I didn't study physics in college nor any other science major, but I love physics and read a lot about it. Still I find troubling contradictions in my understanding of Newton's interpretation of gravity. For starters, how can the force of gravity be directly proportional to the two masses? If two bodies with equal masses are trying to pull each other this will cause them to repel each not attract each other, because each mass is exerting a force of gravity in a direction opposite to the direction of the gravity of the other mass, making the outcome of the two equal opposite forces = zero! I imagine them like two people pulling each other with the same force, this obviously wont cause the two bodies to move closer to each other, like two kids with equal mass playing tug of war. Therefore, if a planet was close to Earth, according to Newton, they will both move closer to each other, but according to the people pulling each other, they will never touch each other! What are you guys think? Is this a flaw in Newton's theory, or am I missing something?