This function is a generalization of Astronomy_LongitudeFromSun,
which it replaces. It calculates the relative ecliptic longitude of one body
with respect to another body, as seen from the Earth.
After implementing the same function in C#, JavaScript,
and Python, I will come back and create a generalized
search algorithm to find the next time two bodies are
at a given apparent relative longitude. Even though this
is a generalization of SearchRelativeLongitude, I will have
to figure out a more general way of tuning the search.
Before making these changes, I had the following discrepancies
between the calculations made by the different programming
language implementations of Astronomy Engine:
C vs C#: 5.55112e-17, worst line number = 6
C vs JS: 2.78533e-12, worst line number = 196936
C vs PY: 1.52767e-12, worst line number = 159834
Now the results are:
Diffing calculations: C vs C#
ctest(Diff): Maximum numeric difference = 5.55112e-17, worst line number = 5
Diffing calculations: C vs JS
ctest(Diff): Maximum numeric difference = 1.02318e-12, worst line number = 133677
Diffing calculations: C vs PY
ctest(Diff): Maximum numeric difference = 5.68434e-14, worst line number = 49066
Diffing calculations: JS vs PY
ctest(Diff): Maximum numeric difference = 1.02318e-12, worst line number = 133677
Here is how I did this:
1. Use new constants HOUR2RAD, RAD2HOUR that directly convert between radians and sidereal hours.
This reduces tiny roundoff errors in the conversions.
2. In VSOP longitude calculations, keep clamping the angular sum to
the range [-2pi, +2pi], to prevent it from accumulating thousands
of radians. This reduces the accumulated error in the final result
before it is fed into trig functions.
The remaining discrepancies are largely because of an "azimuth amplification" effect:
When converting equatorial coordinates to horizontal coordinates, an object near
the zenith (or nadir) has an azimuth that is highly sensitive to the input
equatorial coordinates. A tiny change in right ascension (RA) can cause a much
larger change in azimuth.
I tracked down the RA discrepancy, and it is due to a different behavior
of the atan2 function in C and JavaScript. There are cases where the least
significant decimal digit is off by 1, as if due to a difference of opinion
about rounding policy.
My best thought is to go back and have a more nuanced diffcalc that
applies less strict tests for azimuth values than the other calculated values.
It seems like every other computed quantity is less sensitive, because solar
system bodies tend to stay away from "poles" of other angular coordinate
systems: their ecliptic latitudes and equatorial declinations are usually
reasonably close to zero. Therefore, right ascensions and ecliptic longitudes
are usually insensitive to changes in the cartesian coordinates they
are calculated from.
This change has no effect on client-facing behavior.
It just makes the internal data tables for the array of
constellation appear more compact in C, C#, and Python.
This is what the TypeScript/JavaScript code was already doing.
The demo shows how to correct for light travel
time to render Jupiter's moons as they appear
from the Earth.
Created an addition operator for the Vector
class in the Python code, because it is handy.
Corrected a bug in the string representation
of the Python StateVector class.
Now there are constants for the mean radii of Jupiter's
four major moons available in the C, C#, Python, and JavaScript
versions of Astronomy Engine.
Clarified that these are all mean radii.
Fixed some lingering "//" comments in the C code
(I want to keep ANSI C code as portable as possible.)
To assist software that wants to depict Jupiter and its 4 major moons
as they would appear in a telescope, it is important to know their
physical sizes. I already had constants for Jupiter's equatorial
and polar radii. Here I add constants for the radii of the moons
Io, Europa, Ganymede, and Callisto. They are all nearly spherical,
so a single mean radius value is sufficient.
My pydown.py custom Markdown generator was printing bogus
warnings about unknown symbol types, when it was actually
generating correct documentation for those symbols.
Eliminated the warnings, and improved the output format
for global constant documentation: no more extraneous spaces.
If there really is an undocumented symbol detected, fail the build!
Don't just print a warning that slides up the screen unnoticed.
Now callers can create time objects from either UT (UT1/UTC civil time)
or ephemeris/dynamical Terrestrial Time (TT). The new TT functions
numerically solve to find the UT that produces the given TT based
on the Delta-T value at that UT. This is always a very fast
numerical convergence, because TT and UT are almost perfectly
linear over brief time windows.
I increased the error tolerance slightly for the Jupiter moons model.
This shrank the model tables significantly, giving me some more
breathing room to stay under 100K download size.
I don't like how close I am to my 100K target size, now
that I'm calculating Jupiter's moons.
Simplified the spin() function so its minified code is smaller.
I will look for other things I can shrink too.
The optimizer makes the Jupiter moons series as short as
possible while keeping error within an acceptable limit.
This should help produce much smaller code, especially
for JavaScript where it really matters.
Output the Jupiter moon model data tables in a tidier format.
Format the amplitudes as fixed-point instead of exponential,
so that the JavaScript minifier will have an easier time
shrinking the data (later, when I get to the JavaScript version).
I translated the L1.2 FORTRAN code into C, and verified
that the calculations match the Stellarium code I modified
to produce EQJ coordinates. I still need to compare against
JPL Horizons data.
Work in progress.
Generating the data tables for Jupiter's moons, but not using them yet.
Created a stub function Astronomy_JupiterMoons(), but it just
returns invalid vectors. The formulas have not yet been implemented.
I am starting the process of implementing calculation
of Jupiter's four largest moons: Io, Europa, Ganymede, Callisto.
This commit just contains constant declarations for the
equatorial, polar, and volumetric mean radii of Jupiter.
The positions of the moons will be related to the center
of Jupiter and be expressed in Jupiter equatorial radius units,
so I felt it would be good to give users a way to convert to
kilometers, which can in turn be converted to AU.
Python docstrings don't work for variables, so I hacked
a special comment format for helping pydown generate Markdown
text for the README.md for the exported constant KM_PER_AU,
or any other constants I may want to expose in the future.
Also made time parameters to rotation matrix functions be of
type FlexibleDateTime, and internally convert them to AstroTime.
This should be the policy of all exposed functions in the
JavaScript version of Astronomy Engine.
Exposed KM_PER_AU to outside callers.
Use a private enumerated type to select which direction
the precession and nutation is to be done:
- from date to J2000
- from J2000 to date
Normalize the order of parameters to be consistent
between precession() and nutation(), and across languages.
Pass in AstroTime instead of a pair of floating point TT
values (one of which had to be 0).
Added TypeScript version of ObserverVector(),
but it has not yet been documented or tested.
It always seemed a little odd to have to pass in two
time values to the precession() function, when one of
them always had to be 0. I think the logic is clearer
now that I pass in an enum value to select whether I
want a forward transform or a backward transform.
It is cleaner that now I can just pass in an AstroTime.
Ported the ObserverVector function to C#, but it is not tested yet.
While doing that, I realized I needed a way to document newly public
constants DEG2RAD, RAD2DEG, and KM_PER_AU. This led to work
on the 'csdown' project that converts C# XML documentation
into Markdown format.
Then I realized a lot of code would be more elegant if
AstroVector had operator overloads for addition, subtraction,
and dot products.
This in turn required these operators to know which time value
to store in the AstroVector, which led to realizing that I
was sloppy in a lot of places and passed in null times.
So this whole commit contains a variety of unrelated topics,
which is something I don't usually do, but it felt
justified here while I'm in a refactoring mood.
The C functions that took a parameter of a pointer type
'astro_time_t *' were causing incorrect Markdown to be generated.
Now my custom Markdown translator (hydrogen.js) handles this case.
This function calculates the position of an observer on or
near the surface of the Earth (the geoid) in one of two
equatorial coordinate systems: J2000 or equator-of-date.
Moved the following constant definitions from astronomy.c
to astronomy.h, so external code can use them:
DEG2RAD
RAD2DEG
KM_PER_AU
My custom doxygen-to-markdown translator (hydrogen.js)
now emits markdown for the above constants.
Eliminated the obsolete constants MIN_YEAR and MAX_YEAR.
Astronomy Engine is no longer limited to calculating planets
within that range of years.
Fixed a couple of minor documentation issues in the C code.
Started work on a new function Astronomy_ObserverVector,
but it is just a stub for now.
Astronomy Engine used to use USNO historical and predictive tables,
along with linear interpolation, to calculate Delta-T values.
The problem with the USNO tables is, they did not work well outside
a few centuries around present day.
Later I replaced with Espenak & Meeus piecewise polynomials
that work over a much larger time span (thousands of years).
I just discovered there were still comments in the code referring
to the USNO models. I updated the ones I could find to reflect
the current truth about how the code works today.
This is technically a breaking change, but only for clients
that use the cartesian coordinates in an ecliptic coordinate
return type. Before now, the coordinates were just separate
floating-point members ex, ey, ez. Now they are a standard
vector type.
The purpose is to allow seamless interfacing with vector
rotation functions, and to be consistent with the equatorial
coordinate types.
Instead of declaring all the "body" parameters in the
TypeScript/JavaScript code to be strings, I created a
string-valued enumerated type called Body.
The same string values can still be passed in from JavaScript
code, or callers can use syntax like Astronomy.Body.Moon.
This improves the type checking inside the TypeScript source,
plus it adds better documentation for each of the parameters.
In the generated Markdown documentation, the user can click
on the Body type and see all the supported bodies.
The other three supported languages (C, C#, Python)
already use enumerated types for bodies, so this
brings the JavaScript version more in sync with them.
Now that equatorial coordinates include both angles
and cartesian coordinates, there is no need for the
VectorFromEquator function. It has been removed
from all four supported languages.
The expression "VectorFromEquator(equ, time)" can be
replaced with "equ.vec" in any calling code.
This caused me to discover I had forgotten to finish
making the necessary changes to astronomy.ts for saving
the cartesian vector inside the EquatorialCoordinates class.
I also realized I had made a mistake in the documentation
for the y-coordinate of the vector: it is the June solstice;
there is no such thing as a September solstice!
Also fixed some mistakes in demo tests: if something failed,
I was printing out the wrong filename (camera.c instead of camera.cs).
Added a C# demo program camera.cs that works the same way
as the C demo program camera.c.
I realized I can speed up the C# demo tests by directly
running the executables after I build them, instead of using 'dotnet'.
Added 'vec' field to Equatorial class. I just realized I no longer need
the function VectorFromEquator(), because the vector is now available
as 'vec'. I will get rid of it in another commit.
Created new rotation matrix functions for the C# version.
IdentityMatrix creates a new instance of the 3x3 identity matrix
1 0 0
0 1 0
0 0 1
Pivot transforms a rotation matrix by pivoting it about
one of its coordinate axes by a specified angle.
Still need to port the C version of the "camera" demo.
