(415) |

Consider an object which appears stationary in our rotating reference frame:
*i.e.*, an object which is stationary with respect to the Earth's surface.
According to Equation (414), the object's apparent equation of motion in the
rotating frame takes the form

(416) |

where is the displacement vector of the origin of the rotating frame (which lies on the Earth's surface) with respect to the center of the Earth. Here, we are assuming that our object is situated relatively close to the Earth's surface (

It can be seen, from Equation (417), that the apparent gravitational acceleration
of a stationary object close to the Earth's surface has two components. First,
the true gravitational acceleration, , of magnitude
, which always points directly toward the
center of the Earth. Second, the so-called *centrifugal acceleration*,
. This acceleration is normal to the Earth's axis of
rotation, and always points directly away from this axis. The magnitude
of the centrifugal acceleration is
, where
is the perpendicular distance to the Earth's rotation axis, and
is the Earth's radius--see Figure 25.

It is convenient to define Cartesian axes in the rotating reference frame such that the -axis
points vertically upward, and - and -axes are horizontal, with
the -axis pointing directly northward, and the -axis pointing directly westward--see Figure 24.
The Cartesian components of the Earth's angular velocity are thus

(418) |

(419) | |||

(420) |

respectively. It follows that the Cartesian coordinates of the apparent gravitational acceleration, (417), are

The magnitude of this acceleration is approximately

(422) |

Another consequence of centrifugal acceleration is that the apparent
gravitational acceleration on the Earth's surface has a *horizontal*
component aligned in the north/south direction. This horizontal component
ensures that the apparent gravitational acceleration *does not* point
directly toward the center of the Earth. In other words,
a plumb-line on the surface of the Earth does not point vertically
downward, but is deflected slightly away from a true vertical in the north/south
direction. The angular deviation from true vertical can easily be
calculated from Equation (421):

(423) |