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.
Given the right ascension and declination of a star,
expressed in J2000 coordinates, this demo converts those coordinates
to right ascension and declination expressed in the Earth's
equator at any given date and time. This example illustrates
how to use rotation matrices to convert one coordinate system
to another.
This example was prompted by the question at:
https://github.com/cosinekitty/astronomy/discussions/114
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).
