I'm getting much better accuracy sticking with my original
gravity simulator, just with smaller time increments, than
I was with the Runge-Kutta 4 method. The PlutoStateTable
gets a bit larger (51 state vectors instead of 41), but the
accuracy is so much higher.
Removed the Runge-Kutta code because I won't be going back to it.
Reworked the Pluto gravity sim constants so they are defined
in one place: a new header file gravsim/pluto_gravsim.h.
Then the code generator writes the #defines to the C code, instead
of having two independent versions of the same constants.
I will continue down the road of having a single-source-of-truth
for these constants across all 4 supported languages.
Also, confusingly, I had one constant called PLUTO_DT in codegen.c
that was called PLUTO_TIME_STEP in astronomy.c. Also, astronomy.c
had a different constant PLUTO_DT that didn't mean the same thing.
I reworked the naming to be consistent in all places.
I already had a TopPosition() function that knows how to calculate
exact equatorial coordinates, so I eliminated the redundant logic
from gravsim_test.c
Significantly decreased the calculation error:
0.20 arcmin to 0.12 arcmin in my test metric.
However, the amount of extra work may not be
worth the accuracy, compared to just stepping more
increments between the segments, or simply making
more segments in the first place.
As they say in government-funded academia,
"more research is needed."
I have gravsim_test.c to the point where it calculates a
standard deviation of error between TOP2013 and Astronomy Engine
for calculating the position of Pluto over 10 worst-case samples.
My baseline is now 0.205303 arcminutes of heliocentric position error.
For Runge-Kutta (or some other method) to be an improvement, it
has to beat that score without incurring significant extra work
or larger memory consumption.
I updated gravsim_test.c to calculate the Pluto model
at every (exact) state table entry, and every halfway point.
I compare it against (exact) TOP2013 calculations.
As expected, the errors alternate between 0 and nonzero.
I'm trying to get a better feel for the amount of error
in my gravity simulator calculations for the movement of Pluto.
Added conditionally-compiled code to log state vectors calculated
in the forward and reverse time directions, along with the
exact endpoints that frame the interpolated values.
Also log errors measured between both directions.
There is a curious asymmetry in the first case I tried
(roughly the years 2000..2100), where the forward calculation
seems less accurate than the reverse calculation.
