The Scale of the Solar System

In antiquity, the radius of the Earth was a basic unit of length for attempts to infer distances to the Moon and the Sun. Measurement of the distance to the Sun was attempted by Aristarchus, Hipparchus, and Ptolemy, but they failed, since the Sun is so far away. Copernicus’ heliocentric system gave the Earth-Sun distance special importance; it could be used as a measuring ruler within the Solar System (Table 5.1). Kepler’s Third Law emphasized the same thing: the times of revolution around the Sun, obtained from observations, determine the relative sizes of the planetary orbits in Earth-Sun distance units. When astronomers started determining distances (parallaxes) of stars, the Earth-Sun distance finally replaced our planet’s radius as the natural unit.

However, one would also like to know cosmic distances in the earthly units of length used by physicists in their experiments. For example, to know the total radiation power in watts (J/s) of a star, as inferred from its radiation flux measured on Earth in W/m2, one must know its distance from Earth in meters. To derive this distance from the star’s annual parallax, one must know the distance of the Sun in meters! But it is not obvious how to measure this Earth–Sun unit.