If you take millions of tons of metal off the earth in the form of satellites therefore reducing earth's specific mass, would this in turn affect the earth's orbit around the sun?
It affects insignificantly.
4-sd Earth mass in kg is 5.972 E+24 kg. 1-trillion-tons-taken out does not affect the least-sd (lsd) 1.
Our estimates are from scientific computation.
The precision (the number of correct significant digits (sd), in scientific notation) cannot be more than the smallest among the sd in the multitude of data used for computation.
For example, if
If mass is known, as a whole, in all the 25 sd, then removal of mass matters for lower sd of muli-precision values.