measure for measure To the Sun and beyond Tell Bartolo Luque and Fernando Ballesteros how far the Sun is from the Earth, and they will tell you the size of the Universe.

he measures of the heavens and of 149,597,870.7 km obtained by telemetry the Earth have been inextricably and radar5. Once the au was determined, Tintertwined throughout history. the true dimensions of the Solar System Until the seventeenth century, determining could finally be revealed. geographical position required knowledge By the same token, in 1838 Friedrich of the position and the distance to celestial Bessel (1784–1846) determined the first stellar bodies, measures that in turn depended on parallax7 of 61 Cygni, supposedly one of the the distance between two observing sites on closest stars to Earth. From observations from Earth. For example, the first determination opposite extremes of the Earth’s orbit, Bessel of the Earth’s perimeter1, carried out by concluded a parallax of 0.314 arcseconds Eratosthenes of Cyrene (276–194 bc), ('') and realized that the Universe was much crucially depended on the actual distance larger than previously imagined; the au fell between the cities of Alexandria and Syene. short for stellar distances. Such measurements Precision geography was not possible of parallaxes are obtained naturally in parsecs without astronomy or vice versa, and their (pc), where 1 pc is the distance to be moved measurements were always relative to away so that a segment of 1 au subtends an other measurements. Aristarchus of Samos angle of 1''; consequently, 1 pc = 1 au/tan(1'') (310–230 bc) concluded that the distance to Credit: Science History Images / Alamy Stock ≈ 206,264.8 au by definition. Therefore, the the Sun2 — roughly the astronomical unit — Photo absolute length of the parsec depends on the was 19.1 times larger than the distance to the value of the au. Moon; a distance that, in turn, he calculated When converting his angular as a function of the Earth’s diameter. observed the position of Mars with respect measurements of the star 61 Cygni to Nearly two millennia would have to pass to the stars from France and French absolute distances, Bessel realized that the before the next significant step forward was Guiana, estimating that the au was equal to light from the star took 10.3 years to arrive, taken by Johannes Kepler (1571–1630). 141,500,000 km (ref. 5) — 5% lower than the and in the process indirectly invented the His third law3 on planetary motion states current estimate. The net was being tightened. most popular measure today of interstellar that, for every planet, the ratio between the The telescope also allowed the distances: the light year. Now, the Universe’s cube of the semi-major axis of its elliptical observation of transits — tiny solar eclipses diameter is believed to be 93 billion light orbit and the square of its orbital period of the inner planets Venus and Mercury. years — at least the observable bit. The is a constant. This allowed the distance to In 1716, Edmond Halley (1656–1742) precise determination of the au opened a the Sun of a planet to be calculated from proposed a method6 to measure the au new window that allowed us to appreciate the planet’s period, but as a multiple of the more accurately by observing transits of the enormous size of the Universe. ❐ Earth–Sun distance. Venus from two remote locations. Since the The way out of this vicious circle moving observation should be diurnal, it was not Bartolo Luque1 and from a system of relative magnitudes to possible to measure the parallaxes of Venus Fernando J. Ballesteros 2 absolute ones would arrive with the precise and of the Sun with respect to the stars. 1Universidad Politécnica de Madrid, Madrid, Spain. determination of the average distance The ingenious trick of Halley’s method was 2Observatori Astronòmic, Universitat de València, from the Earth to the Sun, known as the that it allowed the real solar parallax to be Paterna, Spain. astronomical unit (au). found from the apparent parallax of Venus e-mail: [email protected]; The first absolute measurements of the au with respect to the Sun. Then, knowing the [email protected] were enabled by the invention of the telescope, distance between the locations, one can Published online: 2 December 2019 which allowed Christiaan Huygens (1629– determine the distance to the Sun. https://doi.org/10.1038/s41567-019-0685-3 1695) in 1659 to make precise measurements During the Venus transits of 1761 References of the angular distance between the Sun (pictured) and 1769, astronomers from 1. Cleomedes On the Circular Motions of the Celestial Bodies and Venus4. Reusing ideas from Aristarchus around the world spread across the planet (circa 50 bc). and assuming that the diameter of Venus to take more than 200 observations. After 2. Aristarchus of Samos On the Sizes and Distances (of the Sun and Moon) (circa 270 bc). is equal to Earth’s, he estimated that the au analysing all the data, in 1771, Joseph Jérôme 3. Kepler, J. Harmonices Mundi Book 5, Ch. 3, 189 (1619). was 157,125,000 km (ref. 5) — exceeding our Lefrançois de Lalande (1732–1807) provided 4. Goldstein, S. J. Jr Observatory 105, 32–33 (1985). current estimate by 5%. Thirteen years later, the most accurate measurement of the au at 5. Beatty, J. K., Collins Petersen, C. & Chaikin, A. (eds) Te New Solar System (Cambridge University Press, 1999). Giovanni Domenico Cassini (1625–1712) that time: the Sun was 153,000,000 km away, 6. Halley, E. Phil. Trans. R. Soc. 29, 454–464 (1716). and Jean Richer (1630–1696) simultaneously which exceeds by 2% the current estimation 7. Bessel, F. W. Astron. Nach. 16, 65–96 (1838).

1302 Nature Physics | VOL 15 | December 2019 | 1302 | www.nature.com/naturephysics