Newton's Universal Law of Gravitation

Newton's universal law of gravitation states: every particle of matter in the universe attracts every other particle with a force whose magnitude is directly proportional to the product of their two masses, and inversely proportional to the square of the distance between them, acting along the straight line joining the two particles. For two point masses $m_1$ and $m_2$ separated by a distance $r$,

where $G$ is the universal gravitational constant, discussed in the next section. A few features of this law are worth stating explicitly, since each of them is essential to everything that follows in this chapter:

• It is always attractive, never repulsive -- unlike the electric force between charges, there is no such thing as gravitational repulsion between two masses.
• It obeys Newton's third law. The force mass $m_1$ exerts on mass $m_2$ is exactly equal in magnitude, and exactly opposite in direction, to the force $m_2$ exerts on $m_1$ -- even when the two masses are wildly different, as for the Earth and a falling apple, in which case the Earth pulls the apple down with the very same magnitude of force with which the apple pulls the Earth up (though the resulting acceleration of the enormously more massive Earth is, of course, utterly negligible).
• It is a central force, acting exactly along the line joining the two masses.
• It is universal, applying without exception to any two masses anywhere in the universe, from subatomic particles to galaxy clusters -- there is no special exemption for astronomical bodies, and no minimum mass or distance below which it stops applying.
• It obeys the principle of superposition. When more than two masses are present, the total gravitational force on any one of them is simply the vector sum of the separate forces due to every other mass individually, each still given by the same inverse-square law, with the direction of each individual force still along the line joining that pair of masses. …