -0.494

B:
(sin(38°57.7') - cos(15°33.4') · sin(30°10.7')) / (cos(30°10.7') · sin(15°33.4')) = 0.623

Q:
(0.55 · 0°40.9'² · cot(15°33.4') · (1 - -0.494²)) / 3438 = 3.321E-4

Cleared LD:
15°33.4' + -0°40.9' · -0.494 + 0°1.7' · 0.623 + 3.321E-4 = 15°54.7'

2200 UT GHA/Dec. Moon:
91°57.3'/S2°46.3'

2200 UT GHA/Dec. Venus:
107°56.5'/S5°05.2'

2200 UT Calculated LD:
acos(sin(-2°46.3') · sin(-5°05.2') + cos(-2°46.3') · cos(-5°05.2') · cos(107°56.5' - 91°57.3')) = 16°06.9'

2300 UT GHA/Dec. Moon:
106°32.5'/S2°34.7'

2300 UT GHA/Dec. Venus:
122°56.3'/S5°03.9'

2300 UT Calculated LD:
acos(sin(-2°34.7') · sin(-5°03.9') + cos(-2°34.7') · cos(-5°03.9') · cos(122°56.3' · 106°32.5')) = 16°32.8'

Interpolated Time:
Error: Measured LD time is before 2200 UT.

2100 UT GHA/Dec. Moon:
77°22.0'/S2°57.9'

2100 UT GHA/Dec. Venus:
92°56.8'/S5°06.5'

2100 UT Calculated LD:
acos(sin(-2°57.9') · sin(-5°06.5') + cos(-2°57.9') · cos(-5°06.5') · cos(92°56.8' · 77°22.0')) = 15°41.2'

Interpolated Time:
(15°54.7' - 15°41.2') / ((16°06.9' - 15°41.2') / 3600) = 1,891 seconds or 31 minutes 31 seconds + 2100 = 21:31:31

Error in longitude:
22:10:00 - 21:31:31 = 0:38:29 or 2,309 seconds
2,309 / 4 = 577.25' or 9°37.3'

*Temp./press. correction negligible

**Altitudes from Stellarium

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