Stellar Parallax

Stellar parallax is the apparent shift in the position of a nearby star against the background of much more distant stars, caused by the Earth's motion around the Sun.The position of the star is measured, and then measured again six months later, when the Earth is on the opposite side of its orbit. The baseline between the two observations is 2 AU. The parallax angle p is half the angle through which the star appears to move, so it is the angle subtended at the star by a baseline of 1 AU (the Earth-Sun distance).For such tiny angles, the small-angle approximation (tan p ≈ p in radians) gives d = 1 AU / p. When p is measured in arcseconds and d in parsecs, this becomes simply:p = 1/dwhere p is the parallax angle in arcseconds and d is the distance in parsecs. This follows from the definition of the parsec: a star with a parallax angle of 1 arcsecond is 1 pc away.Worked example: a star has a parallax angle of 0.25 arcseconds. Find its distance.
d = 1/p = 1/0.25 = 4.0 pc
d = 4.0 × 3.1 × 10¹⁶ = 1.2 × 10¹⁷ mParallax angles are very small (every star has p less than 1 arcsecond), and the atmosphere blurs images, so the method only works for relatively nearby stars. Telescopes in space, such as the Gaia satellite, can measure much smaller angles and so reach stars that are further away.