So, why do objects fall towards the surface of the Earth? The first person, after Aristotle, to seriously
consider this question was Sir Isaac Newton. Since the Earth is not located in a special
place in the Universe, Newton reasoned, objects must be attracted toward the Earth itself.
Moreover, since the Earth is just another planet, objects must be attracted towards other
planets as well. In fact, all objects must exert a force of attraction on all
other objects in the Universe. What intrinsic property of objects causes them
to exert this attractive force--which Newton termed *gravity*--on other objects? Newton decided that the
crucial property was *mass*. After much thought, he was eventually able to
formulate his famous law of universal gravitation:

Incidentally, Newton adopted an inverse square law because he knew that this was the only type of force law which was consistent with Kepler's third law of planetary motion.Every particle in the Universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the particles.

Consider two point
objects of masses and , separated by a distance .
As illustrated in Fig. 104, the magnitude of the force of attraction
between these objects is

(541) |

Let and be the vector positions of the two objects,
respectively. The vector gravitational force exerted by object 2 on object 1 can
be written

(542) |

(543) |

The constant of proportionality, , appearing in the above formulae is called the
*gravitational constant*. Newton could only estimate the value of this quantity, which was first
directly measured by Henry Cavendish in 1798. The modern value of is

(544) |

Let us use Newton's law of gravity to account for the Earth's surface gravity.
Consider an object of mass close to the surface of the Earth, whose mass
and radius are
and
,
respectively. Newton proved, after considerable effort, that the gravitational force
exerted by a spherical body (outside that body) is the same as that exerted by an
equivalent point mass located at the body's centre. Hence, the gravitational
force exerted by the Earth on the object in question is of magnitude

(545) |

(546) |

(547) |

Thus, we conclude that all objects on the Earth's surface, irrespective of their mass, accelerate straight down (

Since Newton's law of gravitation is universal, we immediately conclude that any
spherical body of mass and radius possesses a surface gravity given
by the following formula:

(549) |