DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

(at least), and different observers use different
space and time coordinate functions. Although
the notation {x,y,z} suggests rectangular coordinates,
the constant x− surfaces can in fact
be curved, for instance, if x is really the radius
from the origin in a spherical coordinate system.
In general, the coordinate functions can lead to
curved constant-coordinate surfaces (curvilinear
coordinates). Then the four spacetime coordinates
form a set of functions, sayφ α (P) where
φ α ,α= 0, 1, 2, 3 correspond to the time and the
three spatial coordinate functions;P represents
a point in spacetime.
A coordinate system is closely related to a
reference frame. For instance, one can align
basis vectors (which constitute the frame) along
the intersection of constant-coordinate surfaces,
with some rule for assigning length or magnitude
of the basis vectors.
coordinate time Time defined relative to
an inertial (in particular, nonrotating) reference
frame, whose relationship with time measured
on the surface of the Earth can be calculated
using relativity (not to be confused with
“coordinated time” like Coordinated Universal
Time). General uses are “Geocentric Coordinate
Time” (TCG) and “Barycentric Coordinate
Time” (TCB), the latter referring to the solar
system barycenter.
coordinate transformation in special relativity
The transformation of space-time coordinates
between two reference systems that are
moving uniformly with respect to each other.
Classically, any physical system is composed of
particles, and a full description of the system
is obtained if all the positions of each particle
are known for any given time. The position of
each particle is represented by a trio of numbers
whose value depends on the location of the reference
system. Thus if two observers used two
different systems of reference, then a coordinate
transformation is needed in order to compare the
observations. Classically time is considered to
be an absolute variable; that is its value is the
same regardless of the reference system. Thus,
classical coordinate transformations transform
an arbitrary trio of spatial coordinates at any
given time. Special relativity states that the velocity
of light is constant for two reference sys-
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core
tems that are moving at constant velocities with
respect to each other. In order for this to hold
time can no longer be an absolute variable, and
its value must depend on the reference system.
The universal character of the speed of light plus
the assumption that space is homogeneous and
isotropic leads to the Lorentz transformation of
space-time coordinates. The Lorentz transformations
transform an arbitrary foursome of coordinates
(three spatial coordinates plus time)
from one system of reference to another that is
moving uniformly with respect to the first.
Copernicus, Nicholas Astronomer (1473–
1543). Proposed that the sun, rather than the
Earth, was the center of the solar system.
coplanarity theorem In magnetohydrodynamics,
the coplanarity theorem
n · (Bd × Bu) = 0
states that the shock normal n and the magnetic
fields Bu and Bd in the upstream and downstream
medium all lie in the same plane. The coplanarity
theorem is a consequence of the jump
conditions for the electromagnetic field at the
shock as described by the Rankine–Hugoniot
equations. See Rankine–Hugoniot relations.
Cordelia Moon of Uranus also designated
UV. Discovered by Voyager 2 in 1986, it is a
small, irregular, body, approximately 13 km in
radius. Its orbit has an eccentricity of 0, an inclination
of 0.1 ◦ , a precession of 550 ◦ yr −1 , and a
semimajor axis of 4.98 × 10 4 km. It is the inner
shepherding satellite for Uranus’ epsilon ring.
Its surface is very dark, with a geometric albedo
of less than 0.1. Its mass has not been measured.
It orbits Uranus once every 0.335 Earth days.
cordillera An extensive chain of parallel
mountains or mountain ranges, especially the
principal mountain chain of a continent. The
term was originally used to describe the parallel
chains of mountains in South America (las
Cordilleras de los Andes).
core Differentiated central volume of the
Earth and (some) other planets. Cores vary in
composition, size, and physical state among the
different solar system bodies. In geophysics,