> TL;DR: assuming circular, coplanar orbits, for any planet A, the sun is on average closer to that planet than any other planet B, because planet B spends a lo

> TL;DR: assuming circular, coplanar orbits, for any planet A, the sun is on average closer to that planet than any other planet B, because planet B spends a lot of time on the other side of the sun from planet A, and given the way orbital rates work out the closer a planet is to the sun, the lower its average distance is to any planet farther out than it. It doesn't come from orbital rates; it comes from basic geometry. Imagine that the orbits of Earth and Mercury are perfect circles. Draw them on a piece of paper, and mark the position of Earth. Now, take a compass, place one leg at Earth, and draw a circle (with the Earth at the center) that passes through the Sun. This is a circle of radius 1AU. Now note that slightly less than half of Mercury's orbit is inside this circle: Mercury spends more of its time (in this idealized model) more than 1AU away from Earth. That plus an equivalent result for Venus leads to the finding of this link. This arises because of our old friend, the Pythagorean theorem. When Mercury->the Sun->Earth make a right triangle (that is, when Mercury is neither ahead of nor behind the Sun), the distance between Earth and Mercury is the hypotenuse of that triangle, which has legs of 1 AU and one Mercury-orbit-radius. That's obviously greater than 1AU.