The potentials (both phi and A) are retarded, for any motion of the charge.  But for a charge moving at constant velocity, the fields (both E and B) are relate to the instantaneous position of the charge.   --  Gene From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, July 19, 2015 8:50 AM Subject: [math-fun] Retarded Maxwell charges and approximate generale relativity Lienard–Wiechert potential: https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential and https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential#Defini... (Simplest when beta=0) the retarded potential is generated by where the source charge was a speed of light delay ago, and the corresponding fields ditto. (A statement by Salamin had seemed confused re this.) Newton law with retardation added is not the correct equations of gravity but hopefully are less-incorrect than plain Newton law. Retarded Newton law as I pointed out earlier would cause weird effects like non-conservation of angular momentum in symmetrical rotating scenarios. The post-whoever equations of approximate general relativity all involve retarded locations, but they also involve (what a Newtonian would call) multi-body forces. These equations recast GR in a Newton-like framework and they have been worked out at Kth order for K=1,2,3,4,5 at least, I'm not sure how far they've gone. Last time I checked I think it was not known whether at least one of these sequences can be continued forever, or whether some obstacle arises at some high order.  There are two such sequences.  One is based on a power series expansion about c=infinity.  The other is based on G=0. The first approximant beyond plain Newton is used by NASA to simulate the solar system.