General cross check for any place and time against US Naval Observatory data

If you wish to do your own testing, you can use the more detailed values of Azimuth and Altitude that are repeated if you scroll right on the Sight Planner sheet. Using GMT mode, insert same date, time and assumed position into Astron and the above site and compare results. Only above horizon bodies are shown and these may be in daylight and not visible. USNO bodies are in alphabetical order - Astron in Zn order. So it is easier to compare from Astron to USNO rather than the other way around.

Data. 2017 Jan 5^th. 08:19:42 UTC. Position S41° 06.5 E175° 05.2. HoE 0ft. IC = 0. Std T&P. Venus & Moon Lower limbs. (NB HoE 0 ft used to allow additional cross check with USNO.)

Lunars calculator gives Observed Lunar Distance of 36° 30.0' (Near).
First, check that the initial almanac data and altitude calculations all agree.

	GHA Venus	Dec Venus	GHA Moon	Dec Moon	Venus App Alt	Moon App Alt
Lunars Calculator V4	255° 28.9'	S11° 45.7'	220° 32.8'	N00° 54.9'	22° 20.1 (C) 22° 19.9 (Lower)	36° 14.1 (C) 35° 58.2 (Lower)
Astron V1.13	255° 28.9'	S11° 45.7'	220° 32.8'	N00° 54.9'	22° 19.9 (L)	35° 58.1 (L)
USNO	255° 29.0'	S11° 45.7'	220° 32.9'	N00° 54.9'	22° 19.9 (L)	35° 58.2 (L)

The Astron method uses assumed latitude obtained from a separate (usually meridian passage) observation adjusted for ship’s run, so for this test we use S41° 06.5’. We don’t know GMT or longitude, so ‘guess’ Ass Long E179° 00.0’ and Ass Time 08:00:00. Enter Lunar Calculators’ Observed LD of 36° 30.0' (Near/Near) and use Astron to find if Longitude and Time agree with Lunar Calculators initial position and time. Note, the Astron/Brunner method requires only one (simultaneous) altitude sight, so below worked twice with Venus and Moon.

Stage 1. Synchronise Ass Long to give intercept of 0.0 to Venus altitude 22° 19.9’(L). Revised Long W179° 59.0’.

Iter 1. 08:18:31 E175° 23.2’

Iter 2. 08:19:37 E175° 06.8’

Iter 3. 08:19:40 E175° 05.8’

Iter 4. 08:19:40 E175° 05.7’. Time difference 2 secs earlier than Lunars Calculator, Long Difference 0.5’W

Iter 1. 08:18:31 E175° 23.2’

Iter 2. 08:19:37 E175° 06.8’

Iter 3. 08:19:40 E175° 05.9’

Iter 4. 08:19:41 E175° 05.8’. Time difference 1 sec earlier than Lunars Calculator, Long Difference 0.6’W.

(Ass Long of E179 was chosen to test correct operation when synchronised longitude crosses 180° meridian.)

Now a (stupid) test with a much wider guess of time and longitude, using the same latitude result of S41° 06.5’. Such large longitude and/or time errors can converge to a grossly incorrect result if the bodies have ‘crossed’. The test is done to show the need for ‘secondary’ synchronisation. To be pedantic, secondary synchronisation should be done whenever the intercept (following entering an iteration) is greater than 0.1.

Ass Time: 2017 Jan 07 00:00:00 (40 hours in error) and Ass Long W150 00.0 (35 degrees in error), others as before.

In this case, as time and/or longitude errors are so large, we must re-synchronise after early iterations due to motion of the Moon and (except for stars) motion of the other body. Necessary re-synchronising shown in red below, optional in green.
Stage 1. Synchronise Ass Long to give an intercept of 0.0 to Venus altitude 22° 19.9’(L). This gives a new assumed longitude of W060° 38.7’. The following table shows the values given before and after resynchronisation.

Iter 1. 2017/01/05 09:54:37 E150° 42.0’ 28.5A. Resynchronise to E151° 19.9’

Iter 2. 2017/01/05 08:25:09 E173° 41.9’ 1.1A. Resynchronise to E173° 43.4’

Iter 3. 2017/01/05 08:20:00 E175° 00.8’ 0.1T Resynchronise to E175° 00.7’

Iter 4. 2017/01/05 08:19:41 E175° 05.3’ 0.1A Resynchronise to E175° 05.4’

Iter 5. 2017/01/05 08:19:40 E175° 05.6’ 0.1A Resynchronise to E175° 05.7’

(If re-synchronisation is omitted and only the stage 1 synchronisation is done, a nonsense result of 08:25:01 and E178° 32.4’ will result! However, if those results are re-used as the starting assumed time and longitude, with again only the stage 1 synchronisation, a correct result will be achieved.)

These times are normally only listed to the nearest minute, but for reasons given in 17.10 Astron quotes times to one second, with a believed (calculation) accuracy of 5 seconds, except for near circumpolar situations. We cannot find a separate source to make accurate comparisons. The USNO Celestial Navigation Data omits bodies with an Ho below +1°, so we have compared times when the star is just above 1°.

• 
  1 sec earlier both give GHA as 179 59.8
  

B: Try other side of 180° meridian. Change to 179 59.9W -12 DS +1 (same ship’s time date of 3 March.)

(Section 13.2.) To do this test, Astron display was modified to show angles to 7 decimal places of a minute. Such absolute accuracy is nonsense, but the relative changes with time are thought to be realistic to find the time of culmination.

2012 Mar 20. N50 00.0 W015 00.0. Chosen for Sun near max change in declination. (1 arc minute per hour)

Find transit

Theoretical Correction -18.3 secs.

Enter Astron. 2012 Mar 20. 13:07:37. Sun N50 00.0 W015 00.0. Hs 40 01.4 (IC=-3.8, HoE = 24ft. Lower limb.)

Astron initial position N50 00.0 W015 04.4

Astron Dec at 13:07:37 is N00 07.8 and at 14:07:37 is N00 08.8, so Dec_Rate is +1.0.

Enter Astron correction table with Dec Rate + 1.0 and SOG 0 knots.

Astron formula correction -18secs.

Astron Corrected Time 13:07:19

Astron corrected Lat N50 00.0

Astron corrected Long W014 59.9

(http://www.geoastro.de/TransitCulm/index.html quotes 17.9 secs with Formula 6.)


23.8.2 Test 2. Moon example near major lunar standstill. Stationary observer.

2024 Oct 15 N50 00.0 E000 00.0. Chosen for Moon near max change in declination. (18.2 arc minutes per hour)