That would explain a change in the rotational speed of the sun. Our orbit would then be affected by the tidal bulge on the sun leading us, and millimetres (or less) over the distance involved isn't going to do it, at least not to any degree comparable to the tidal interactions between the Earth and Moon. Also, we're not the only body that would have significant tidal effects on the mass distribution of the sun - we're not even at the top. Venus would have a larger effect pushing us one way; Jupiter a larger effect pulling us the other way. We're a bit of fluff, a dust mote. We're as likely to lose kinetic energy as to gain it, making the year shorter and bringing us closer.