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matter in each.

Together with the inverse square nature of the force, this means that the magnitude of the force of attraction between two particles (or spherical bodies) of mass m1 and m2, separated by a distance r, is Gm1m2/r2, where G is the same for all bodies in the Universe (known as the 'universal constant of gravitation'). The fact that the (gravitational) masses in this expression are the same as the (inertial) masses that appear in the second law of motion (Eqn (8.1)) is, in Newton's system, simply an experimentally observed fact. If it were not the case, pendulums made of different materials but of the same length would have different periods. The equivalence of these quantities lies at the heart of Einstein's general theory of relativity (see Chapter 12).

In the case of a single planet orbiting the Sun, it follows that we should not treat the Sun as a fixed object because it is attracted by the planet. Newton thus

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