Precision of internal calculations
==================================

MountWizzard4 is using for all calculations the skyfield 
(https://rhodesmill.org/skyfield/) from Brandon Rhodes. As for the new command 
set offered with 10microns FW3.x it needs to calculate the alt/az coordinates 
for a satellite track each second for the entire track. As you would like to 
follow the as precise as possible I made some comparisons between the internal 
calculations done in 10micron mount and the results provided by skyfield.

In skyfield there is a chapter about satellite calculations and precision:
https://rhodesmill.org/skyfield/earth-satellites.html#avoid-calling-the-observe-method
Despite the fact that the observe method is expensive the difference in calculation
time for a 900 step track is on my computer 120ms (using more precise observe
method) to 7ms (using the less precise difference).

Brandon writes about it:

.. epigraph::

    While satellite positions are only accurate to about a kilometer anyway,
    accounting for light travel time only affected the position in this case by
    less than an additional tenth of a kilometer. This difference is not
    meaningful when compared to the uncertainty that is inherent in satellite
    positions to begin with, so you should neglect it and simply subtract
    GCRS-centered vectors instead as detailed above.

Here the charts for NOAA 15 [B] at julian date JD=2459333.26498 for the transit
happening. The used TLE data was:

.. code-block:: python

    NOAA 15 [B]
    1 25338U 98030A   21104.44658620  .00000027  00000-0  29723-4 0  9990
    2 25338  98.6888 133.5239 0011555 106.3612 253.8839 14.26021970192127

You could see the alt/az of the sat track.

.. image:: image/sat_track.png
    :align: center

the difference for altitude between 10micron and skyfield

.. image:: image/sat_altitude.png
    :align: center

the difference for azimuth between 10micron and skyfield

.. image:: image/sat_azimuth.png
    :align: center

the difference for right ascension between 10micron and skyfield

.. image:: image/sat_ra.png
    :align: center

the difference for declination between 10micron and skyfield

.. image:: image/sat_dec.png
    :align: center


There is a set of plots for another satellite, which shows the same behavior. The
used TLE data was:

.. code-block:: python

    RAAVANA-1
    1 44329U 98067QE  21134.29933328  .00044698  00000-0  30736-3 0  9995
    2 44329  51.6342 100.9674 0004554 122.3279 237.8162 15.74179130108776

You could see the alt/az of the sat track.

.. image:: image/sat2_track.png
    :align: center

the difference for altitude between 10micron and skyfield

.. image:: image/sat2_altitude.png
    :align: center

the difference for azimuth between 10micron and skyfield

.. image:: image/sat2_azimuth.png
    :align: center

the difference for right ascension between 10micron and skyfield

.. image:: image/sat2_ra.png
    :align: center

the difference for declination between 10micron and skyfield

.. image:: image/sat2_dec.png
    :align: center

For all calculations is valid:

- they are using refraction correction with the same values.

- the coordinates from 10micron are gathered with :TLEGEQJD#, :TLEGAZJD# commands

- julian date is in UTC time system

- 10micron firmware 3.0.4

- skyfield version 1.39