Newton's third law says that if object A ``exerts" a force on object B called $F_{AB}$ then there is a force which B exerts on A $F_{BA}$ such that $F_{BA} = -F_{AB}$. With this in mind, consider the following two situations:
A person stands on earth and the earth induces a force $mg$ on him where $m$ is the persons mass and $g$ is the acceleration due to gravity. By the third law, this means the earth has a reciprocal force $-mg$. However, the person also stands on the surface of the earth and hence he exerts a force $mg$ onto the surface and hence again by the third law, the surface exerts a reciprocal force back onto the person $-mg$. Hence, there are is a total of force of $-2mg$ on the person. Is this reasoning correct?
Two planets $A$ and $B$ exist and planet $A$ exerts a gravitational force on $B$ $F_{AB}$ by Newton's law of universal gravitation. Hence by the third law there is a reciprocal $F_{BA}$ which $B$ exerts on $A$. However, we can invoke the Newton's law of universal gravitation again with the perspective of planet $B$ and say that $B$ exerts a force on $A$ $G_{BA}$ which is of course equal to $F_{BA}$. Does this mean that the total amount of force on planet $A$ is $2F_{BA}$? Or am I incorrectly understanding the assumptions which are needed to invoke the laws I've used?
