Mass of Earth 16x more?

Question

What would happen to the radius so your weight would not change?

Answer 1

1) The acceleration of gravity @ the surface of the Earth is K / R^2; where K is a constant proportional to the mass of the Earth; and R is the radius of the Earth.

2) My weight, w = mK / R^2; where m is my mass

3) If K increases by a factor of 16 and my weight is unchanged, then Rnew^2 = m* (16K) /w = 16 * (mK/w) = 16R^2

4) So, Rnew = 4 * R;

5) If the mass of the Earth increased by a factor of 16, and the radius of the Earth increased by a factor of 4, my weight would be unchanged.

Answer 2

Since gravity changes by 1/r^2 then the radius would need to be 4X