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The biggest oscillation in the positions of the stars is "stellar aberration" or "aberration of starlight". It can be a surprise to celestial navigators since it's hidden in the tables. The Wikipedia article is over-detailed but useful: https://en.wikipedia.org/wiki/Aberration_of_light.

As the Earth travels around the Sun, all stars, especially those generally perpendicular to the direction of the Earth's travel in any season, are shifted forward (towards the Earth's direction of motion) by an angle equal to the ratio of the Earth's speed around the Sun relative to the speed of light: (30km/s)/(300,000km/s) or 1/10,000 as a pure angle which can be converted to minutes of arc by multiplying by 3438 which gives 0.34'. This shift is reversed about six months later for any given star. Note that if the Earth were simply gliding along in a straight line, there would be no detectable change. The annual range then is twice that 0.34' or 0.68'.

This aberration is measurable even with an average sextant. Find a pair of stars about 80° apart, one of which is near the ecliptic, opposite the Sun. Regulus works well. The other can be wherever is convenient, and the North Star fits the bill. Measure the angle between them in early May. Then come back six months later. You should be able to detect the change in angular distance between them without much trouble. With this observation, you are detecting and measuring the speed of light. Cool, right?

Note that there's no detectable annual parallax. None of the true stars are close enough for that to matter in celestial navigation. The distance where annual parallax is one second arc (and beyond which observable parallaxes are less than one second of arc) is called a parsec and is approximately 3.26 lightyears or 19 trillion miles or 3438·60 AUs (where 1AU, astronomical unit, is the mean distance from the Earth to the Sun). There are no stars closer than this, so all stellar parallaxes are less than a second of arc --unmeasurable with a sextant.

The existence of aberration is the primary reason why the positions of the stars are listed at every opening of the Nautical Almanac (once every two weeks would really be sufficient but for convenience they're listed at every opening, every three days). That's "hidden in the tables" as I noted above. If there were no stellar aberration, almanacs might be designed to give the positions of the stars on January 1 with monthly changes for precession and proper motion alongside. And if changes in position less than 0.5 minutes of arc are counted as irrelevant, that's a viable approach.

Frank Reed