If the sun as a charge of 6.7e22 C, what would the charge of the earth have to be to begin being pushed away?

Answer 1

KQ1Q2/r^2 = GM1M2/r^2

Qe = GMeMs/(k(6.7e22C)) = 1.32e12C

Answer 2

Any charge at all of the same polarity would make the sun repel the earth. Gravity might still hold it in orbit, but its orbit would be more elliptical.