Gravitational force: action and reaction

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In an isolated system with two interacting particles, if particle 1 exerts a gravitational force on particle 2, particle 2 must exert an equal and opposite force on particle 1, adhering to Newton's third law. The discussion raises the question of whether the net force on particle 1 is the sum of the gravitational forces exerted by both particles on each other. The gravitational force is defined by the equation F=G(m1*m2)/r^2, indicating that the forces are equal in magnitude but opposite in direction. Thus, the force on particle 1 is equal to the negative of the force on particle 2, confirming F1 = -F2. This illustrates the fundamental principle of action and reaction in gravitational interactions.
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Consider two particles 1 and 2 that can interact with each other but are isolated from their surroundings. If an internal force from particle 1, for example, a gravitational force, acts on particle 2, then there must be a second internal force—equal in magnitude but opposite in direction—that particle 2 exerts on particle 1.
But if the particle 2 exerts a gravitational force too? Will the net force exerted on particle 1 be the sum of the gravitational forces 1 to 2 and 2 to 1?
 
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the force is given by

F=G \frac{m_1 m_2}{r^2}

the force on 1 = - force on 2

so F1= -F2
 
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