Figure: Introducing the astronomical unit (the AU), the natural unit of planetary system distances

Image 1 Caption: The image shows the orbits of Mercury, Venus, Earth, and Mars with the planets shown and the astronomical unit (the AU) indicated.

The astronomical unit (AU) is the disance equal to the mean Earth-Sun distance. It is, of course, the mean orbital radius of the Earth's orbit. The astronomical unit is the good natural unit for Solar System distances and by valid extrapolation all planetary system distances.

Note, in the image the orbits (with their eccentricities) are to-scale, but the astro-bodies are not.

Further Explication:

1. In dealing with the Solar System, the natural unit of distance is the mean Earth-Sun distance: mean distance because the actual distance varies by about 3.3 %.

   Note that distances between astronomical objects are usually center-to-center distances if there are well defined centers. If there are NOT well defined centers, then more specifications are needed about what distance means.

2. The mean Earth-Sun is, of course, the mean orbital radius of the Earth's orbit.

   It is called the astronomical unit (AU).

3. Of course, the astronomical unit is a good natural unit for us since we live on Earth. The Martians use the mean Mars--Sun distance.

   However, the astronomical unit is actually a generally good natural unit since all easily observed Solar System objects are a few or a few tens of astronomical units from the Sun.

4. Very roughly speaking other planetary systems have the same size scale as the Solar System, and so the astronomical unit is a universally good natural unit for planetary systems. A special reason for us for it to be good is that we are very interested in finding Earth analog planets which would have to be ∼ 1 astronomical unit from their solar analog stars.

5. The value of the astronomical unit (AU) in metric units is
   1 AU = 1.495978707 × 10¹¹ m
   ≅ 1.496 × 10¹¹ m
   ≅ 1.5 × 10¹¹ m
   Since 2012, the astronomical unit has been defined to be exactly 1.495978707 × 10¹¹ m

   Values for the observational astronomical unit (which was used before 2012) depend on many finicky rules and people finally gave up trying to satisfy them. Also the observational astronomical unit varies slowly in time because the Solar System is evolving in time (see Wikipedia: Formation and evolution of the Solar System). This makes it unsuitable in principle for being a dependable unit for widespread use.

   The now defined exact value is a sufficiently accurate/precise mean Earth-Sun distance for virtually all purposes, is easy to understand, and will NOT fluctuate with finicky rules and observations.

   But, of course, it differs slightly from the mean Earth-Sun (i.e., observational astronomical unit) given to many digits (high accuracy/precision) in tables.

   

6. Image 2 Caption: The Sun-Earth-Moon system shown not-to-scale.

   The image shows the Earth's orbit and the Moon's orbit, and compares Earth-Moon distance to the astronomical unit (AU), but NOT-to-scale.

   To be precise,

   R_Mo = 384,748 km = 1.28338 light-seconds = 2.57188 mAU = 60.3229 R_eq,⊕ ≅ 60 R_eq,⊕ (center-to-center),

   where the

   1. light-second = 299792.458 km (exactly).
   2. astronomical unit (AU) = 1.495978707 × 10⁸ km exactly.
   3. Earth equatorial radius = R_eq,⊕ = 6378.1370 km .

   Images:

   1. Credit/Permission: © User:Huritisho, User:Mrmw, 2020 / Creative Commons CC BY-SA 3.0.
      Image link: Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Astronomical_unit.svg.
      
   2. Credit/Permission: © David Jeffery, 2003 / Own work.
      Image link: Itself.
      

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