The radiative and particulate loss of mass by the Sun, -9.13*10^-14 Solar masses per year or more causes the orbits of the planets to expand at the same rate, and their periods to lengthen at twice this rate. Unfortunately, under the present definition of the Astronomical Unit (AU) based on the fixed Gaussian gravity constant kGS = 0.01720209895 (AU)^1.5/day, the value AUmet of the AU in meters must decrease at 1/3 this rate, all these rates being expressed logarithmically. The progress of the planets along their orbits slows quadratically with time. For example, in one century Mercury would lag behind the position predicted using constant solar mass by almost 1.4 km, in two centuries 5.5 km. The value of AUmet can be made constant by redefining it, based on a reference solar mass unit, such as the solar mass at J2000; else, the solar Gaussian gravity constant kGS used in defining the AU could be redefined proportional to the square root of the solar mass. Improved accuracy of the ephemerides would impose useful bounds on losses due to axion emission (Sikivie 2005). With no axion emission the Earth's semi-major axis grows 1.37 m/cy; with the maximum allowable such emission the result is 1.57 m/cy. Under reasonable assumptions about alternate gravity theories, radar delay data are used to show that the effect of a changing Newtonian gravity constant is negligible.