Why isn AU the average Earth-Sun distance?
The astronomical unit (AU) may be defined as the distance from the Sun that a massless particle would require for a circular, Keplerian orbit with an exact period of 2*pi/0.01720209895. The denominator, denoted by “k”, is the “gaussian constant”, and its value, in radians/day, comes from a measurement of the earth’s mean motion taken back in the 19th century when it was far easier to measure the orbital period of the earth than it was to measure its distance from the Sun. In such an idealized (circular, Keplerian) orbit, the AU would be equal to the semi-major axis of the orbit and would also be equal to the mean distance of the particle from the Sun. However, neither is exactly the case. With an eccentric orbit, the mean distance is not equal to the semi-major axis, a; instead, it is equal to a*[1+(e^2/2)], where e is the eccentricity. Furthermore, the earth’s motion is not Keplerian; only approximately so. Thus, the orbit is not periodic and there is no exact semi-major axis nor is t
