http://www.ck12.org Chapter 9. Newton’s Universal Law of Gravity
gat moon=Gme
r^2=
Gme
( 60. 27 R)^2=
Gme
( 60. 27 )^2 R^2=
1
( 60. 27 )^2
Gme
R^2
→gat moon=1
( 60. 27 )^2
ge=1
( 60. 27 )^2
(
9. 81
m
s^2)
= 0. 00270
m
s^2We see the results are same, to three significant figures, using the equation for the centripetal acceleration we derived
earlier and Newton’s Universal Law of Gravity.
Another Inverse Square Law
It often happens in Physics that the form of an equation which describes one phenomenon is found describing a
seemingly different phenomenon. This is the case with static electricity. Fifty-eight years after the death of Isaac
Newton, in 1785, the French physicist, Charles Augustin de Coulomb (1736 - 1806),Figure9.9, published a work
giving the force of attraction between two charge particles asF=kqr^12 q^2. In this equation,q 1 andq 2 are two charges
measured in units of coulombs (C),kis a constant of proportionality, andrthe distance between the two charges.
FIGURE 9.9
Charles Augustin de Coulomb.You can very quickly get an idea of the force of electric charges by ripping a small piece of paper into even smaller,
tinier pieces. If you then have a plastic pen, try rubbing the pen on your shirt and then hold the pen over the tiny
pieces of paper. You will probably see some of the tiny pieces attach themselves to the pen. This is the result of an
electrical attraction. Clearly, the force of gravity was unable to keep the tiny bits of paper from sticking to the pen
and therefore we can conclude that the electrostatic force involved in this activity is greater than the gravitational
force. Electrostatics will be discussed in much greater detail later. We will note, however, that the force between
a positive and negative charge of 10−^6 C, the typical unbalanced charges produced by the kind of action described
above, at a distance of 2.00 m, gives rise to an attractive force of 2. 5 × 10 −^2 N. Recall that the gravitational force
between two 10.0-kg objects was of the order of 10−^9 N. In other words, the electric attraction is of the order of ten
million times larger in comparing these two examples. Had we used the actual masses of 10−^6 Cand computed the
gravitational attraction, we would have found that the electric force is some 40 orders of magnitude( 1040 )greater
than the gravitational force!
Even though mathematically Newton’s Universal Law of Gravity and Coulomb’s Law are similar, the forces they
describe have different natures and, usually, very different magnitudes. Also, whereas gravity is always an attractive
force, the electrostatic force can either attract (opposite charges) or repel (like charges).