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If you walk through vertical rain, you tilt your umbrella forward. The faster you walk, the more you tilt. James Bradley found the same effect in starlight, because Earth moves through falling light the way you move through rain. This post covers the observations he made, the physics behind the tilt, a worked calculation with real numbers, common mistakes, and what you can take from how he worked.
Who was James Bradley?
According to his MacTutor biography at the University of St Andrews, Bradley was born in March 1693 in Sherborne, Gloucestershire, and died on 13 July 1762 at Chalford. His uncle, the Reverend James Pound, was a skilled astronomical observer who introduced him to Edmond Halley. Bradley became Savilian Professor of Astronomy at Oxford in 1721, and in 1742 succeeded Halley as the third Astronomer Royal.
MacTutor credits him with two major discoveries: the aberration of light, and nutation, a small wobble in the direction of Earth's axis. He received the Royal Society's Copley Medal in 1748.
What did Bradley see in the sky?
In December 1725 Samuel Molyneux invited Bradley to his house at Kew, near London, to help observe the star Gamma Draconis. They hoped to measure its annual parallax, the small yearly shift caused by viewing it from opposite sides of Earth's orbit, which would give its distance. The star passes almost overhead in London, so the atmosphere bends its light very little.
MacTutor explains what went wrong. Parallax predicted the star should be furthest south in December and furthest north in June. Instead it reached its southern limit in March and its northern limit in September, three months out of step, with a total shift of about one hundredth of a degree. From August 1727 Bradley observed other stars and found they all showed a similar yearly motion.
The story goes that while sailing on the Thames, he noticed a vane on the mast changing direction each time the boat turned, though the wind had not changed. The apparent direction depended on the boat's motion. Bradley's explanation for the stars was the same: their apparent position combines the finite speed of light with Earth's motion around the Sun. He set it out in a letter to Halley in the Philosophical Transactions, read to the Royal Society in January 1729. MacTutor adds that he concluded the true parallax was too small for his instruments, so the stars had to be even further away than people thought.
How big is the aberration angle? A worked example
This is a relative velocity problem, the same as rain and a moving walker. Light arrives at speed c; Earth moves sideways at speed v. The light appears tilted by an angle θ where, for small angles,
θ ≈ v / c (in radians)
From the NASA Earth fact sheet, Earth's mean orbital speed is 29.78 km/s. With c = 299,792 km/s:
θ ≈ 29.78 / 299,792 ≈ 9.93 × 10⁻⁵ rad
One radian is about 206,265 arcseconds, so θ ≈ 9.93 × 10⁻⁵ × 206,265 ≈ 20.5 arcseconds.
Over a year Earth's direction of motion reverses, so a star swings by up to about twice this, roughly 41 arcseconds, the same order as the one-hundredth of a degree (36 arcseconds) MacTutor reports for Gamma Draconis.
Now work backwards, in the spirit of Bradley's own estimate. Earth travels a circle of radius 1 AU in one year, so v = 2π × 1 AU / T. Light takes t = 1 AU / c to reach us from the Sun. Dividing, v/c = 2πt / T. MacTutor says Bradley's measurements gave t = 8 minutes 12 seconds = 492 s. With T = 365.25 × 86,400 ≈ 31,557,600 s:
v/c = 2π × 492 / 31,557,600 ≈ 9.80 × 10⁻⁵, about 20.2 arcseconds
The modern value of t is about 8 minutes 20 seconds, so Bradley was within about 2%.
What mistakes do students make with aberration?
Confusing aberration with parallax. Parallax depends on Earth's position and shrinks with distance; aberration depends on Earth's velocity and does not depend on the star's distance at all.
Using the wrong speed. It is Earth's orbital speed, about 30 km/s, not its spin speed at the equator.
Forgetting to convert radians. v/c gives radians; multiply by 206,265 for arcseconds.
Tilting the wrong way. Like the umbrella, the telescope tilts towards the direction you are moving.
For the umbrella version of this problem, practise relative velocity with rain and rivers. For an earlier estimate of the speed of light, read Ole Rømer and the speed of light.
What can a student learn from how Bradley worked?
Bradley's experiment failed at what it set out to do. Instead of discarding the strange data, he observed more stars, looked for a pattern, and found an explanation that turned the failure into a new measurement. When a lab reading or a problem answer comes out wrong, record it, check whether it is consistent, and ask what it might be measuring instead.
Relative velocity is easier to see when you can change the speeds and watch the angle respond. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read.
Work out the aberration angle for an observer moving at 300 km/s, ten times Earth's speed, and check that it is about 205 arcseconds.
