DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

TOPEX/POSEIDON
stability condition Qs(r)≡σR(r)κ(r)/3.36G
(r) > 1 and the single unstable wavelength
in the Qs(r) = 1 stellar disk λ∗(r) =
(2π × 3.36/ √ 0.948)G(r)/κ 2 (r) can be derived
from a dispersion relation for axisymmetric
perturbations in a differentially rotating stellar
disk with the local radial velocity dispersion
σR(r).
TOPEX/POSEIDON A cooperative project
between the U.S. and France to develop and
operate a satellite dedicated to observing the
Earth’s oceans. Since its launch in 1992, this
satellite has used an advanced radar altimeter
to measure sea surface height over 90% of the
world’s ice-free oceans. By determining the
orbit of the spacecraft to within a few centimeters,
the project has produced global maps
of ocean topography significantly more accurate
than any previous satellite altimeter. A
second goal of the project was the production
of accurate global tide maps. Consequently,
the TOPEX/POSEIDON orbit was designed to
avoid the aliasing of the solar tides into undesirable
frequencies, and this repeat orbit covers the
globe every 10 days. See also satellite altimetry.
Top hat detector A toroidal-geometry focusing
detector for low energy ions and electrons
(e.g., 100 to 30,000 eV) widely used in magnetospheric
research. It gives high counting rates
and uses fast electronic circuits to sort particles
by their time of flight through the instrument.
topocentric system This spherical coordinate
system (range, altitude, azimuth) serves to
specify a direction in space relative to the local
horizontal, vertical, and North, as well as the
distance from the location of the observer. See
altitude, azimuth, zenith, zenith angle, nadir.
topographic wave An orographic wave; a
wave in moving air driven by irregularities in
the surface topography of the Earth.
topography The elevation of the Earth’s surface
above sea level. Topography is created by
active mountain building processes and is destroyed
by erosion.
© 2001 by CRC Press LLC
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topological defect See cosmic topological
defect.
topology of space The set of properties of
a space that can be established without using
the notion of distance. Two spaces are said
to be topologically equivalent if one of them
can be obtained from the other by stretching,
squeezing, and any other deformation that does
not involve disruption or gluing points together.
For example, the outer surface of an open bottle
is topologically equivalent to the top surface
of a coin. However, the surface of a bicycle
tube is not topologically equivalent to the
coin-surface. The topology of the space we
live in is usually imagined to be that of the
Euclidean space, i.e., infinite in every direction,
with no identification of points. However,
general relativity and Einstein’s equations allow
more complicated topologies. The simplest
(e.g., Robertson–Walker) solutions to Einstein’s
equations for cosmology admit 3-spaces that are
Euclidean, or 3-hyperboloidal, or 3-spherical.
More complicated spaces are admitted; for example,
cosmological space could be that of a
three-torus, a three-dimensional analog of the
bicycle tube surface, which has the property
that it can be circled around in three different
directions after covering only a finite distance.
The attractive feature of such a space (called a
“small Universe”) would be that, given a sufficiently
long but finite time, all of matter existing
in the universe would come into view of every
observer. Whether our real universe is small is
a question that is in principle decidable by (very
difficult) observations.
tornado An intense cyclonic wind (windspeeds
up to 450 km/h) in contact with the
ground and locally associated with a thunderstorm.
Most frequently occurring in summer
and the early autumn in the midwestern U.S.
and in Australia. Typically characterized by a
funnel-shaped condensation cloud extending toward
the ground, though simply a debris cloud
beneath a thunderstorm is evidence of a tornado.
torque The product of a force F times the
lever arm from a fulcrum, measured perpendic-