# parallax

Parallax is the apparent change in position of a relatively close object compared to
a more distant background as the location of the observer changes. **Annual
parallax** is the change in the apparent position of a star resulting
from Earth's annual motion around the Sun; it is defined as the angle subtended
at the object by the semimajor axis of
Earth's orbit.

The largest parallax known for an object outside the Solar System is that
of the nearest star, Proxima Centauri,
0.762"; the first stellar parallax to be measured was that of 61
Cygni. Knowing the parallax *p* of a star in arcseconds, it is
a simple matter to work out the star's distance *d* in parsecs:

*d* = 1/*p*

In the case of Proxima Centauri, *d* = 1/0.762 = 1.31 pc. Multiplying
this by 3.26 gives the distance in light-years (4.28 light-years).

There are other ways to measure a stellar distances, which, though not involving trigonometric parallax, are still referred to as varieties of parallax.

**Spectroscopic parallax** is the most widely used
technique for determining the distances of stars that are too distant for
their trigonometric parallaxes to be measured. From an analysis of a star's
spectrum, its position is determined on the Hertzsprung-Russell
diagram, which gives the absolute
magnitude. By comparing the star's absolute magnitude with its apparent
magnitude, its distance follows directly. **Dynamical parallax** is a method for determining the distance to a visual binary
star. The angular diameter of the orbit of the stars around each other
and their apparent brightness are observed. The distance comes from an application
of Kepler's laws of planetary motion
and the mass-luminosity relation.

The **mean parallax** is the distance, derived by means of statistical studies of brightnesses and motions, for a group of stars whose individual distances are unmeasurable.