| Leagues (lea) | Astronomical units (au) |
|---|---|
| 1 League | 0.0000000322734005331 au |
| 2 Leagues | 0.0000000645468010662 au |
| 3 Leagues | 0.0000000968202015993 au |
| 4 Leagues | 0.000000129093602132 au |
| 5 Leagues | 0.000000161367002665 au |
| 10 Leagues | 0.000000322734005331 au |
| 20 Leagues | 0.000000645468010662 au |
| 25 Leagues | 0.000000806835013327 au |
| 50 Leagues | 0.00000161367002665 au |
| 100 Leagues | 0.00000322734005331 au |
| Reference | Leagues (lea) | Astronomical units (au) |
|---|---|---|
| A sheet of A4 paper (long side) | 0.0000615157 lea | 1.98532 × 10-12 au |
| Average adult human height | 0.00035211 lea | 1.13638 × 10-11 au |
| A football pitch (length) | 0.021748 lea | 7.01882 × 10-10 au |
| A marathon | 8.73959 lea | 0.000000282056 au |
| Height of Mount Everest | 1.83284 lea | 0.0000000591519 au |
The league is a unit of length equal to three miles, 24 furlongs, or exactly 4828.032 metres. It is obsolete in every practical sense, surviving mainly in literature and in historical documents.
The unit originated as a measure of how far a person could walk in an hour, which explains both its rough magnitude and its variability. Ancient and medieval leagues differed widely between regions. The Roman leuga was about 2.2 kilometres. French, Spanish and Portuguese leagues each had their own values, and the Spanish legua used in colonial land grants in the Americas differed again, complicating the interpretation of old property records in Texas and the American southwest.
English usage settled on three miles, a figure that was never especially precise in practice because it depended on the mile in force at the time. Since the mile itself was fixed at 5280 feet in 1593, the league inherited that definition, giving the modern value of 4828.032 metres.
Its cultural persistence far exceeds its practical use. Jules Verne's Twenty Thousand Leagues Under the Seas measures a journey rather than a depth, a distinction frequently lost in casual reference: twenty thousand leagues is roughly 96,000 kilometres, more than twice the circumference of the Earth and vastly greater than any ocean depth. Seven-league boots appear in French fairy tales as a device for covering ground in single strides. Tennyson's Charge of the Light Brigade opens with half a league onward.
The unit was formally abolished for trade in the United Kingdom long ago and has no legal standing. It appears occasionally in nautical contexts, where the marine league of three nautical miles is a separate and slightly longer unit.
Because the unit is so variable across languages and centuries, translations of older works can mislead badly. A distance given in leagues in a Spanish colonial document, a French medieval chronicle and an English statute may differ by a factor of two, and historians working with such sources generally convert to modern units and state which league they have assumed.
One league equals 3 miles, 4828.032 metres, or 4.828032 kilometres. A brisk hour's walk covers rather less than one.
The astronomical unit is a length equal to exactly 149,597,870,700 metres, or very nearly 150 million kilometres. The symbol is au. It approximates the mean distance between the Earth and the Sun and is the standard measure for distances within the solar system.
The unit was originally defined by that orbital relationship rather than by a fixed number. Earlier definitions tied it to the properties of a hypothetical body orbiting the Sun, which meant its value depended on the gravitational constant and was subject to revision as measurements improved. The International Astronomical Union ended that dependence in 2012 by fixing the astronomical unit as an exact number of metres. The change simplified calculations and removed an inconvenience: a unit whose length shifted whenever a physical constant was refined.
Determining its value was one of the great problems of observational astronomy. Transits of Venus across the Sun's disc, observed from widely separated points on Earth, allowed the distance to be triangulated. Expeditions were mounted for the transits of 1761, 1769, 1874 and 1882, and James Cook's first Pacific voyage was organised around the 1769 event. Radar ranging to Venus in the 1960s eventually settled the figure far more precisely than any optical method.
The unit makes solar system distances legible. Mercury orbits at 0.39 au, Mars at 1.52 au, Jupiter at 5.2 au and Neptune at 30.1 au. The Kuiper Belt extends to roughly 50 au. Voyager 1, the most distant human-made object, has passed 165 au. Light takes about 499 seconds to cover one astronomical unit, so the Sun is a little over eight light minutes away.
Beyond the solar system the unit becomes unwieldy, and astronomers switch to light years and parsecs. One parsec is 206,265 au.
Spacecraft navigation depends on the unit being exact rather than approximate. Trajectories to the outer planets are computed over distances of tens of astronomical units, and an error in the length of the unit itself would propagate into every position calculation. Fixing the value in 2012 removed that source of drift from the ephemerides used for mission planning.
One astronomical unit equals 149,597,870.7 kilometres, or about 92.956 million miles.