"Uh, oh! Looks like somebody's forgotten that all motion is relative." - Physicist
Wow, where do I start? Your comment is more than just wrong, it's wrong in multiple dimensions.
For one thing, acceleration and deceleration are NOT relative (hey, decelerate objects, even uniformly, enough and you will see the temperature of those objects drop to Absolute Zero, too cool).
For another thing, motion, even when relative between two objects (e.g. uniform), still matters.
And that fact brings us back to my point and away from your red herring statement above.
Consider, for instance, that our Sun and Earth are BOTH moving in the same direction as the rest of our Solar System, and that our Solar System is moving in uniform concert with the rest of our Galaxy (which itself is moving through our Universe).
Now, even though the relative motion of the Earth and the Sun would APPEAR to make the Sun seem stationary as the Earth orbits around it, in reality the Sun (as well as the Earth) will be in a different physical location in the 8.3 minutes that it takes light to reach the Earth.
Thus, observers on Earth will currently percieve the Sun to be in the location it occupied 8.3 minutes ago.
This brings up an interesting consideration: does the Earth orbit around the ACTUAL position of the Sun (implying a near instantaneous speed of gravity as predicted by Newton), or does the Earth orbit the PERCIEVED position of the Sun (implying a speed of Gravity equal to that of Light as predicted by Einstein)?
If the Sun and the Earth (OK, our whole Solar System) are both moving North at the same speed even as Earth orbits the East-West axis of the Sun, then both the Sun and the Earth will be 8.3 minutes North of the percieved position of the Sun (due to the 8.3 minute delay for light reaching the Earth from the Sun).
Thus, planetary orbits based on a speed of Gravity at that of the speed of Light will have a "lag" South of the Sun (and this "lag" will be more pronounced the further away fromt he Sun that a planet orbits), whereas planetary orbits based upon a speed of Gravity equal to the Speed of Light squared will have no discernable lag South of the uniform movement of our Solar System.
Thus, if Jupiter lags further South of the Sun than does Earth, then you and the authors of the article for this thread are correct.
On the other hand, if the planets generally orbit the Sun in the same plane (i.e. there is no lag South of the Sun by the planets), then Gravity must travel substantially faster than the speed of Light.