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I would instinctively guess that a less massive earth would have less gravitational attraction to the sun, therefore widening the orbit. However, I understand that orbital mechanics can run counter-intuitively, and of course there are relativistic issues involved.

Here is an article that claims an estimated loss of 50,000 tons per year.

http://gizmodo.com/5882517/did-you-know-that-earth-is-getting-lighter-every-day

I will attempt to perform the calculation myself of the change in orbital length per millenium. Anyone have a ballpark estimate? Perhaps a kilometer longer? That's assuming a lighter earth moves away from the sun.

I'd also like to take into account the effect of a lighter earth on the distance to the moon. At this rate of Earth mass loss, how many millenia does is take for the moon to be moving away in kilometers per year, not cm?