The Coulomb-force in a star is equal to 3.4 octillion times of universal gravitation (neglect the effect of electricity charge tending to the surface).
Anyway, the point is that Newton's law of gravitation is just an approximation - good enough to get us to the moon, but not perfect. General relativity is better.
If you measured the deflection accurately and worked out the mass of the mountain, you could calculate the universal gravitational constant that is, the basic value of gravity, known as G and along with it the mass of the Earth.
This is how scientists explain the existence of dark matter: according to Newton's law of gravity, stars orbiting the center of a galaxy should slow down the farther they are from the center.