6.4. Common Forces http://www.ck12.org
6.4 Common Forces
Universal Gravity
In previous chapters we learned that gravity — near the surface of planets, at least — is a force that accelerates
objects at a constant rate. At this point we can extend this description using the framework of Newton’s Laws.
Newton’s Laws apply to all forces; but when he developed them only one was known: gravity. Newton’s major
insight — and one of the greatest in the history of science — was that the same force that causes objects to fall when
released is also responsible for keeping the planets in orbit. According to some sources, he realized this while taking
a stroll through some gardens and witnessing a falling apple.
After considering the implications of this unification, Newton formulated theLaw of Universal Gravitation: Any
two objects in the universe, with massesm 1 andm 2 with their centers of mass at a distancerapart will experience a
force of mutual attraction along the line joining their centers of mass equal to:
F~G=Gm^1 m^2
r^2
Universal Gravitation [3],where G is the Gravitational constant:
G= 6. 67300 × 10 −^11 m^3 kg−^1 s−^2Here is an illustration of this law for two objects, for instance the earth and the sun:
Gravity on the Earth’s Surface
In the chapter on energy, we saw that the gravitational potential energy formula for objects near earth,Ug=mgh,
is a special case of a more general result. It so happens that the fact that gravity accelerates near earth objects at a
constant rate is an almost identical result.
On the surface of a planet — such as earth — therin formula [3] is very close to the radius of the planet, since a
planet’s center of mass is — usually — at its center. It also does not vary by much: for instance, the earth’s radius is
about 6,000 km, while the heights we consider for this book are on the order of at most a few kilometers — so we
can say that for objects near the surface of the earth, therin formula [3] is constant and equal to the earth’s radius.
This allows us to say that gravity is more or less constant on the surface of the earth. Here’s an illustration: