Bessel to Gaia: Parallax comes full circle

Königsberg Observatory (left) where Friedrich Wilhelm Bessel made the first successful distance measurement to a star other than the Sun (Credit: Wikipedia).  The Gaia satellite (right) which has determined the distance to millions of stars to high degree of accuracy (Credit: ESA/ATG medialab; background: ESO/S. Brunier). 

By Dirk Goës BSc(CompSc) UOW, MSc(Astronomy) Swinburne

The observation phase of the European Space Agencies (ESA) groundbreaking Gaia mission ended on 15th January 2025. One of Gaia’s key capabilities was being able to accurately measure the distance to millions of stars using the technique of parallax. Parallax was first used to successfully measure the distance to a star, other than the Sun, in 1838 by astronomer Friedrich Wilhelm Bessel. In acknowledgement to Bessel’s pioneering work, the Gaia mission’s final image is of binary star ‘61 Cygni’, the same star system Bessel used to make his measurement.

It took Friedrich Wilhelm Bessel several years of painstaking observations to calculate the parallax of 61 Cygni whereas the Gaia space-based telescope was able to calculate the parallax of approximately two billion stars in a decade of observations. 

Figure 1: A false colour image of the binary star system 61 Cygni.  This is the final image from the Gaia mission and was taken on 10th January 2025 (Credit: ESA/Gaia/DPAC). 

What is parallax?

Parallax is a method of triangulation, and it relies on being able to measure the angle of a star’s movement across the sky against a more distant background star.  Measurements are made six months apart from opposite sides of Earth’s orbit around the Sun.  This allows a right-angled triangle to be drawn where one side is known (the Earth-Sun distance) and one angle is known (the measured angle of parallax).  The distance can now be calculated using simple trigonometry. 

While the maths is relatively straightforward, measuring parallax angles is difficult because they are so small.  Proxima Centauri, the closest star to the Sun has a parallax angle of less than one arcsecond.  An arcsecond is 1/3600 of a degree.  Proxima Centauri has a parallax angle of ~768.07 milliarcseconds (mas) which gives a distance of 4.24 light years from the Sun.  61 Cygni has a parallax angle of ~287.18 milliarcseconds (mas) which gives a distance of 11.35 light years from the Sun.

Figure 2: The geometry of calculating parallax.  A relatively nearby star is observed against distant background stars from on opposite sides of Earth’s orbit around the Sun.  This allows the parallax angle to be measured.  Since the Earth-Sun distance is known (~150 million km or 1 AU) the distance to the star can be calculated with trigonometry (Credit: University of Virginia). 

Who was Friedrich Wilhelm Bessel?

Friedrich Wilhelm Bessel (1784 – 1846) was a German astronomer who dramatically improved the accuracy of calculating the position of stars and in doing so laid the foundation for the science of astrometry.  Modern astrometry deals with determining the precise position of stars as well as their distance from the Sun and motion across the sky. 

In 1813 Bessel established the Königsberg Observatory in the Kingdom of Prussia.  It is from here that he made his observations that allowed him to calculate the parallax of 61 Cygni.  For his measurements he used a special type of telescope called a heliometer, which was originally designed to measure the angular diameter of the Sun.  A heliometer has a split lens which creates a double image.  One side of the split lens can be moved back and forth with a micrometre.  A pair of stars is placed in the field of view and then the lens is adjusted so that the first star lines up with the second star in the other half of the split lens.  The angular separation value can now be read from the micrometre. 

Bessel is also well known for calculating that the brightest star in the sky Sirius must have an unseen companion star orbiting it, even so he could not see it with his equipment.  Today we know that the companion is Sirius B, a white dwarf star. 

Figure 3: The split optical lens of a heliometer.  On the right is the micrometre that is used to offset the lenses and to measure the angular separation of two objects (Credit: Wikipedia). 

The Gaia mission

While Earth based parallax observations can only measure the distance to stars within a few hundred light years, the ESA Gaia space-based telescope has been able to measure parallax out to beyond the centre of the Milky Way or over 30,000 lights years distant.  It has done this from a stable orbit at the L2 Lagrange point 1.5 million kilometres away from Earth, which is also the location of the James Webb Space Telescope (JWST).  Gaia operated from 24th July 2014 to 15th January 2025. 

The stable orbit and lack of interference from Earth’s atmosphere allows Gaia to make much more accurate measurements than is possible from Earth.  As well as parallax Gaia also makes other astrometry measurements including the position of stars and their rate of motion across the sky.  It also employs photometry and spectroscopy.  Gaia uses photometry to measure the intensity and colour of starlight, to calculate properties such as temperature, age, mass and brightness.  Gaia uses spectroscopy to determine the chemical composition of stars as well as calculating their radial velocity (the speed with which a star is moving either towards or away from Earth).  By employing such a large range of techniques Gaia has built a comprehensive map of the Milky Way.  The data making up this map is contained in three publicly available data releases, with two more data releases to come in 2026 and 2030. 

Figure 4: A summary of the observations made and the data collected by the ESA Gaia mission (Credit: ESA/Gaia/DPAC, Milky Way impression by Stefan Payne-Wardenaar). 

Figure 5: The observing techniques used by Gaia and the types of measurements taken (Credit: ESA). 

The ‘61 Cygni’ star system

61 Cygni consists of two dwarf stars, smaller than the Sun, which orbit each other over a period of about 659 years.  Under dark skies 61 Cygni can be seen with the naked eye, appearing as a single star.  With binoculars or a small telescope both stars can be seen. 

It is the 61st star in the constellation of Cygnus as measured eastward along the celestial equator according to the ‘Atlas Coelestis’, the most comprehensive star atlas of its day.  It was compiled by the Astronomer Royal John Flamsteed and published posthumously by his wife Margaret Flamsteed in 1725. 

61 Cygni resides in the constellation of Cygnus.  In the southern hemisphere Cygnus appears above the northern horizon between late August and early November reaching its highest point in late September.  In high northern latitudes such as northern Europe and the northern United States and Canada, Cygnus is circumpolar, meaning it can be seen all year round. 

Figure 6: The location of 61 Cygni in the constellation of Cygnus, as seen from Sydney Australia in late September (Credit: Stellarium). 

From single observations to automation

This short insight into measuring the distance to stars via parallax, from the first success to the most recent, demonstrates how astronomical observations have dramatically advanced from individual astronomers observing individual stars to fully automated space-based telescopes and instruments that can measure multiple properties of billions of stars. 

The data collected by automated telescopes such as Gaia is available for download by astronomy researchers and the public.  Astronomers use data analysis tools, programming code and advanced tools such as machine learning to interrogate the data and pursue their research goals.  For example, to date 13,000 peer reviewed research articles have been published based on Gaia data. 

References:

Cygni marks the end of Gaia's science observation phase, https://www.cosmos.esa.int/web/gaia/iow_20250115 (accessed 27th January 2025)

Last starlight for ground-breaking Gaia, https://www.esa.int/Science_Exploration/Space_Science/Gaia/Last_starlight_for_ground-breaking_Gaia (accessed 27th January 2025)

Friedrich Wilhelm Bessel, https://www.britannica.com/biography/Friedrich-Wilhelm-Bessel (accessed 3rd February 2025)

How does Gaia study the Milky Way?, https://www.esa.int/Science_Exploration/Space_Science/Gaia/How_does_Gaia_study_the_Milky_Way (accessed 10th February 2025)

Stellar Parallaxes - How to measure stellar distances with the Gaia satellite, https://www.youtube.com/watch?v=m1ZNSPrH0q8 (accessed 10th February 2025)

John Flamsteed, https://en.wikipedia.org/wiki/John_Flamsteed (accessed 10th February 2025)