Frontier Science › Physics and Space · Feature · Practical STEM, Part 4
Bessel's tiny angle: how Königsberg measured the distance to a star
In 1838, Friedrich Wilhelm Bessel, working at the Königsberg Observatory, became the first person to measure the distance to a star other than the Sun. His mathematics now helps carry phone calls, music and internet traffic.
For thousands of years, the stars were simply “far away.” Nobody knew how far. Astronomers knew a method in theory, but the measurement was so delicate that every attempt had failed.
The method: parallax
Hold a finger at arm’s length and close one eye, then the other. Your finger seems to jump against the background. That shift is parallax. The closer the finger, the bigger the jump.
Earth does the same on a grand scale. Six months apart, it sits on opposite sides of its orbit around the Sun. A nearby star should shift very slightly against more distant stars. Measure that shift, and simple geometry gives you the distance.
The man and the observatory
Bessel was largely self-taught. He started as a clerk at a trading firm and taught himself astronomy at night. In 1810 he was appointed to lead the new observatory at Königsberg, where he spent the rest of his career.
He chose a star called 61 Cygni, which moves unusually fast across the sky — a hint that it is close. Using a precise instrument called a heliometer, he tracked it for more than a year. In 1838 he announced a parallax of about a third of an arcsecond: roughly the width of a coin seen from several kilometres away. It put 61 Cygni about 10 light-years away — close to today’s value of about 11.4. For the first time, humanity knew the scale of the stars.
Bessel’s other gift: his functions
To solve problems in astronomy, Bessel studied a family of mathematical curves now called Bessel functions. They describe waves in round things: the vibrations of a drum, heat moving through a cylinder, light travelling in an optical fibre. Engineers use them to design antennas, analyze FM radio signals and build the fibre-optic cables that carry most internet traffic.
The practical lesson
Bessel succeeded because he took measurement seriously. He studied every error in his instruments — temperature, wobble, the shape of the lenses — and corrected for each one. Big discoveries often hide in tiny numbers. To find them, you must first understand everything that could fool you.
Try it yourself
Hold your thumb at arm’s length and switch eyes. Then bring it halfway closer and repeat. Notice how the jump grows. You have just run Bessel’s experiment, on a much smaller stage.
Sources: Bessel, report on the parallax of 61 Cygni, Astronomische Nachrichten 16 (1838) · Hirshfeld, Parallax: The Race to Measure the Cosmos (2001) · Watson, A Treatise on the Theory of Bessel Functions (1922) · Current catalogue distance for 61 Cygni (e.g. ESA Gaia).
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.