Newton's Law of Gravity

If object A has mass Ma and object B has mass Mb,
then the force F on object A is directed toward object B
and has magnitude

F = G M_a M_b / r²

So, considering the force between an Sun and the Earth

• The force exerted on the Earth by the Sun is equal and opposite to the force exerted on the Sun by the Earth.
• If the mass of the Earth were doubled, the force on the Earth would double.
• If the mass of the Sun were doubled, the force on the Earth would double.
• If the Earth were twice as far away from the Sun, the force on the Earth would be a factor four smaller.

• If the two objects are very small compared to the distance between them, then the force is given by Newton's formula with r being the distance between the objects.
  
  
• If one of the objects is very small and the other is spherically symmetric, then the same formula holds with r being the distance from the small object to the center of the big object.
  
  
• Point two is a consequence of point one. Newton proved it by adding up the forces.