Lunar distance presetting

Today I conducted a quick exercise presetting a sextant to the Sun-Moon near-limb distance (no refraction corrections).
Sextant: Astra III Professional with the 7×35 Celestaire telescope
Calculations with Navigation Spreadsheets (screenshots attached)

Date: May 26, 2019
Local time: 9:25 am, U.S. Mountain Daylight Time
Universal Time: 15:25
Location: 35° 53’ N, 106° 19’ W

GHA: 51° 59.4’
Dec: N 21° 08.8’
SD: 15.8’

GHA: 137° 19.1’
Dec: S 13° 17.7’
SD: 14.8’
HP: 54.3’

Topocentric lunar distance: 91° 07.0’
Subtracting the sum of the two semidiameters: 30.6’
Presetting the sextant to: 90° 36.4’

Then, I pointed the sextant at the Moon and soon the Sun appeared right on top of Moon’s limb, as expected. I did not even check the index error beforehand (the sextant has been sitting in its box for months). The whole procedure lasted less than 15 minutes; doing this write-up took somewhat longer than that. 🙂  A good result overall.sunmoonld_prec

22 February 2015 conjunctions

A recent thread on NavList pointed out that a number of celestial objects appear in close proximity during the second half of February 2015. A quick application of the relevant spreadsheets show Venus and Mars separated by 24.7’, which is less than the apparent Moon disk size. The spreadsheet sailings.xls can be used in this case, since the angle of 1 minute of arc corresponds to the distance of 1 nautical mile on the surface of the Earth.



With a Moon crescent in the vicinity of the two planets, it has been mentioned that Uranus is also in the area, separated from the Moon limb by about 2 degrees. While in the first example the parallaxes were essentially negligible (and hence the sailings.xls spreadsheet could be used to calculate the Venus-Mars angular separation), this is not the case for the Moon. Therefore, to compute the lunar distance, there is a dedicated spreadsheet (ld_prec.xls) which takes the viewing location on the surface of the Earth (“AP”) as additional input to account for the parallax effect.


Uranus appears slightly to the west of the (almost new) Moon crescent, so the interesting quantity is its distance from Moon’s illuminated near limb. Subtracting the Moon semidiameter (16.4′) from the topocentric centered lunar distance of 2° 15.6′ yields a value that is very close to 2 degrees.


Ephemerides for the planet Uranus (along with Neptune and Mercury) are not listed in celestial navigation almanacs, as these objects are not suitable for astronavigation purposes. Nevertheless, we provide almanac spreadsheets for those three planets as well, since their data can be computed from the same VSOP87 planetary theory that we use for the other planets.

Mercury in January 2015

In January 2015 Mercury is visible just northwest of Venus in the evening sky. Its horizontal parallax (HP) is twice that of Venus, so current Earth-Venus distance is about twice the current Earth-Mercury distance. 2015 Nautical Almanac Commercial Edition mentions the two planets in its “Do Not Confuse” paragraph on page 8. Spreadsheets mercury.xls and venus.xls show that the geographic positions (GP) of the two planets are very close to each other at this time.



Venus-Jupiter conjunction of August 2014

As Frank Reed pointed in a recent NavList posting, Venus and Jupiter appeared close to each other in the morning sky of August 18, 2014, separated by about half a degree (30′, or by about the Moon apparent diameter). A quick use of spreadsheets venus.xls, jupiter.xls, and sailings.xls confirms this fact. The first two spreadsheets provide the planets’ ephemerides. The third one calculates the great circle distance of the bodies’ subpoints (geographical positions) in nautical miles, which is numerically very close to their angular separation in the sky in minutes of arc.



Additional details can be found on Steve Owens’s blog.

Five years of Navigation Spreadsheets

Navigation Spreadsheets logo
Navigation Spreadsheets

At the fifth anniversary of our website’s launch we review some of Navigation Spreadsheets functions.  All three examples are taken from the 2014 Nautical Almanac Commercial Edition.

1) Ephemeris (almanac data), Venus GP on 2014 May 5 at 13h 15m 18s (p. 256):


UT: 2014 May 5, 13:15:18

GHA = 58º 58.0’
Dec = S 0º 14.1’



2) Sextant altitude corrections (Venus, p. 259)

Input: Hs = 4º 32.6’
Output: Ho = 4º 17.6’



3) The calculated altitude and azimuth (pp. 279-280)

GP: GHA = 53º    Dec = S 15º
AP: Lat = N 32º    Long = W 16º
to which we add Ho = 30º 30.0’ in order to allow the calculation of the intercept and the plotting of the LOP.



The resulting LOP (intercept 38 NM away, azimuth 223) is plotted with the T-Plotter.




As it was also calculated by intercept.xls this LOP crosses:
the AP’s meridian at 52 NM north of the AP
the AP’s parallel at 56 NM east of the AP



(first published on February 15, 2014)

Example of a great-circle route

In a recent NavList thread titled “Great Circle Puzzle” it is revealed that a great-circle (i.e., straight, or, direct) sailing path exists between Pakistan and Russia.  This may seem impossible based on a quick look at the world map.  However, several NavList contributors established the end points and provided a general description of such a path.  Using these results it is possible to calculate this path in detail with sailings.xls and waypoints.xls spreadsheets:



If you have a globe handy, check it out!



For additional details see this post and the entire thread.

World map credits:

(first published November 3, 2013)

Advancing/retarding of position lines due to vessel motion

This sample problem created by Greg Rudzinski provides a nice illustration of the importance of accounting for vessel motion in order to obtain the best attainable accuracy for the many-body fix.  The first plot shows the three LOPs computed and plotted at their respective times (i.e., ignoring vessel motion) forming a small triangle (“cocked hat”):



In the second plot these LOPs were adjusted for vessel motion, i.e., the were advanced/retarded as needed to a common moment in time).  As a result, the previously plotted cocked hat tightens to a pinwheel:



There are several methods to advance or retard LOPs in time (see, for example, running fix). In this plot the LOPs were shifted by recalculating their intercepts with the formula presented by Gary LaPook ( change ~ time × cosine( azimuth – course ) ) and implemented in spreadsheet alt_move.xls.

In the following illustrative calculation of Ho adjustment, the distance traveled is DR = 1 mile, the course and azimuth differ by 60º, therefore the Ho (and, in the end, the intercept and LOP location) changes by 0.5′ ( = 1 mile × cos 60º ).




(first published on July 6, 2013)

Ex-meridian latitude calculation

A meridian transit observation allows the determination of latitude by simple arithmetic – spherical trig is not needed in this case.  For example, a noon altitude of 40º (i.e, zenith distance of 50º) of the sun with declination of S 20º observed due south from the northern hemisphere translates into latitude of N 30º (= -20º + 50º).

If, however, this altitude was observed not quite at the time of local apparent noon (LAN) but, say, 10 minutes before or after LAN, then this observed altitude is slightly less compared to what it otherwise would have been, had it been measured at LAN.  As a result, in our example, the LAN zenith distance is lower than 50º by a certain small amount, which means that the latitude is N 30º minus that value.  In cases like these it is still possible to avoid a more complicated calculation with the use of Bowditch Tables 24 and 25 to compute this small correction.  Alternatively, one might use the ex_meridian.xls spreadsheet to find that, in this example, the correction amounts to 3.5′, resulting in latitude of N 29º 56.5′.


(first published on April 14, 2013)

Many-body celestial fix for a moving vessel

In a recent NavList posting Jeremy provided a set of high-quality real-life observations that can be reduced to a celestial fix for his vessel at a specified moment in time.  The application of Navigation Spreadsheets to this data set results in a very good fix, both by direct computation as well as by plotting.

The following table shows the computed ephemeridescorrected sextant altitudes, line-of position (LOP) characteristics for two choices of an assumed position (AP), and the accounting of vessel motion through dead reckoning (where the mini-spreadsheet time.xls was used to express the time intervals in decimal hours).


The fix at 19:00:00 local time (= 11:00:00 UT, since ZD = -8) is computed to be:
Latitude: N 8º 49.0′
Longitude: E 109º 45.2′

from the many_body_fix.xls spreadsheet:


This location is marked by a black square on the two subsequent plots.

The first plot uses the VSOP plotting sheet (scale 20 nautical miles per inch) with AP at N 9º and E 110º.  The LOPs were drawn with a T-Plotter.  The LOPs in this plot are not shifted by DR.



The second plot “zooms in” with the scale of 1 NM per centimeter to get a more accurate look.  The reference AP is N 8º 50′ and E 109º 40′, which has been individually shifted for each observed celestial body along the vessel’s track (037) in order to account for the motion of the vessel.



The results are excellent, with all LOPs running within a mile of the computed fix.

In the above procedures all LOPs were treated as equally valid.  The fact that there are pairs of LOPs that run nearly parallel to each other complicates matters somewhat.  The GPS fix given by Jeremy:

Latitude: N 8º 48.4′
Longitude: 109º 45.0′

is recovered almost exactly (both by computation and by plotting) if only Jupiter, Rigel, and Fomalhaut LOPs are used.

For comparison, Jeremy’s position is marked by the square in Google Earth at the top of this post.


(first published on March 8, 2013)

Celestial line of position with the T-Plotter

The recent addition of a protractor to the T-Plotter makes it a fully self-contained tool for plotting of celestial LOPs, as is shown in this demonstration video.  It is important to note, that the use of the T-Plotter is not limited to the scale of 20 nautical miles per inch printed on the instrument.  It is always possible to read off the equivalent number of tics from the latitude scale of any chart according to the picture below.



(first published on December 20, 2012)