## How far from earth is a star? What is Parallax?

This short intro on the concept of parallax is required in order to understand how brightness can be measured for NEARBY stars. The problem is that distances are useful to calculate many astronomical features of stars like luminosity, mass, motion/velocity and size, but distances are very hard to measure. With current technology, given a specific measurement precision, we are basically constrained to stars in our local neighborhood and within the Milky Way.

Literature often use parsecs or ‘pc’ in order to talk about distances. One pc is equal to 3.26 ly. Using parallax is to apply a form of stereoscopic vision, extended by Earth’s orbit, to measure distances to nearby stars. The brain judges distances to objects by comparing the view from the left eye with the view from the right eye. Similarly, if you use the changing perspective of Earth through the year, you can approximate the distances to nearby stars. For example, one can take one picture of a night sky region today and then, wait 6 months and take one picture again of the same region. One can also use two telescope at opposite sides of the earth and observe the same region of the night sky. After comparing the two pictures, some stars will have shifted positions, this is called the ‘parallax’.

In the figure above, with ‘AB’ being the earth diameter and ‘Parallax’ being 2 times the angular parallax, and ‘d’ the distance to the object from the earth center. The angular parallax (p) is equal to and for small angles:

$\sin p \sim p= \frac{AB}{2} / d$

Instead of taking two points on earth, if you take the measurements during summer and winter on the earth orbit. With 1 AU/astronomical unit being the mean distance earth-sun: AB = 2 AU, so the equation becomes:

$d = \frac{1}{p}$

The units are distance in pc (3.26 ly) and p in arcsec (1/3600 degree). The angular parallax (p) is inversely equal to the distance (d) to the star. Therefore, this method does not work in practice for stars that are very far away.

Experimentally, earth-based telescopes can only achieve a parallax measurement of minimum 0.01 arcsec due to the effects of earth’s atmosphere and only 100 stars are within this range of detection from the earth. One satellite/space-based telescope (Hipparcos) has been used to measure the distance to many more nearby stars. Hipparcos stands for High precision parallax collecting satellite and also a reference to the ancient Greek astronomer Hipparchus, the catalogue it produced includes parallax measurements for 100000 stars, with an accuracy of about 0.002 arcsec.

The follow up mission Gaia, is an ESA mission to survey one stars in our galaxy and local galactic neighborhood, in order to build the most precise 3D map of the Milky Way and answer questions about its origin and evolution. The mission’s primary scientific product will be a catalog with the positions, motions, brightness, and colors of the surveyed stars. The nature of the Gaia mission leads to the acquisition of an enormous quantity of data, and the data-processing challenge is a huge: the mission states that about 20 million stars will be measured with a distance precision of 1% and about 200 million will be measured to better than 10%. Distances accurate to 10% will be achieved as far away as the galactic center, 30000 ly away.

To end this post, it is important to stress that parallax is not the only way to measure the distance of stars from earth. There are actually 3 other methods: color/spectroscopy, variable stars and supernovas. The former method can be applied to any stars but it is not very accurate due to matter from the ISM interfering with the measurements. The latter two methods are only applicable to few stars which have specific properties. In the next posts I will introduce these other methods.