Geography Reference
In-Depth Information
0°
0°
6 hr
3 hr
A
A
B
0°
9 hr
B
12 hr
A
B
A
C
C
0
°
Fig. 1.7
Motion of a frictionless object launched from the north pole along the 0˚ longitude meridian
at t
=
0, as viewed in fixed and rotating reference frames at 3, 6, 9, and 12 h after launch. The
horizontal dashed line marks the position that the 0˚ longitude meridian had at t
=
0, and
short dashed lines show its position in the fixed reference frame at subsequent 3 h intervals.
Horizontal arrows show 3 h displacement vectors as seen by an observer in the fixed reference
frame. Heavy curved arrows show the trajectory of the object as viewed by an observer in
the rotating system. Labels A, B and C show the position of the object relative to the rotating
coordinates at 3 h intervals. In the fixed coordinate frame the object oscillates back and forth
along a straight line under the influence of the restoring force provided by the horizontal
component of gravitation. The period for a complete oscillation is 24 h (only 1/2 period is
shown) . To an observer in rotating coordinates, however, the motion appears to be at constant
speed and describes a complete circle in a clockwise direction in 12 h.
angular momentum. Because is constant, the relative zonal velocity must change.
Thus, the object behaves as though a zonally directed deflection force were acting
on it.
The form of the zonal deflection force can be obtained by equating the total
angular momentum at the initial distance
R
to the total angular momentum at the
displaced distance R
+
δR:
(R
R
2
+
u
R
u
δu
δR)
2
+
=
+
+
+
R
δR
where δu is the change in eastward relative velocity after displacement. Expand-
ing the right-hand side, neglecting second-order differentials, and solving for δu
gives
u
R
δR
δu
=−
2δR
−
