Newton's gravitational force states that the force a gravity between two objects is given by:
[tex]F=G\frac{mM}{r^2}[/tex]The gravitational acceleration is defined as the acceleration exerted by a mass in another and it is related to the weight of the mass as:
[tex]W=mg[/tex]Plugging this force in Newton's gravitational law we have that:
[tex]\begin{gathered} mg=G\frac{mM}{r^2} \\ g=G\frac{M}{r^2} \end{gathered}[/tex]Let's assume M and r are the mass and raidus of earth respectively, then we have that the gravitational acceleration on earth is:
[tex]g=G\frac{M}{r^2}[/tex]Now, in planet Nelson the mass is 4 times that of earth and its raidus if four times the raidus on earth, then we have:
[tex]\begin{gathered} g^{\prime}=G\frac{4M}{(4r)^2} \\ g^{\prime}=G\frac{4M}{16r^2} \\ g^{\prime}=\frac{1}{4}G\frac{M}{r^2} \\ g^{\prime}=\frac{1}{4}g \end{gathered}[/tex]Therefore, the acceleration of gravity in planet Nelson is 1/4 the acceleration of gravity on earth.
