| Astronomical units (au) | Nautical leagues (nlea) |
|---|---|
| 1 Astronomical unit | 26925462.689 nlea |
| 2 Astronomical units | 53850925.378 nlea |
| 3 Astronomical units | 80776388.067 nlea |
| 4 Astronomical units | 107701850.756 nlea |
| 5 Astronomical units | 134627313.445 nlea |
| 10 Astronomical units | 269254626.89 nlea |
| 20 Astronomical units | 538509253.78 nlea |
| 25 Astronomical units | 673136567.225 nlea |
| 50 Astronomical units | 1346273134.45 nlea |
| 100 Astronomical units | 2692546268.9 nlea |
| Reference | Astronomical units (au) | Nautical leagues (nlea) |
|---|---|---|
| A sheet of A4 paper (long side) | 1.98532 × 10-12 au | 0.0000534557 nlea |
| Average adult human height | 1.13638 × 10-11 au | 0.000305976 nlea |
| A football pitch (length) | 7.01882 × 10-10 au | 0.0188985 nlea |
| A marathon | 0.000000282056 au | 7.59449 nlea |
| Height of Mount Everest | 0.0000000591519 au | 1.59269 nlea |
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.
The nautical league is a unit of length equal to three nautical miles, or exactly 5556 metres. It is longer than the land league by about 728 metres, since it is built from the nautical mile of 1852 metres rather than the statute mile.
The unit belonged to an era when it was the practical measure of coastal jurisdiction. The cannon shot rule, articulated in the seventeenth and eighteenth centuries, held that a state's authority extended as far as it could defend from shore, conventionally taken as three nautical miles. That distance became the standard territorial sea limit and was expressed as one marine league. Many older treaties and statutes define maritime boundaries in leagues for this reason.
The three-mile limit held for centuries before eroding through the twentieth. States progressively claimed wider waters, and the United Nations Convention on the Law of the Sea settled the matter in 1982 by establishing a twelve nautical mile territorial sea and a two hundred mile exclusive economic zone. Both figures are stated in nautical miles rather than leagues, and the older unit fell out of legal use.
Charts and pilot books from the age of sail used the league routinely for describing offshore distances and the visibility of landmarks. Reading those sources accurately requires knowing which league is meant, since the same word could refer to a land league, a marine league or a Spanish or Portuguese variant, and the differences are large enough to matter when reconstructing a historical position.
Today the unit has no navigational role. Charts are marked in nautical miles, and distances at sea are quoted the same way. The nautical league appears only in historical and legal texts.
The unit also underlies a familiar figure in visibility calculations. From a height of about three metres above sea level, the horizon lies roughly one nautical league away, which is why the three-mile limit corresponded loosely to what a lookout could see as well as to what a gun could reach.
One nautical league equals 3 nautical miles, 5556 metres, 5.556 kilometres, or about 3.452 statute miles.