What would the density of a sphere of radius 1.07 m have to be in order to produce a gravitational acceleration of 1.01 m/s2 at the surface of the sphere?

M G/r^2 = a

where M is the mass, a the acceleration, and r is the radius. The mass is given by:

M = 4/3 pi r^3 rho

with rho the density, so:

4/3 pi G rho r = a ----->

rho = 3 a/(4 pi G r)