DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

oceans, and also in other surface waters in underground
waters, and in glacial deposits. The
term hydrosphere should also include water involved
in the hydrologic cycle, i.e., water vapor
in the air and droplets in clouds.
hydrostatic Related to still water. For example,
hydrostatic pressure is the pressure resulting
from a stationary column of water.
hydrostatic approximation An approximation
in which the pressure is assumed to be equal
to the weight of the unit cross-section column of
fluid or air overlying the point.
hydrostatic equation The variation of pressure
(p) with depth (d) in a fluid at rest is one of
the fundamental relationships in fluid mechanics:
dp = −ρgdz. The change in pressure
(dp) of the fluid is equal to the unit fluid weight
(ρg) over some vertical distance (dz), which we
can integrate from the bottom of a fluid column
(z =−d) to the surface (z = 0):
ps
p
0
dp =−ρg dz
−d
whereps is the pressure at the surface. Integrating,ps−p
=−ρg[0 −(−d)],orp−ps =ρgd,
which can be used to calculate the absolute pressure
at any point in a static fluid. Commonly we
take the fluid pressure at the surface to be zero
gage pressure (ps = 0), or the fluid pressure
relative to atmospheric pressure. The absolute
pressure is then the sum of gage pressure and
atmospheric pressure. If p is the gage pressure
and the fluid is static with a constant density
(ρ), then pressure increases linearly with depth:
p=ρgd.
hydrostatic equilibrium The condition in
a star or other object where the inward force
of gravity is precisely balanced by the outward
force due to the gradient of pressure, that is
dP
dr =−GM(r)ρ ,
r
where P and ρ are the local values of pressure
and density at radiusr,M(r)is the mass interior
to this point, andG is Newton’s constant of gravity.
In the absence of hydrostatic equilibrium, a
© 2001 by CRC Press LLC
hysteresis
star will expand or contract on the free-fall time
scale (about 1 hour for the sun). A slight imbalance
can lead to stellar pulsation (see, e.g.,
Cepheid variables). A large imbalance leads to
either catastrophic collapse or violent explosion,
or both (see supernova, type II). In general relativity
in spherical systems the equation is modified
to require larger |dP/dr| to maintain equilibrium;
as a result, such systems are less stable
when analyzed in full general relativity then as
predicted from Newtonian theory.
hydrostatic pressure The hydrostatic pressureph
is the pressure in water, say the oceans,
as a function of depth h,
ph =ρwgh
where ρw is the density of water and g is the
acceleration of gravity.
Hygiea Tenth asteroid to be discovered, in
1849. Diameter 430 km. Orbit: semimajor axis
3.1384 AU, eccentricity 0.1195, inclination to
the ecliptic 3 ◦ .847, period 5.56 years.
hygrometer A device to measure relative humidity.
Hyperion Moon of Saturn, also designated
SVII. Discovered by Bond and Lassell in 1848,
it is one of the largest non-spherical bodies in
the solar system. Its orbit has an eccentricity of
0.104, an inclination of 0.43 ◦ , and a semimajor
axis of 1.48 × 10 6 km. Its size is 205 × 130 ×
110 km, its mass, 1.77 ×10 19 kg, and its density
1.47 g cm −3 . It has a geometric albedo of 0.3,
and orbits Saturn once every 21.28 Earth days.
hypersonic Pertaining to speeds or flows
with Mach number exceeding 5. In hypersonic
motion of a body through a fluid, the shock wave
starts a finite distance from the body. See Mach
number.
hysteresis The property whereby a dependent
variable can have different values according
to whether the independent variable is increasing
or decreasing. In hydrologic systems,
a loop-like curve develops that relates pairs of
hydraulic properties of an unsaturated porous
medium because volumetric moisture content
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