The demo program ecliptic_of_date.py shows how to
calculate the true ecliptic of date (ECT) angular coordinates
of the Sun, Moon, and planets for an observer somewhere on the Earth.
It calculates the equatorial of date (EQD) coordinates, then uses
a rotation matrix to convert the vector to ECT, then converts
the vector to spherical coordinates: latitude, longitude, and distance.
Applying the same recent fixes to C and C# to the Python code.
I'm also changing my philosophy of representing times.
From now on, they will be truncated to the floor millisecond,
not rounded to the nearest millisecond. This means we don't reach
another calendar date until we have had 60 full seconds after
the last minute. Otherwise there is too much nasty logic for
rounding up calendar dates. I will follow suit across all languages.
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 ported the NOVAS C 3.1 functions julian_date and cal_date to Python,
and removed the dependence on the standard datetime class for calculating UT.
Now we can create Time objects for a much wider range of year values.
Simplified the julian_date formula in C and C#.
In the Python version, I had to account for a difference
in the way integer division works for negative numbers.
In Python, integer division always rounds down, not toward
zero like it does in C/C#. So I reworked the formulas to
avoid dividing a negative integer (month-14), dividing the
positive quantity (14-month) instead and toggling addition
of the term with subtraction of the term.
I use the reworked (14-month) version in C and C# for consistency.
Also, the formatting of the formula was wacky and didn't make sense,
so now it easier to read and understand.
The Python regex for parsing dates has been expanded to allow
years before 0 and after 9999.
Allow converting Python Time to string for years before 0 and after 9999.
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.
