Astronomical Algorithms, Tables of Meeus

[Gil]

Question

Has somebody implemented, on a pocket calculator or computer, the tables given by Meeus at the end of his book Astronomical Algorithms, 1991, for the abridged version of VSOP87?

Regards,
Gil

[Felix Gross]

This may help

http://www.naughter.com/aa.html

I have not used that code but I want to (at one point...). Therefore, I would be interested at your feedback.

Felix

[PedroLeiva]

What an interesting project! I would like to ask for which calculator model are you planning to program? Pedro

[Gil]

The book is really a "must", with full detailed formulae and examples.

I used it to implement the formulae relative to my EPHEMERID.4XI.D.HP program (formerly for Earth ecliptic, nutation, Julian Dates, seasons) on my HP50G (EMU48 version).

Jean Meeus gives 3 ways to calculate the season.
I chose the intermediate one, that gives DT results within 50 seconds of precision.

I tried to use his abridged tables, but there I get some small differences with the results given by the author. It's strange, because normally all the working examples should be exact to the last but one digit.

Regards,
Gil

[Klaus]

Years ago I wrote a program on the HP50 that uses the Meeus shortened VSOP. Running time, for example for Venus ~2.5 min
Later, with NewRPL for the HP50, a program with the complete VSOP theory.
Running time, e.g. for Venus under 1 min
Programs are not mature and can still be optimized and run with an inserted SD card.

[Gil]

Interesting, indeed.
A lot of work, sure.

As I am no astronomer, I just used some of the given algorithms.

I used, in particular, the ones given for the axial tilt and tropical year.

Then I found some newer, for example contacting directly IMCCE.

When trying to improve the seasons calculations (my prior version being based on simplified Meeus' algorithms, with results correct to about 10-50"), now with tables given by Meeus at the end of his book, I mixep up different theories.

A very bad idea!

With this confusion, I could not find (of course) the exact result given by Meeus
(normally within 2-3" in within with apparent sun longitude = k×90) with his Bretagnon's simplified tables.

Fortunately, I understood my error... including two digits inversions.

Therefore, soon I will be able to publish a new version of EPHEMERID, with quite accurate seasons begins, in both TT/DT & UT, with an error of about 2-3".

Regards,
Gil

[HP67]

I found the sunrise/sunset algorithm here https://edwilliams.org/sunrise_sunset_algorithm.htm

valuable and implemented it in FORTRAN IV, modern Fortran, and on the 50g.

I like Meeus' books, but I haven't coded from his examples.

The position of the moon looks interesting.

[Gil]

Have you checked with official, exact values as given for example by IMCEE?

Skimming through the formulae, it all seems to give a very rough idea of the exact sunrise and sunset tines, nothing then to be compared with what you might find in Jean Meeus' book Astronomical Algorithms.

Regards,. Gil