A Classical Approach of Newtonian Mechanics

12 ORBITAL MOTION 12.3 Gravity

1 2

f = G m m / r 2

m 2

m 1

Figure 104: Newton’s law of gravity.

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:

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.

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.

Consider two point objects of masses m 1 and m 2 , separated by a distance r.

As illustrated in Fig. 104 , the magnitude of the force of attraction between these

objects is

f = G

m 1 m 2

. (12.1)
r^2
The direction of the force is along the line joining the two objects.

• f
  r

f