Underground Rivers - University of New Mexico

Case 3: Gravitation plus 17.1 rotation/day
centrifugal force
Chapter 14 -- Hollow Earth Geophysics
DRAFT 1122//66//22001122
Case 4: 17.1 rotation/day centrifugal force
alone
Case 3 spins our earth 17.1 times/day -- a "day" by our current timepiece, that is, not the solar
day in the faster-rotating world -- the ω required for centrifugal acceleration at the equator to be
9.81 meters/second 2 , counterbalancing the inward gravitational force. Could we do this, objects
would weight nothing at the equator. At the poles, however, gravity would be unopposed and
they'd weigh the weights to which we're accustomed.
Case 4 is Teed's model, that of a hollow earth with centrifugal force pushing us against the shell's
inside. What physics tells us -- though it may not be what we expect -- is that there's no
gravitational attraction between a shell of any thickness and an object within. There is no
gravitational pull whatsoever on objects within this world; there's just the centrifugal push that the
rotation exerts.
To make Teed's world function like the one we see, we need this centrifugal force to equal the
gravitational force with which we are familiar. At a ω of 17.1 rotations/day, an object dropped at
the interior world's equator travels straight toward the surface, accelerating at 9.81 meters/
second 2 , exactly as Teed would want.
At higher latitude, however, r is smaller. As centrifugal force is reduced, an object falls toward the
shell more slowly than does an object dropped at the equator. Moreover, the path of descent is
inclined to what the locals would call "down."
At the poles where there's no centrifugal force, objects in Teed's world don't fall. While few of us
have been to either pole, we're quite certain that a dropped glove falls to the snow.
In Case 5, a miniature sun at the sphere's
center exerts a thin ring of inward gravitational
pull. An object loosened at the poles would
obey the small sun's gravity and lift away from
the shell's inner surface. Rotating the interior
sun about a sister changes nothing but the
gravitational magnitude. Add a pair of internal
moons and we're approaching Seaborn's
universe, but we're not helping our case.
Our conclusion: Centrifugal force cannot
simultaneously maintain the same centrifugal
force at every point on the shell, what's needed
for falling objects to behave the same,
independent of latitude.
Case 5: Gravitation plus 17.1 rotation/day
centrifugal force
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