NavList:

Dear Andrés and Rick,

Very good Andrés that you have identified here the SIMPLIFIED SOLUTION used by celestial_navigation_pi-master.zip , i.e. Jean Meeus' book "Astronomical Algorithms".

For Rick:

(1) - Resulting from in-depth talks I had face to face with late Mr Pierre Bretagnon for the SUN and PLANETS and with now retired Mr and Mrs Jean & Michelle Chapront for the MOON - the following is a good estimate of the expected accuracy you can achieve if you use this full simplified solution.

(1.1) - PLANETS

VSOP87 yields the Heliocentric Coordinates in the 2000.0 Ecliptic .

To get Geocentric Apparent Equatorial Coordinates comparable to Nautical Almanac (NAL), you then need to perform Precession, then Nutation, then correction for relative movement between Body and Earth (light time correction).

1.1.1 - For the SUN itself, the smallest term published for SUN Ecliptic Longitude is #64 with an amplitude of 25 * 10-8 Radian, i.e. 0.05" . Then at 4 sigma, 99.98% of the resulting heliocentric coordinates can be expected to be accurate to +/- 1" for both Heliocentric Ecliptic Coordinates. The same +/-1" accuracy holds as well for the SUN Geocentric Equatorial Apparent Coordinates (Apparent = corrected for relative body motion) with the latter being directly comparable to the ones in the NAL.

Remember : this +/- 1" accuracy level is achieved if and when using the full simplified solution given in Jean Meeus' book ... requiring for these VSOP87 R,L,B series to be adequately truncated in a consistent manner between them to achieve the same level accuracy on all 3 coordinates, as explicitly mentioned by Jean Meeus.

1.1.2 - For VENUS, the smallest published Ecliptic Longitude Term is #24 at 0.22" . Then Venus Heliocentric Longitude can be expected to be always (4 sigma) equal or better than 2" . Seen from the Earth in the most unfavorable conditions, - i.e. when its geocentric distance is minimum at 0.264 UA - the Venus Geocentric Longitude should be always (4 sigma) equal or better than +/- 8" yielding equatorial coordinates always better than +/- 8"

1.1.3 - For MARS, smallest Ecliptic Longitude Term at 0.21", yielding Heliocentric Longitude accurate to +/- 4" at 4 sigma. Under the most unfavorable conditions when Mars geocentric distance is minimum at 0.37 UA, its Geocentric Longitude as well as its Geocentric Equatorial coordinates should always (4 sigma) be equal or better than +/- 12"

1.1.4 - For JUPITER, smallest Longitude term at 0.22", Heliocentric Longitude expected to be better than +/-5". Minimum Geocentric distance at 3.9512 UA and minimum Geocentric Equatorial coordinates expected to be at +/- 8"

1.1.5 - For SATURN, smallest Longitude term at 0.22", Heliocentric Longitude expected to be better than +/-6", Minimum Geocentric distance at 8.04 UA yielding minimum Geocentric Coordinates expected to be at /- 8" equally.

For SUN and PLANETS, we can achieve accuracies almost as good as the NAL ones.

(1.2) - MOON

The Moon coordinates are computed and published in the Mean Ecliptic of Date since this is the natural plan in which the MOON moves. No need for Precession then. Only perform Nutation and light time correction.

Smallest published Longitude term at 294 10-6 Degree, i.e. 60.6" . Hence overall expected accuracy for the Moon Equatorail Apparent Coordinates should always be +/- 12' (Arc minutes !) which is certainly insufficient for Celestial Navigation.

If you intend rather to match NAL accuracy at +/- 6" on Coordinates (including Horizontal Parallax) you better use the more complete Table Simplifiée and retain all its terms bigger than 0.25" for both Longitude and Latitude and 10 km for distance.

(2) - STARS

Jean Meeus book referenced here-above also gives detailed information on the way to compute apparent equatorial coordinates. The current Star catalog source for the Stars is the Hipparcos Catalog. The more recent Gaia catalog is better, but for 6" accuracy Hipparcos is already an overkill.

(3) - Use for celestial Navigation

Rick, once you have performed all the operations here-above, you should have at hand a solid tool which should favorably compare to the NAL.

You are left with only the heights corrections procedure and solving the "Observer's Latitude /  Body Local Hour Angle / Body Declination" well known triangle required to compute Intercept/Azimut (Marcq Saint Hilaire LOP Method) and there are plenty of excellent sources to explain that.

As a final note, yes, I would also fully endorse Andrés' view point : it is more expensive to modify the code than to start over to achieve the required accuracy  .

Accuracy has been addressed here-above in adequate detail because there is almost no similar or equivalent published information of this kind - anywhere - I know of.

Big task ahead.

The great advantage of Jean Meeus book also comes from all its detailed published numerical examples, a must for step by step software checking.

Good Luck ! And

Very Best Regards

Antoine M. "Kermit" Couëtte   antoine.m.couette[at]club-internet.fr