The Aberration of Starlight: Relativity’s Crucible

The Earth races around the sun with remarkable speed—at over one hundred thousand kilometers per hour on its yearly track.  This is about 0.01% of the speed of light—a small but non-negligible amount for which careful measurement might show the very first evidence of relativistic effects.  How big is this effect and how do you measure it?  One answer is the aberration of starlight, which is the slight deviation in the apparent position of stars caused by the linear speed of the Earth around the sun.

This is not parallax, which is caused the the changing position of the Earth around the sun. Ever since Copernicus, astronomers had been searching for parallax, which would give some indication how far away stars were. It was an important question, because the answer would say something about how big the universe was. But in the process of looking for parallax, astronomers found something else, something about 50 times bigger—aberration.

Aberration is the effect of the transverse speed of the Earth added to the speed of light coming from a star. For instance, this effect on the apparent location of stars in the sky is a simple calculation of the arctangent of 0.01%, which is an angle of about 20 seconds of arc, or about 40 seconds when comparing two angles 6 months apart.  This was a bit bigger than the accuracy of astronomical measurements at the time when Jean Picard travelled from Paris to Denmark in 1671 to visit the ruins of the old observatory of Tycho Brahe at Uranibourg.

Fig. 1 Stellar parallax is the change in apparent positions of a star caused by the change in the Earth’s position as it orbits the sun. If the change in angle (θ) could be measured, then based on Newton’s theory of gravitation that gives the radius of the Earth’s orbit (R), the distance to the star (L) could be found.

Jean Picard at Uranibourg

Fig. 2 A view of Tycho Brahe’s Uranibourg astronomical observatory in Hven, Denmark. Tycho had to abandon it near the end of his life when a new king thought he was performing witchcraft.

Jean Picard went to Uranibourg originally in 1671, and during subsequent years, to measure the eclipses of the moons of Jupiter to determine longitude at sea—an idea first proposed by Galileo.  When visiting Copenhagen, before heading out to the old observatory, Picard secured the services of an as yet unknown astronomer by the name of Ole Rømer.  While at Uranibourg, Picard and Rømer made their required measurements of the eclipses of the moons of Jupiter, but with extra observation hours, Picard also made measurements of the positions of selected stars, such as Polaris, the North Star.  His very precise measurements allowed him to track a tiny yearly shift, an aberration, in position by about 40 seconds of arc.  At the time (before Rømer’s great insight about the finite speed of light—see Chapter 1 of Interference (Oxford, 2023)), the speed of light was thought to be either infinite or unmeasurably fast, so Picard thought that this shift was the long-sought effect of stellar parallax that would serve as a way to measure the distance to the stars.  However, the direction of the shift of Polaris was completely wrong if it were caused by parallax, and Picard’s stellar aberration remained a mystery.

Fig. 3 Jean Picard (left) and his modern name-sake (right).

Samuel Molyneux and Murder in Kew

In 1725, the amateur Irish astronomer Samuel Molyneux (1689 – 1828) decided that the tools of astronomy had improved to the point that the question of parallax could be answered.  He enlisted the help of an instrument maker outside London to install a 24-foot zenith sector (a telescope that points vertically upwards) at his home in Kew.  Molyneux was an independently wealthy politician (he had married the first daughter of the second Earl of Essex) who sat in the British House of Commons, and he was also secretary to the Prince of Wales (the future George II).  Because his political activities made demands on his time, he looked for assistance with his observations and invited James Bradley (1693 – 1762), the newly installed Savilian Professor of Astronomy at Oxford University, to join him in his search.

Fig. 4 James Bradley.

James Bradley was a rising star in the scientific circles of England.  He came from a modest background but had the good fortune that his mother’s brother, James Pound, was a noted amateur astronomer who had set up a small observatory at his rectory in Wanstead.  Bradley showed an early interest in astronomy, and Pound encouraged him, helping with the finances of his education that took him to degrees at Baliol College at Oxford.  Even more fortunate was the fact that Pound’s close friend was the Astronomer Royal Edmund Halley, who also took a special interest in Bradley.  With Halley’s encouragement, Bradley made important measurements of Mars and several nebulae, demonstrating an ability to work with great accuracy.  Halley was impressed and nominated Bradley to the Royal Society in 1718, telling everyone that Bradley was destined to be one of the great astronomers of his time. 

Molyneux must have sensed immediately that he had chosen wisely by selecting Bradley to help him with the parallax measurements.  Bradley was capable of exceedingly precise work and was fluent mathematically with the geometric complexities of celestial orbits.  Fastening the large zenith sector to the chimney of the house gave the apparatus great stability, and in December of 1725 they commenced observations of Gamma Draconis as it passed directly overhead.  Because of the accuracy of the sector, they quickly observed a deviation in the star’s position, but the deviation was in the wrong direction, just as Picard had observed.  They continued to make observations over two years, obtaining a detailed map of a yearly wobble in the star’s position as it changed angle by 40 seconds of arc (about one percent of a degree) over six months. 

When Molyneux was appointed Lord of the Admiralty in 1727, as well as becoming a member of the Irish Parliament (representing Dublin University), he had little time to continue with the observations of Gamma Draconis.  He helped Bradley set up a Zenith sector telescope at Bradley’s uncle’s observatory in Wanstead that had a wider field of view to observe more stars, and then he left the project to his friend.  A few months later, before either he or Bradley had understood the cause of the stellar aberration, Molyneux collapsed while in the House of Commons and was carried back to his house.  One of Molyneux’s many friends was the court anatomist Nathaniel St. André who attended to him over the next several days as he declined and died.  St. André was already notorious for roles he had played in several public hoaxes, and on the night of his friend’s death, before the body had grown cold, he eloped with Molyneux’s wife, raising accusations of murder (that could never be proven). 

James Bradley and the Light Wind

Over the following year, Bradley observed aberrations in several stars, all of them displaying the same yearly wobble of about 40 seconds of arc.  This common behavior of numerous stars demanded a common explanation, something they all shared.  It is said that the answer came to Bradley while he was boating on the Thames.  The story may be apocryphal, but he apparently noticed the banner fluttering downwind at the top of the mast, and after the boat came about, the banner pointed in a new direction.  The wind direction itself had not altered, but the motion of the boat relative to the wind had changed.  Light at that time was considered to be made of a flux of corpuscles, like a gentle wind of particles.  As the Earth orbited the Sun, its motion relative to this wind would change periodically with the seasons, and the apparent direction of the star would shift a little as a result.

Fig. 5 Principle of stellar aberration.  On the left is the rest frame of the star positioned directly overhead as a moving telescope tube must be slightly tilted at an angle (equal to the arctangent of the ratio of the Earth’s speed to the speed of light–greatly exaggerated in the figure) to allow the light to pass through it.  On the right is the rest frame of the telescope in which the angular position of the star appears shifted.

Bradley shared his observations and his explanation in a letter to Halley that was read before the Royal Society in January of 1729.  Based on his observations, he calculated the speed of light to be about ten thousand times faster than the speed of the Earth in its orbit around the Sun.  At that speed, it should take light eight minutes and twelve seconds to travel from the Sun to the Earth (the actual number is eight minutes and 19 seconds).  This number was accurate to within a percent of the true value compared with the estimates made by Huygens from the eclipses of the moons of Jupiter that were in error by 27 percent.  In addition, because he was unable to discern any effect of parallax in the stellar motions, Bradley was able to place a limit on how far the distant stars must be, more than 100,000 times farther the distance of the Earth from the Sun, which was much farther away than any had previously expected.  In January of 1729 the size of the universe suddenly jumped to an incomprehensibly large scale.

Bradley’s explanation of the aberration of starlight was simple and matched observations with good quantitative accuracy.  The particle nature of light made it like a wind, or a current, and the motion of the Earth was just a case of Galilean relativity that any freshman physics student can calculate.  At first there seemed to be no controversy or difficulties with this interpretation.  However, an obscure paper published in 1784 by an obscure English natural philosopher named John Michell (the first person to conceive of a “dark star”) opened a Pandora’s box that launched the crisis of the luminiferous ether and the eventual triumph of Einstein’s theory of Relativity (see Chapter 3 of Interference (Oxford, 2023)), .

One Comment

Comments are closed.