Orbital Velocity and Mass

For a comet orbiting the sun, as the comet gains speed on its inbound approach toward the sun, from the comet's frame of reference, the sun is moving rapidly closer. Does the comet's view of the sun then indicate that the sun is gaining mass as it's gaining speed? If so, then wouldn't the gravitational field of the sun also be increasing at a greater rate than simply the square of the distance? Does any of this have an effect on the comet's orbit?



Maybe the sun is too small to have a measurable effect, but approach this from a purely theoretical standpoint.

via JREF Forum http://forums.randi.org/showthread.php?t=272080&goto=newpost