We know the gravity well. Then, Is the gravitational constant always constant? Is the present gravitational constant same as that of 10 million years ago ?

Currently G is changing no faster than about a part in 10^12 per year

 

http://arxiv.org/pdf/gr-qc/0411113 (ArXiv copy of a PRL)

 

I don't know if you can determine G from remote measurements (which would be old measurements by virtue of d =ct), because we assume the value to deduce the masses. The papers I can find all measure G-dot.

Why G is changing --albeit very slowy? Can general relativity live with changing G?

Why G is changing --albeit very slowy? Can general relativity live with changing G?

 

Nobody has claimed that it is (in the papers I found). The results are consistent with zero and place an upper bound on how fast it could be changing, which is a function of the experimental accuracy and precision. A claim that G was changing would require that zero be statistically excluded.