A spherical planet for out in space has a mass M_o and diameter D_o. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

$\frac{4 \mathrm{GM}_{\mathrm{o}}}{\mathrm{D}_{\mathrm{o}}^2}$

Let g_o to the acceleration thin mg_o = $\frac{\mathrm{GM}_{\mathrm{o}} \mathrm{m}}{\left(\frac{\mathrm{D}_{\mathrm{o}}}{2}\right)^2}$

$\mathrm{g}_{\mathrm{o}}= \frac{4 \mathrm{GM}_{\mathrm{o}}}{\mathrm{D}_{\mathrm{o}}^2}$