The Astronomical Unit – Definition
The distance from a particle (or a planet) to the Sun, is measured in terms of the semimajor axis of the ellipse traced by that body around the Sun. According to Kepler’ law, the square of the period (time that the body takes to go once around de Sun in years) is directly proportional to the cube of the semimajor axis, in Astronomical Units. The Astronomical Unit by definition is the semimajor axis value (in A.U.) for which it takes 1 year to revolve around the Sun. That means actually that the distance from the Earth to se Sun is larger that one A.U. The difference is small and negligible though. We take then 1 A.U. = the distance from Earth to the Sun. It is close to 150 million kilometers.
If you like to watch the math explanation for this lesson, you may click on this link
https://www.showme.com/sh?h=Vxyt4pk
If the link does not direct you to the site, just copy and paste it in your search engine.
AstroDidactics 