NavList:

Rafal's question is spot on.  He computes where the bodies are "now", but due to the travel time of light from that body, the position where they are now cannot be where we observe them.

Consider the classic case of Jupiter's moons.  Longitude may be accurately determined (on land) by the arrangement of those moons about Jupiter, knowing their orbital periods.  Yet it was noted that the longitude observed at a given spot on the earth changed over time.  How could that be?  It was due in fact to the change is distance betwixt the earth and jupiter, at the instant of observation, yielding a delta in the travel time of light.  When that delta is unaccounted for, then longitude will shift. 

Rafal is attempting to compute where the body will be observed, which cannot be where the body is, as the speed of light is not infinite.  Rather light has a known velocity (rate) which has a direct affect on the problem statement.  Given that rate, we can compute travel time for a body.  For example Alpha Centauri is 4 light years away from us, meaning it takes 4 light years for the light to arrive here.  We do not observe where Alpha Centauri is, we observe where it was 4 years ago.

For bodies within our solar system, the light time is more readily measured in minutes.  If the sun is 92,000,000 miles away, and light travels at 186,000 miles/second in a vacuum, then light takes over 8 minutes for it to arrive here on earth [just numbers for the point of the discussion, not meant as a precise set of figures]. Similar computations can be applied to any two bodies within our solar system, yielding a time travel offset.

"But what does that matter?"  If the position of the sun "now" differs by (an admittedly rounded) 8 minutes from the position where we observe it, then the position observed will move us 120 nm, given 4 seconds per nautical mile.  

In other words, failure to account for the travel time of light will yield erroneous results.  The key point for Rafal is that he is computing the position of where the body is and wishes to transform that into a position that will be observed.  Indeed, he must account for the travel time of light 

Brad