Does parallax measurement depend on position in the sky Naturally, the parallax is easier to measure for stars that are closer than farther away. But if all stars were the same distance from the Sun, and if there were some other reference to measure the parallax, would all stars show the same parallax?
In other words, does the position of a star (the right ascension and declination) affect the parallax measurement and calculation? For example, are stars near the ecliptic or equator or celestial pole easier to measure than other locations on the sky?
Feel free to include any equations or references if it helps.
It's all about basic geometry.
Base for the parallax measurements is Earth's orbit around the sun, giving you a maximum of 300 Mio km. With a given base dimension, you get the best precision when the base is orthogonal to the star direction. (In the other extreme, you get no parallax at all if the base is in line with the star).
For stars close to the ecliptic you get this optimum base angle only using two specific dates, half a year apart from each other (those when the star appears 90 degrees distant from the sun).
For stars nearly perpendicular to the ecliptic, you can choose any two dates half a year apart, giving you more chances to contribute max-precision measurements.
If doing a continuous observation of the star over e.g. a year, the difference should amount to a factor of sqrt(2), if the other parameters are comparable.