6.1. The Big Idea http://www.ck12.org
Universal Law of 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^2Universal Law of Gravity,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 force, we saw that the gravitational force or weight formula for objects near earth,Fg=mg, is a
special case of a more general result.
On the surface of a planet — such as earth — therin the Universal Law of Gravity is very close to the radius of
the planet. A planet’s center of mass is approximately at its center (for a spherical planet with azimuthal symmetry
of density this is exactly true). In addition, we can safely ignore the increase in height off the surface of Earth. 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 to very good accuracy that for objects near the surface of the earth, therin the
formula is constant and equal to the earth’s radius. This allows us to say that gravity is constant on the surface of the
earth. Here’s an illustration: