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Question:
Although the Coriolus effect is zero on the equator, the rotation of the Earth may still affect ballistics there. For example, suppose that a shell is fired directly eastward along the equator, in the absence of wind, and it hits a target ten miles away. When the shell is fired it has an eastward motion due to the rotation of the Earth plus a force (explosion) that sends the shell out of the barrel of the gun in the same direction. If the same target is relocated ten miles to the west of the original firing spot, and another shell is fired under identical conditions (same gun, same type of ammunition, same angle of elevation), the shell will theoretically land where?



Replies:
It lands where it was aimed.

The Coriolus effect (there is no Coriolus force any more than there is centrifugal force) happens when an object moves north or south on a rotating body, free from the surface.

A shell shot north from the equator leaves the gun with an E-W velocity the same as the tangential velocity of Earth's equator. It flies north, free from contact with the surface and moves to a place where the tangential (not angular) velocity of Earth's surface is less. To the earthbound observer, it veers east.

A shell fired along a line of latitude is fired and lands at points that are moving at the same tangential velocity so the earthbound observer sees no effect.

Note that the frame of reference is crucial. We launch rockets west to east as close to the equator as possible because orbital velocity is measured in not relation to the ground, but the earth's center, as it were.

R. W. "Bob" Avakian
Instructor
B.S. Earth Sciences; M.S. Geophysics
Oklahoma State Univ. Inst. of Technology


There should actually be a small Coriolis effect that will make the shell's ranges different in the two directions, even if it never leaves the plane of the equator.

The initial velocity imparted to the shell relative to the spinning earth has the same magnitude in both cases. In the eastward case, the firing of the shell will cause the earth to spin a little slower (until the shell lands); in the westward case, the firing of the shell will cause the earth to spin a little faster (again, until the shell lands).

The Coriolis effect influences the shell's motion only when it changes its distance to the Earth's axis of rotation. Changing latitude does this, which is the context in which the Coriolis effect is ordinarily encountered. At the Equator, the only factor that can change distance to the rotation axis is the height attained in the trajectory.

Think of it in terms of a shell fired straight up (vertically) from the equator. (Neglect air resistance for this argument.) As the shell rises, its eastward velocity remains the same as the Earth's at the equator. However, its radius from the axis becomes larger, so the land surface would appear to turn faster. Relative to the land, the shell would appear to move to the west. Then, as the shell falls, its radius decreases, its westward movement appears to pick up again, reaching the same value as the earth's surface when it reaches the surface. So, from a perspective on the surface of the rotating earth, the projectile's trajectory would start vertical, curve to the west, and then return to earth exactly vertical.

Richard Barrans, Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming



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