Coding classes in North Ayrshire

Astronomers locate stars with two angles, much like longitude and latitude on Earth: right ascension and declination. The trouble is that these are measured from the Earth's axis and equator, and the axis slowly wobbles, completing one circuit in roughly 25,800 years. So a star's coordinates change even when the star itself barely moves. The learner takes six bright stars from the Bright Star Catalogue, with positions for the epoch 2000, turns each into an arrow in 3D, and applies the standard precession formula, three rotations multiplied together into a single matrix, to rotate the sky back to 1638.

Look at the columns. In the usual equatorial coordinates the changes are all over the place: Polaris, close to the celestial pole, swings nearly 31 degrees in right ascension, while Vega moves just 3. But measured along the Sun's path, the ecliptic, every star shifts by the same 5.05 degrees, and their distance from that path hardly changes at all, never more than 0.007 degrees. That is because precession is really a slow rotation about the pole of the ecliptic. Pick the right coordinate system and a messy problem becomes one number. The check is simple arithmetic: about 50.3 arcseconds a year, the rate astronomers use, times 361.5 years gives 5.05 degrees.

The learner also tries a shortcut: shift every star's right ascension by the same average amount and leave declination alone. It looks reasonable and is wrong by between 1 and 2 degrees for these stars, four times the width of the full Moon at worst. A rotation matrix keeps lengths and angles exactly, which the learner can confirm: its determinant comes out as 1.

Knowing whether a formula is exact or just a shortcut is exactly why North Ayrshire teenagers should keep learning to code in 2026. The longer argument is in why teenagers should still learn to code in 2026.