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My quick testing makes it seem that the center of a circle is closer to the circle "on average" than any point on the circle is. A quick Python script suggests

My quick testing makes it seem that the center of a circle is closer to the circle "on average" than any point on the circle is. A quick Python script suggests that a point on the circle is about 1.273 radii away from the other points on the circle on "average", while (by definition) the center is 1 radius away from all points on the circle. So this fact about orbits seems related: the closest point to your orbit (on average) are things in the middle of it, which are near the center of your "circle". Further testing supports this -- there's a gradient from the 1.273 at the "edge" to the 1.0 in the "center", as you shrink the radius of the circle you measure from.

mc32 8y ago
So depending on Mercury’s distance from the center of the Earths orbit, it could be closer on average than an average point in the Earth’s orbit.
- NotAnEconomist 8y ago
  > So depending on Mercury’s distance from the center of the Earths orbit, Yep, there's basically there's two groups of things: 1. Those with smaller orbital radii (ie, Mercury which orbits between the Earth and Sun) will always be closer on average -- with a limit of the center point having the minimal average distance of "1 orbital radius". 2. Those with larger orbital radii (ie, Jupiter which always has the Earth between the Sun and itself) will always be further away on average. This effect happens even when talking about abstract circles and measuring points on them -- not about real orbits.