It was possible for certain starting times to have a search
failure in this demo, because it could place more than
one zero-crossing of the function in the same time interval.
So now we iterate over an interval of 10 days at a time
until we find the solution.
This demo shows how to search for the next time
the Moon reaches extreme ecliptic latitude or
extreme declination. In other words, it finds
when the Moon reaches the farthest north or south,
expressed in either ecliptic coordinates or equatorial
coordinates.
Both angles are measured using the Earth's equator of date.
While trying to convert ecliptic coordinates from mean
equinox of date to true equinox of date, I ran into excessive
overhead from the IAU2000B nutation model. The fact that it
uses 77 trigonometric terms made the calculations a lot slower.
https://apps.dtic.mil/sti/pdfs/AD1112517.pdf
Page 4 in the above document mentions a shorter series
“NOD version 2” that has 13 terms instead of 77 as used in IAU2000B.
I had not noticed NOD2 before, because it appears only in
the FORTRAN version of NOVAS 3.x, not the C version.
After reading the FORTRAN code, I realized NOD2 is the same
as IAU2000B, only it keeps the first 13 of 77 terms.
The terms are already arranged in descending order of
significance, so it is easy to truncate the series.
Based on this discovery, I realized I could achieve all of
the required accuracy needed for Astronomy Engine by
keeping only the first 5 terms of the nutation series.
This tremendously speeds up nutation calculations while
sacrificing only a couple of arcseconds of accuracy.
It also makes the minified JavaScript code smaller:
Before: 119500 bytes.
After: 116653 bytes.
So that's what I did here. Most of the work was updating
unit tests for accepting slightly different calculation
results.
The nutation formula change did trigger detection of a
lurking bug in the inverse_terra functions, which convert
a geocentric vector into latitude, longitude, and elevation
(i.e. an Observer object). The Newton's Method loop in
this function was not always converging, resulting in
an infinite loop. I fixed that by increasing the
convergence threshold and throwing an exception
if the loop iterates more than 10 times.
I also fixed a couple of bugs in the `demotest` scripts.
I refactored the unit tests for all the demo programs
to follow a different pattern that makes it simpler
to add more demo tests in the future.
The main thing is that correct output and generated
output are now in separate directories `correct` and `test`.
I have moved the test scripts from `test/test` to `./demotest`
in all the langauge demo directories.
This makes it simpler to clean up any stale generated
files before each test run by `rm -f test/*.txt`.
I stumbled across this while making the Java demo tests,
and it was a better solution, so now all the other languages
are consistent with the Java demo tests.
In the C demo tests, I also decided to compile all the
binary executables into a subdirectory `bin` that can
be cleaned out before each run, to make sure there are
no stale executables from an earlier run.
