Carusus wrote:

Many thanks for your prompt answer and clear explanations. However, your
first answer does not seem to take account of the increasing density of
the sun, which presumably affects its gravitational pull.

As Greg points out (it appears his posting arrived just after you
sent the above) the density or distribution of mass in a body has no
effect on the gravitational force it produces from a distance: only
the total mass counts, and it may be treated as if it were all
located at the body's centre of mass.

So if the sun's density is increasing this implies it will contract
more than one would expect from the loss of mass alone, but the
gravitational force experienced by the earth will continue to be a
simple function of the sun's remaining mass and the distance to its centre.

--Odysseus