|MadSci Network: Astronomy|
Excellent question with a surprising answer. The mass of the Sun is decreasing, as you note, and the Earth is getting farther away. The reason we don't observe the change is so small. The Sun weighs 2 x 10^27 tonnes, which is well over 99% of the mass in the entire solar system! It loses about 4 million tonnes a second. Although this seems like a huge amount, but it is actually is less than a millionth of a millionth of a millionth of a millionth (actualy 1 x 10^-21) of the Sun's mass. As you say, gravitational attraction is directly proportional to the Sun's mass, so a small change in one produces a small change in another. It's just a small change...
This huge mass of the Sun explains why most of the other planets have no effect at all on the Earth. There are always reports circulating that the planets are always about to line up causing havoc on Earth. But in reality the pull from the Sun always outweighs by a huge factor the other planets.
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