Is the ratio between earth's distance from the sun and the speed of light just a coincidence? I was doing some calculations to see how hard it would be to observe the speed of light and discovered an interesting correlation between the speed of light and the average distance from the earth to the sun. In my example, an object would be placed in orbit around the sun so that its  shadow would pass over the earth at the speed of light.  After doing some math, I found that an object roughly 1 km above the sun, orbiting at 2 m/s would achieve this.  I though that these numbers were a bit odd, so I took a closer look at the speed of light (299,792,458 m/s) and AU (149,597,871 km.)  I found that 299,792,458 / 149,597,871 = 2 within a .2% degree of inaccuracy.  To me, this seems too close to be chance.  Is there an established relationship here, or is this just luck?
It is a co-incidence. The units are what you need to look at, in both the speed of light and the distance of the Sun the units of length are the same (m) (your ratio is $\approx 0.002 s^{-1}$ when you use metres as the unit for the distance to the Sun). The definition of the second is in a sense arbitrary and is a consequence of how we have chosen to sub-divide the day into smaller units of time (there is nothing cosmic in dividing the day into 24 units each subdivided into sixtieths which are again subdivided into sixtieths).

If we had chosen to take as our basic unit of time $1/100000$ of a day rather than $1/86400$ the nice round answer vanishes (if my calculations are right the $\approx 0.002$ becomes $\approx0.0023$)