17.1A. Calculate time of rise or set of any body at any location. 15
17.1B. Calculate time of upper meridian passage of any body. 15
17.2. Compass check. (Traditionally naked eye bearing at sunrise or sunset) 15
17.3. Latitude from Local Lower Meridian Passage of any circumpolar body. (IE body at minimum altitude) 16
17.4. Sextant damaged or overboard! (but chronometer ok) 16
17.5. Exact time of full or new Moon. 16
17.6. Artificial horizon sights. (New V1.08) 16
17.7. Back (“over the top”) sights. (New V1.08) 17
17.8. Latitude from simultaneous sights of two stars. (Sextant OK, inaccurate timepiece.) 17
17.9. NOTES TO ABOVE INDIRECT USES. 18
18. LUNAR DISTANCES (New V1.12) 19
18.1. Observed Lunar Distance Pop-Up 19
18.2. Find Longitude and GMT from Lunar Distance (Lunars) 19
19. DISCUSSION ON TIME ENTRY MODE. 23
20. RECENT REVISION HISTORY. 23
21. ACKNOWLEDGEMENTS. 23
22. MODIFYING ASTRON. 24
23. ACCURACY AND TESTS. 24
1A. Description. Astron (ἄστρον – Greek for Star) is an Excel programmed worksheet for sextant users. Its primary objective is to combine almanac calculations, apparent body position calculations and sextant altitude corrections into an easy to use single sheet utility. Astron is a large spreadsheet and may load or run slowly on older machines. In fact, it was the predominance of Greek characters in the many formulae used that inspired the name Astron.
As an almanac, Astron will, for an entered date and time, calculate the GHA, Dec, HP & SD of a body selected from a list of the 57 navigational stars, Polaris, Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. In context, it also calculates Sun and star rise and set times, Moon phase, body magnitudes and twilight times. Although intended for practical use in the present era, dates between 1905AD and 2999AD may be entered.
If an assumed position is also entered, Astron will also calculate the Azimuth and Altitude of the selected body. (If the body is unidentified, a sidebar utility can identify it given its approximate azimuth and altitude.)
If a sextant altitude is also entered, together with instrument correction, height of eye, temperature, pressure and observed limb, Astron will also calculate the Azimuth and Intercept from the assumed position.
Several supplementary features, such a sight planner, are also included.
1B. Initial Data. V1.14. The V1.14 distribution version is initially set to the following contrived values to trigger the four (seldom seen all together) pop-ups: Interstellar arc, Lunar Distance, Upper Meridian Passage and Star Rise/Mer Passage/Set
Settings: Ship’s Time Mode, Time Zones, Metres, Celsius and hPa.
Date/Time: 2017 June 05th. 20:05:46 ship’s time. Watch Correction 0, Time Zone -5, Daylight Saving 0.
Body: Spica. Assumed Position: 40N 75W.
Unidentified body: Approximate bearing 320ºT and altitude 10º.
Sextant: Index Correction +0.6. (0.6 off arc.)
Sight: Hs 38° 23.4’, HoE 3.0m, T 10°C, P 1010 hPa, Centre limb.
The following comments on the example initial data may be of interest. Please read the relevant user notes that follow for explanations.
Spica sight. For this observation time, Astron calculates the magnitude, GHA and Declination of Spica, followed by the azimuth and altitude of Spica as would be observed from the assumed position at that time. Given the subsequent sextant reading, index correction, eye height, temperature and pressure, Astron calculates that the azimuth and intercept were 173.2º and 10.3nm Away. Thus, the observer was somewhere on a line through a point 353º / 10.3nm from the assumed position drawn in direction 083º/263º.
The above almanac and sight reduction process is the main purpose of Astron. All the following utilities are supplementary to this prime purpose.
Advance line of position. (First supplementary block below main display.) If you took this sight as one of several for a fix at 21:00:00 and your vessel was tracking 060° at 6 knots, you would need to advance the position line in direction 060º for 5.4 nm. (Alternatively, plot the azimuth and intercept from N40° 02.7' W074° 53.9').
Twilight. The observation window that evening was between 19:40 and 20:19 ship’s time. (If the Sun had been the selected body, this area would have displayed Sun rise and set times.)
Unidentified body. That body about 15° altitude in the North West is Capella.
Arc distance. The calculated observed arc distance between Capella and Spica, allowing for refraction, on this date was 120° 07.16’.
Observed Lunar Distance. Astron calculates the observed lunar distance between Spica and the near limb of the Moon at the entered time and location as 14º 38.4’.
Lunars utility. (Third block below main display). If you had been at the Assumed Latitude of exactly 40N and had measured the angle between Spica and the near limb of the Moon with your sextant (IC=+0.6) as 14º 37.8’, your longitude would have been W074º 59.0’ and the ship’s time would have been 20:05:42. (Not really a valid lunar example as the iterative process and longitude synchronisation with a second body have both been omitted. Also, for lunars, you should really work in GMT mode. See Section 18 for the full method.)
Upper Meridian Passage. (The pop-up refers you to the second block below main display – Upper Meridian Passage.) If you had been stationary taking sights of Spica before and after it reached maximum altitude and had entered Hs as 38º 23.4’ as the maximum observed altitude and 20:05:46 as the (deduced) time of maximum altitude, then your position at that time would have been N40º 25.2’ W069º 33.2’. However, if you had been moving at 060º at 6 knots, you would have been at N40º 25.2’ W069º 45.0’ at 20:06:33.
Sight Planner. (Separate sheet accessed using tabs at bottom of screen.) Should you wish to use this Spica sight with other bodies for a fix, the best cut for a two-body fix would be from Spica and Rasalhague, though you would probably choose Regulus as it is brighter. For a three-body fix, you would use Spica, Vega and Pollux. For a four-body fix, the lack of bodies suggests that you should try a different ‘reference body’ to Spica. (The obvious ones are the Moon or Jupiter, but Spica was necessary to trigger all the various pop-ups!)
More on lunars. (Still on sight planner sheet.) If you are a lunar freak, you would further observe that Jupiter, Denebola, Regulus and Pollux would also give lunar opportunities. (Zuben’ubi is too close: zodiacal bodies are indicated by a period (.) after their name.)
Star rise, upper meridian passage and set times. (Now on computer almanac sheet again, lower right.) Spica rose at 15:03:23, was at maximum altitude at 20:27:30 and set (earlier that morning) at 01:55:32. These are theoretical times. Section 17.1A of these notes points out that, because of atmospheric extinction, Spica would not be visible to the naked eye below altitudes of about 1° 48’.