What Is Parallax – Definition of Parallax

Access list of astrophysics formulas download page:

What is Parallax?

Before answering this question, we point out that the main objective in astronomy and astrophysics in studying parallax is to understand how it can be used to measure distances from the Earth to nearby stars. It is known as the method of parallax for determining distances.

Parallax Effect

What Is Parallax? Definition of Parallax in astronomy is a specific case of the parallax effect in general. The phenomenon, stellar parallax, refers to the apparent shift of the target (e.g., a star) against a fixed background of objects (e.g. other stars) that are much further away than the target (relative to the observer) as observer changes her observation position. The larger the difference in distance between the two observations posts, the larger is the apparant shift (i.e., the parallax). The shift is measured in terms of angle rather than the length of line tracing the shift of the target against the background. In other words, what angle does a ray between the observer and the target have to turn through in order to go through a fixed point in the background? Measuring this angle from the two observations posts and taking the difference gives a certain angle, and the parallax angle is formally defined as half of this angle. The distance between the two observation posts is measured and then lines joining the target star to the two observation points gives a simple trigonometric problem. The parallax angle will be very small because the distance to the nearest start is so much larger than the largest observation baseline separation for Earth-bound measurements (i.e., it is the “diameter” of the Earth’s orbit around the Sun if the measurements are made from the position on Earth but separated by six months or so). Since the parallax angle, $\theta$, is small, we can say

$\tan{\theta} \sim \frac{x}{d} \sim \theta \sim \sin{\theta}$

where $x$ is the half of the baseline seperation distance of the two observations, and $d$ is the distance between the observer and the target star. Once the relation has been calibrated with absolute distances we can use the convenient units of the parsec (or pc) for distances to stars (etc.). The parsec is defined so that a distance of 1 parsec is actually equivalent to a parallax angle of 1 arcsecond (or [1/3600] degrees):

$d = \frac{1}{{\rm parallax} ({\rm in \ arcseconds})} \ \ {\rm pc}$

Spectroscopic Parallax

This refers to the method of measuring the distance to a star by means of deducing the stellar temperature from its spectrum, calculating its absolute luminosity from that based on stellar models, and then comparing with the apparent magnitude to deduce the distance (since the luminosity is diminished by the inverse square law). The method actually has nothing to do with parallax, despite its name.