GRAVITY AND MOUNTAINS
The force of
causes every particle that has mass to attract every other particle.
As the amount of
mass increases, the gravitational attraction in
As the distance between the particles increases,
the gravitational attraction de
To describe the attractive force between bodies composed of
many particles (for example, gravitative force between your body and the earth), it is convenient to think
of all of the mass to be located at a single point – the object’s “center of gravity.”
For example, the
earth’s center of gravity lies at its physical center.
The mathematical expression is:
Force of gravity is proportional to m
, where m
are two masses, and r is the distance
between their centers of gravity.
We may describe the shape of the earth by a series of approximations.
To a first approximation the earth
Even if it had not started out with a spherical shape, it would have become a sphere as
every particle tries to get as close as possible to the center of the earth (its center of gravity).
implies that the shape of the earth can change; the earth can deform, which implies further that rocks in
the deep interior, although solid and under very high pressure, do not have much strength.
On a short
time scale, a rock acts as a
; it shatters when hit by a hammer or it ruptures by fault
On a long time scale of thousands of years or longer, rock acts as a
; it flows
just as a ball of silly putty flattens under its own weight. (On a short time scale, silly putty also acts as a
If you throw a ball of silly putty at a hard surface, it bounces; if you abruptly stretch the
silly putty it breaks apart.)
Secondly, the spherical earth is rotating, which draws the equatorial region outward into a bulge while
the polar regions are flattened.
A sphere, and the modified shape of a rotating earth, the
smooth surfaces described by simple mathematical expressions.
If you were standing at sea level on the Equator, you would weigh less than if you were standing at the
This is because (i) the earth’s equatorial radius is larger than polar radius (at the Equator
there is a greater distance between you and the earth’s center), and because (ii) the daily rotation tends
slightly to “levitate” you away from the earth at the Equator, but not at the North Pole.
Thirdly, the spheroid is the basis for a further approximation, an irregular shape with depressions and
Sea level describes the shape of the geoid.
Because each water molecule is able
freely to seek the lowest possible elevation, the sea surface is
(It is not
; it wraps around the
Sea level in the interior of a continent could be determined in principle by digging a slot canal
to that spot, and connected to the world ocean at the other end.
The ups and downs of the geoid are not
well understood, as they are the result of uneven distribution of mass (and associated gravity field) very