Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

Подождите немного. Документ загружается.

(McConnell, 1980, pp. 26 – 29). Hansteen used it for indicating

both declination and horizontal intensity. Other magnetic researchers

across Europe used and designed fiber-suspension instruments, includ-

ing François Arago and C.F. Gauss (Multhauf and Good, 1987,

pp. 15– 16). Around 1830, the word magnetometer was applied to

these instruments that measured magnetic intensity.

By 1800, all of the forms of magnetic instruments based on mag-

netic needles, for both application and research, were available, but

the most dramatic innovations were still to come. The efforts by Arago

and Humboldt to improve the quality of magnetic observations and to

popularize them established a solid trade in magnetic instruments. The

favorite maker of magnetic instruments of Arago and Humboldt, H.P.

Gambey of Paris, supplied variation and dip instruments around the

globe during the 1820s– 1840s (see Figure I17). Soon, Gauss and

Weber would change how the instruments were used and how the data

obtained were analyzed, bringing on a new period of instrumental

innovation in the 1830s.

Class ical geomag netic inst ruments, from Gaus s

and W eber to the 1920s

When Carl Friedrich Gauss and Wilhelm Weber turned to geomagnet-

ism in the 1830s, they developed several new geomagnetic instruments

and procedures. Gauss and Weber developed a much larger fiber-

suspension instrument than usual for determining declination. Their

magnetic needle weighed over 2 kg (and later ones 10 kg or more), in

contrast with, e.g., Hansteen ’s needles measured in grams, to mitigate

the effects of air currents. They used a much longer suspension, about

2 m. Hansteen ’s suspensions were under 20 cm. Most importantly,

Gauss and Weber borrowed an innovation from J.C. Poggendorff.

He had fixed a mirror to the end of the needle and observed it from

about 5 m away using an observing telescope, arranged so that he

could see in the mirror a scale fixed to the base of the tripod of the

telescope. Gauss wrote that this new instrument, the Gauss-Weber

magnetometer, let them measure declination with a dramatically higher

precision, similar to that known in astronomy. Indeed, he wrote that

this instrument made possible the scientific study of declination and

horizontal intensity (Gauss and Weber, 1837, p. 11).

Gauss and Weber also changed the fiber-suspension, horizontal

magnetometer fundamentally by changing the way it was used. Gauss

announced a two-step procedure in 1832 for calculating Earth ’s hori-

zontal magnetic intensity in mechanical terms, i.e., length, mass, and

time. He called this an “absolute ” method (see Gauss ’ determination

of absolute intensity ). Gauss and Weber ’s magnetometer described

above was so large it filled the building. It became the standard obser-

vatory instrument for the Magnetische Verein, an association of mag-

netic observatories, which collaborated with Gauss and Weber in

the 1830s and 1840s. They worked with instrument makers Moritz

Meyerstein of Göttingen, F.W. Breithaupt of Kassel, and others to sup-

ply more than a dozen of these instruments for observatories from the

United States to Russia. They also developed the first bifilar magnet-

ometer for direct indication of changes in the horizontal magnetic force

and several portable instruments. In the bifilar instrument, the two-

filament suspension was twisted so that the magnetic needle was held

perpendicula r to the magnetic meridian. As the Earth ’s magnetic force

changed, the needle moved (Multhauf and Good, 1987, pp. 16– 19).

This instrument type was later termed a “variometer ” becaus e it indi-

cated directly the variation of a magnetic variable. Hence, while they

did not use the word, Gauss and Weber ’s bifilar magnetometer was

the first variometer.

Besides Gauss and Weber, Humphrey Lloyd ( q.v. ) most carefully

analyzed magnetic instruments and their use in the 1830s. Like Gauss

and Weber, Lloyd investigated sources of error and ways to optimize

instruments. He developed “ Lloyd ’s balance ” to indicate changes in

the vertical magnetic force (hence the second variometer) and an indir-

ect method of measuring the vertical force through induction, in addi-

tion to his own designs for unifilar and bifilar magnetometers, both for

observatories and for field use. He, like Weber, recognized that no por-

table magnetic instrument could match the precision of an observatory

magnetometer. Also like Weber, he designed portable instruments of

the greatest possible precision. Lloyd’ s instruments supplanted Gauss

and Weber ’s for the British “Magnetic Crusade” of the 1840s and

1850s. C.J.B. Riddell illustrated and explained the selection of mag-

netic instruments used by British observers during the Magn etic Cru-

sade, including their shortcomings, in his Magnetical Instructions

(1844). He even included a catalog of the instruments, available from

three British instrument-making shops.

Clearly, the mid-19th century witnessed a remarkable burst in

instrumental innovation. The best illustration of this goes far beyond

any instruments seen before: photographically self-registering instru-

ments. Introduced in 1846, they transformed magnetic research.

Variants came and passed quickly at first, but by the 1850s the market

settled to just a few models, especially those by Charles Brooks and

Patrick Adie, both of London. Self-registering instruments used a tightly

focused light beam, directed by mirrors attached to the instruments’ mag-

nets, to trace a graph of varying declination, intensity, etc., on a moving

film or paper. These instruments removed the drudgery of oft-repeated

visual measures. The data cascaded and overwhelmed magnetic workers,

requiring greater staffing and more computational power.

National or regional magnetic surveys in France, England, the

United States, and India, for example, in the late 19th century orga-

nized and routinized magnetic measurements. This spurred agencies

in several countries to produce lightweight, robust field instruments.

The “Kew-pattern” dip circle and magnetometer became standard in

Britain, its colonies, and in the United States ( Figures I18

and I19 ,

Multhauf and Good, 1987, Figure 63). For the French magnetic sur-

vey, elegant, gem-like magnetometers and dip circles were fashioned

of brass (Figure I20; Multhauf and Good, 1987, Figures. 38, 61, 64).

The Prussian survey adopted a design by J.F.A.M. Eschenhagen,

which other agencies decided was more appropriate for observatories

because of its complexity (Multhauf and Good, 1987, Figure 41).

From the 1890s until about 1915, the US Coast and Geodetic

Survey and then the Carnegie Institution of Washington’s Department

Figure I17 Variation transit by H.P. Gambey, Paris. This

instrument was used by A.D. Bache in his magnetic survey

of Pennsylvania in the 1830s. (Photo courtesy of Smithsonian

Institution.)

436 INSTRUMENTATION, HISTORY OF

of Terrestrial Magnetism (DTM) (q.v.) systematically extended the tra-

ditional instruments based on magnetic needles and induction almost

as far as they could go. The culmination was the DTM “Univer-

sal Magnetometer,” (Figures I21 and I22) which packaged nearly

everything needed for a complete magnetic survey in Tibet or deepest

Amazonia into a wooden box barely 20 cm square and weighing

17 kg.

Schmidt’s vertical balance, designed by Adolf Schmidt in 1915 at

the Prussian Meteorological Institute, improved the measurement of

vertical intensity. Instruments by Askania-Werke AG were very popu-

lar in prospecting in the mid-20th century. The Askania firm resulted

from the combination of Werkstätten für Praezisions-Mechanik und

Optik of Berlin with Centralwerkstatte Dessau in 1921.

Figure I18 Kew-pattern magnetometer by John Dover of London.

(Photo courtesy of Smithsonian Institution.)

Figure I19 Kew-pattern dip circle by John Dover. (Photo courtesy

of Smithsonian Institution.)

Figure I20 Magnetometer and dip circle by Brunner-Chasselon,

Paris. These instruments were developed for the French magnetic

survey and were purchased by the US Coast and Geodetic Survey

in the 1880s. (Photo courtesy of Smithsonian Institution.)

Figure I21 DTM universal magnetometer, open to show needles

and suspension. (Photo courtesy of Carnegie Institution of

Washington.)

INSTRUMENTATION, HISTORY OF 437

The ultimate instruments along traditional lines were devised by

Daniel La Cour of Denmark for the Second International Polar Year

(1932–1933). His quartz horizontal magnetometer (QHM) and balance

magnétique zero (BMZ) were “semiabsolute ” instruments, which only

required calibration yearly (Parkinson, 1998, p. 450; Chapman and

Bartels, 1940, 1: 89–93). The QHM’s high standard of accuracy

within 1g or nT kept the La Cour instruments in use even into the

1980s (Forbes, 1987). Nevertheless, even in the 1920s and 1930s

instruments were beginning to change dramatically again.

Geomagnetic instruments since 1920: a second

generation

As Parkinson has written, advances in magnetic materials and

improvements in electronics ushered in the “second generation” of

magnetic instruments around World War II(Parkinson, 1998, p. 450).

Efforts to develop electrical methods of measuring geomagnetic

variables started on simpler lines, shortly after 1900, under Arthur

Schuster, L.A. Bauer, Adolf Schmidt, and others. These first instru-

ments of the second generation used accurately determined electrical

currents and tight engineering standards to measure magnetic vari-

ables. The Carnegie’s DTM developed the first practical field earth

inductor in 1913. Earth inductors improved the accuracy of inclination

measurements to 0.1 min and eliminated time-consuming procedures

with dip circles. In 1921, S.J. Barnett also developed a sine galvan-

ometer at the DTM for absolute measurement of horizontal intensity.

Frank Smith, at Britain’s National Physical Laboratory (NPL) in

Teddington, developed one of the first standard instruments to use

Helmholtz-Gaugain coils to measure a magnetic variable, in this case

horizontal force. He did this in 1920, following an idea that Schuster

suggested in 1914. According to one estimate, the Schuster-Smith

magnetometer required only 8 min to produce and reduce an absolute

measure of H, whereas the Gaussian oscillation/deflection method

required 2.5 h. This magnetometer had an accuracy for horizontal

intensity of 1g or nT. In 1928, D.W. Dye developed a similar instru-

ment at the NPL for vertical intensity, accurate to between 2 and 4g.

The US Naval Research Laboratory and Gulf Research and

Development perfected absolute magnetometers based on Helmholtz-

Gaugain coils in the 1930s and 1940s, with one eye especially on

improving measurement of vertical intensity (always problematic)

and the other eye on greater magnetic stability and greater accuracy

in measuring horizontal intensity and declination as well. Victor Vac-

quier started developing a vertical-force instrument in 1940 in coop-

eration with the US Coast and Geodetic Survey. Vacquier continued

during the War, and announced the Gulf Absolute Magnetometer in

1945. Commercialized forms of Helmholtz-Gaugain coil instruments

became standards at observatories for decades.

The biggest changes came, however, when researchers started

applying totally new materials and ideas to magnetic measurements

from 1940 onward. Vacquier developed the saturable-core magnet-

ometer (or fluxgate magnetometer) about 1940 for the Gulf Research

and Development Corporation (see Magnetometer). He based it on

the first saturable-core compass, patented in 1931 by H.P. Thomas,

and a simple, saturable-core magnetometer by H. Aschenbrenner and

G. Goubau of 1936. The core of the sensing element has a high mag-

netic permeability and is surrounded by an excitation coil. This is a

vector instrument, which measures magnetic intensity in the direction

of the sensor core.

World War II spurred on development of a fluxgate magnetometer

in the United States for the detection of German submarines. Vacquier

elaborated his “fluxgate” instrument and method. In 1941 Vacquier and

a team developed a device called the magnetic airborne detector

(MAD). The challenge was to align the magnetometer along Earth’s

total magnetic vector, a goal achieved by a stabilizing system driven

by input from two mutually perpendicular “orienting” fluxgates in a

plane perpendicular to the sensing fluxgate. One system used servo

motors to move the instrument in a gimbal and a second system used

an air-driven gyroscope by Sperry Gyroscope to maintain orientation.

After the War, investigators in many countries developed numerous var-

iants of these airborne magnetometers. Some were towed behind naval

ships or airplanes and contributed to military purposes, but these instru-

ments also led ultimately to the discovery of mid-ocean, seafloor

spreading and to the mapping of mineral deposits. Other versions of

fluxgates gradually replaced classic variometers (Forbes, 1987, p. 111)

in magnetic observatories, or took their place in satellites (see Magsat

and Ørsted ) and planetary probes.

Other new types of magnetometers were introduced in the late 20th

century, including proton precession, Superconducting Quantum Inter-

ference Devices (SQUIDs), optically pumped sensors, and others

(see Magnetometers). The use of these newer instruments is discussed

in other articles in this volume (see Aeromagnetic surveying; Archae-

ology, magnetic methods; Magnetic surveys, marine; and Repeat

stations). The most important change in instrumentation in the last

half-century, however, may have been the automation of observation

and the direct connection of sensors to data storage and computational

facilities (see Observatories, automation; Observatories, instrumenta-

tion). But perhaps it is too early to have historical perspective on these

events. (See also Campbell, 2003, Chapter 4 for a current discussion of

“Measurement methods,”

pp. 189–227.)

Gregory A. Good

Bibliography

Campbell, W.H., 2003. Measurement methods. In Campbell, W.H.

(ed.), Introduction to Geomagnetic Fields, 2nd edn. Cambridge,

UK: Cambridge University Press, pp. 189–227.

Figure I22 DTM universal magnetometer, closed. Set up for

intensity measurements. (Photo courtesy of Carnegie Institution

of Washington.)

438 INSTRUMENTATION, HISTORY OF

Chapman, S., and Bartels, J., 1940. Geomagnetism, 2 vols. Oxford:

Clarendon Press, especially Vol. 1, pp. 29–95.

Fara, P., 1998. Compass, variation. In Bud, R., and Warner, D.J. (eds.),

Instruments of Science: An Historical Encyclopedia. New York:

Garland Publishing, pp. 136–138, 709 pp.

Forbes, A.J., 1987. General instrumentation. In Jacobs, J.A. (ed.),

Geomagnetism, 2 vols. London: Academic Press, pp. 51–142.

Good, G.A., 1998a. Dip circle. In Bud, R. et al., (eds.), Instruments of

Science: An Historical Encyclopedia. New York and London:

Garland Publishing, pp. 175–177.

Good, G.A., 1998b. Magnetometer. In Bud, R., et al., (eds.), Instru-

ments of Science: An Historical Encyclopedia. New York and

London: Garland Publishing, pp. 368–371.

Gauss, C.F., and Weber, W., 1837. Resultate aus den Beobachtungen

des magnetischen Vereins im Jahre 1836. Göttingen: Dieter-

ischsche Buchhandlung.

McConnell, A., 1980. Geomagnetic Instruments before 1900: An Illu-

strated Account of their Construction and Use. London: Harriet

Wynter Ltd., 75 pp.

Multhauf, R.P., and Good, G., 1987. A brief history of geomagnetism

and a catalog of the collections of the National Museum of Amer-

ican History. In Smithsonian Studies in History and Technology

No. 48. Washington, DC: Smithsonian Institution Press, 87 pp.

Parkinson, W.D., 1998. Instruments, geomagnetic. In Good, G.A.

(ed.), Sciences of the Earth: An Encyclopedia of Events, People,

and Phenomena. New York and London: Garland Publishing,

pp. 446–453.

Smith, J., 1992. Precursors to Peregrinus: the early history of magnet-

ism and the mariner’s compass in Europe. Journal of Medieval

History, 18:21–74.

Cross-references

Aeromagnetic Surveying

Archaeology, Magnetic Methods

Carnegie Institution of Washington, Department of Terrestrial

Magnetism

Compass

Gauss, Carl Friedrich (1777–1855)

Gellibrand, Henry (1597–1636)

Gilbert, William (1544–1603)

Hansteen, Christopher (1784–1873)

Humboldt, Alexander von (1759–1859)

Lloyd, Humphrey (1808–1881)

Magnetic Surveys, Marine

Magnetometers, Laboratory

Norman, Robert (1560–1585)

Observatories, Automation

Observatories, Instrumentation

Oscillations, Torsional

Repeat Stations

INTERIORS OF PLANETS AND SATELLITES

Introduction and background

The planets and satellites (or moons) of our solar system are of several

types. The terrestrial planets and moons are bodies like the Earth,

which are made mainly of rocks and metals like iron. The inner pla-

nets, Mercury, Venus, Earth, and Mars are terrestrial planets. The

Moon and some of the satellites of the planets in the outer solar system

are terrestrial type bodies. The outer solar system planets are the gas-

eous giants Jupiter and Saturn and the icy giants Uranus and Neptune.

The gaseous giants are made mainly of hydrogen while the icy giants

are built mainly from things like water and methane. The substances in

the gaseous and icy giants are under enormous pressures and tempera-

tures, so their physical states are very different from those that we

encounter on Earth. At the very centers of Jupiter and Saturn there

may be cores that resemble the terrestrial planets of the inner solar sys-

tem. The satellites of the solar system reside mostly in orbits around

the outer planets. Only Earth’s moon and the small moons of Mars,

Phobos and Deimos, circle the inner terrestrial planets. The outer solar

system satellites are either terrestrial type bodies, like Jupiter’s moon

Io, or icy moons like Jupiter’s moons Ganymede and Callisto, Saturn’s

moon Titan, and Neptune’s moon Triton. As the name implies, the icy

satellites are made mainly of a mixture of water ice, rock, and metal,

with the ice making up typically around 50% of the moon by mass.

Pluto and its moon Charon are icy bodies much like the icy satellites

of the large outer planets. The interiors of many of the planets and

moons of the solar system are depicted in Figure I23/Plate 12. The

internal structures of all these bodies are based on theoretical models

strongly constrained by observations, as discussed in the remainder

of this article.

Density an d the interior of a planet

How do we know what the planets and moons are made of? There are

clues from what we can identify either on the surfaces of these bodies

or in their gaseous envelopes (elemental atmospheric compositions,

Figure I23/Plate 12 Cutaway views of what lies beneath the

surfaces of many of the planets and moons of the solar system.

These models of the planetary interiors are based on a variety of

geophysical observations as discussed in this article. Starting at

the top and proceeding down to the right and then to the left are

Neptune, Uranus, Saturn, Jupiter, Mars, Earth, Venus, and

Mercury. Jupiter’s four Galilean moons are arranged in line to the

left of the planet (in order from right to left are Io, Europa,

Ganymede, and Callisto). Earth’s moon lies to its lower right. The

bodies are not shown to proper relative scale. The figure was

prepared by Calvin J. Hamilton and included here with

permission.

INTERIORS OF PLANETS AND SATELLITES 439

chemical compositions and mineralogy of surface materials, surface

geology), but one of the main indicators of overall composition is

the density of the body, the ratio of its mass to volume. The sizes

and masses of almost all planets and moons have been known for

some time from astronomical observations, but the most current and

accurate values are based on measurements by spacecraft that have

landed on, orbited, or flown close by the bodies. The orbits of space-

craft are determined by the gravitational fields of the planets and

moons, especially the fields of those bodies that are close to the space-

craft. The gravitational field of a body is the result of its mass and the

way the mass is distributed inside the body. Therefore, tracking a

spacecraft using its radio communication signal determines its orbit

or trajectory from which the gravitational field and mass of a body

can be inferred. The size and shape of a planet or moon can be

obtained from images of the body acquired telescopically or by cam-

eras onboard spacecraft. Detailed topographic maps of several bodies,

e.g., Venus, Moon, and Mars, have been made by radar and laser

altimeters on orbiting spacecraft. The volumes of planetary bodies

follow directly from these types of measurements. Planets and moons

are nearly spherical in shape and often the specification of a single

average radius suffices to characterize the size of the body. Table I4

lists the masses, radii, and densities of the planets and major moons

of the solar system.

The density of a planet or moon immediately tells us something

about its interior because the materials from which planets are formed

have characteristic densities. Rocks typically have densities about

3000 kg m

3

, metals have densities higher than about 5000 kg m

3

and ices have densities of about 1000 kg m

3

. The density of any

material depends on pressure and temperature, variables that take on

extreme values deep inside large planets. Accordingly, the significance

of a planet’s density also depends on its size. The inner terrestrial

planets and the Moon have densities between about 3300 and

5500 kg m

3

(Table I4). These bodies are mostly made of metal (iron)

and rock. The Moon is relatively small, and its density reveals that it

must be predominantly rock. Mercury’s radius is only about 50% lar-

ger than the Moon’s radius, but Mercury’s much higher density

requires that it be mostly metal compared to the mostly rocky Moon.

The moons Ganymede and Titan are somewhat larger than the planet

Mercury (Some moons are larger than some planets!), but they have

densities of only about 2000 kg m

3

. Ice must be a major component

of these moons to explain such a low density. Triton, Pluto, and

Charon are similar icy bodies.

Two-layer model of planetary interiors

The inference of interior composition and structure from density can

be made more quantitative by constructing a model of a planet or

moon. One of the simplest models of a planet is the so-called two-

layer model in which the planet is represented by a spherical core of

radius r

and density r

surrounded by a spherical shell of outer radius

R and density r

. The average density r of such a model planet is

r ¼ r





þ r

1 



(Eq. 1)

The average density

r is an observed quantity and is known. The

quantities on the right-hand side of the equation r

, r

, and r

=R are

model parameters and are unknown and to be determined. There

are three unknowns in this simple model, core and shell densities

and fractional core radius ðr

=RÞ and only one equation to constrain

their values, so it is not possible to obtain a unique model of the pla-

net. However, if, for example, reasonable values of the model densities

can be assumed, then the fractional core radius can be determined.

Of course, the model can be made more deterministic by adding

additional observational constraints (equations) as we discuss later.

The simple two-layer model is in fact a reasonable first-order repre-

sentation of the interiors of many planets and satellites. This is because

many planets and moons are differentiated, i.e., the rock and metal

have separated into a metallic core surrounded by a rocky shell or

mantle. This likely happens during the early evolution of a planet

when temperatures in its interior are high enough to melt the heavy

metal (iron) which subsequently sinks and accumulates into a core at

the center of the planet. We know this has happened for the Earth

because seismological observations of the Earth ’s interior have

detected the Earth’s metallic core and have measured its density and

radius. The Earth occupies a special position in the discussion of pla-

netary interiors because we have observations of the Earth’s interior,

mainly from seismology, that are unavailable for other planets and

moons. The one exception to this is the Moon; we also have seismic

observations of the lunar interior from seismic stations placed on the

Moon’s surface during the Apollo exploration era. However, these data

are not as informative about the Moon’s interior as are the seismic data

sets collected on Earth. For example, the lunar seismic data are unable

to confirm the presence or absence of a small metallic core in the

Moon. Seismic instruments placed on the surface of Mars by the

Table I4 Properties of planets and satellites

Body Mass (kg) Radius (km) Density ðkg m

3

Þ C/MR

Mercury 3302:2  10

2439.7 5430 –

Venus 4869  10

6051.8 5240 –

Earth 5973:7  10

6371.0 5514.8 0.33078

Moon 7347:7  10

1737.1 3341 0.3935

Mars 641:91  10

3397 3940 0.365

Jupiter 1898:7  10

71492 1330 0.25

Io 8:932  10

1821.6 3527.5 0.378

Europa 4:800  10

1565.0 2989 0.346

Ganymede 1:482  10

2631.2 1942 0.3115

Callisto 1:076  10

2410.3 1834 0.3549

Saturn 568:51  10

60268 700 0.22

Titan 1:345  10

2575 1880 –

Uranus 86:849  10

25559 1300 0.23

Neptune 102:39  10

24764 1640 0.24

Triton 2139:8  10

1352.6 2065 –

Pluto 1250  10

 1200 1750–2150 –

Charon 180  10

 600 1300–2200 –

440 INTERIORS OF PLANETS AND SATELLITES

Viking spacecraft did not provide data that could be used to determine

the planet ’s internal structure. For Earth, seismology has not only

revealed the metallic core and the rocky mantle around it, but it has

also shown that the core consists of a solid inner part and a liquid outer

shell. Thus we talk about the inner core and the outer core of the Earth

(Figure I23/Pl ate 12).

Two- layer model of Merc ury

Mercury, Venus, Mars, and the Galilean satellite Io are all believed to

have metallic cores made mostly of iron surrounded by rocky shells or

mantles (Figure I23/Plate 12). The first-order interiors of these bodies

can be represented by a two-layer model. In the case of Mercury, the

existence of a metallic core is based almost entirely on its density.

Mercury ’s high density (Table I4 ) requires that it consist of more than

50% iron by mass, and it is likely that the iron has concentrated into a

central core. If we assume that the density of Mercury’ s core is

8000 kg m

3

(a reasonable value for a mostly iron core) and that the

density of its mantle is 3000 kg m

3

(a representative value for rock)

then according to (Eq. 1) , the radius of Mercury ’s core would be

nearly 80% of the planet’s radius. Mercury can be thought of as a ball

of iron with a relatively thin coating of rock (Figure I23/Plate 12). This

result can also be seen in Figure I24, a graphical representation of

(Eq. 1) . Figure I24 plots r

=r against r

=R for different values of

=r. With the above values of r

; r

, and r; r

=r is about 1.5, r

is about 0.55, and the position of Mercury on the plot would

correspond to r

=R almost equal to 0.8. For the Moon, on the other

hand, r

=r would be in excess of 2, r

=r would be nearly 1

(Table I4), and the position of the Moon on the plot would correspond

to small values of r

=R.

Mercury is also known to have a magnetic field that is believed to

be generated by a dynamo in its metallic core. The existence of Mer-

cury’s magnetic field supports the existence of its metallic core if the

magnetic field is indeed generated in the way the Earth’s magnetic

field is produced, by convective motions of the highly electrically con-

ducting core metallic fluid, i.e., by a core dynamo. Dynamo action

requires a core to be at least partially fluid, so if Mercury’s magnetic

field is produced by a dynamo, then not only must Mercury have a

metallic core, but its core must also have a substantial liquid portion.

Earth’s metallic core is partially solidified, a result of the cooling of

the core over geologic time. Dynamo action in the Earth occurs in

its molten outer core. Mercury’s core could also be solidifying from

the inside out, similar to Earth’s core, but the present operation of a

dynamo in Mercury means that the planet, like Earth, has a liquid outer

core sufficiently thick for a dynamo to operate. We will learn much

more about the interior of Mercury with the successful completion of

the Messenger mission. The spacecraft is presently on its way to orbit

the planet; it is planned to make detailed measurements of Mercury’s

gravitational and magnetic fields and Mercury’s rotational state, obser-

vations that can reveal a great deal about the interior of the body.

Two-layer model of Venus

Like Mercury, the main constraint on the interior of Venus is its den-

sity. Venus is slightly smaller than Earth and its density is about 5%

less than the density of the Earth (Table I4). Based on these similar

properties, it is generally believed that the interior of Venus is like

the interior of Earth, i.e., that Venus has a metallic, mainly iron core

with a radius about half the planet’s radius surrounded by a rocky

mantle (Figure I23/Plate 12). Many spacecraft have orbited and landed

on Venus, and we are quite certain that the planet does not have a

magnetic field. So, unlike Mercury, we cannot use the existence of a

magnetic field to support the existence of a metallic core inside Venus.

Instead, we must explain why, if Venus is like Earth in its interior,

Venus does not have a magnetic field like Earth does. There are sev-

eral possible explanations for this, including the absence of a solid

inner core in Venus. Because Venus is somewhat smaller than Earth

and the pressure at its center is less than at the center of the Earth,

Venus’ core, though cooling over geologic time, may not have yet

cooled sufficiently to freeze out an inner core. Inner core solidification

might be necessary to drive a dynamo in the outer liquid core of a pla-

net because the freezing of the inner core releases energy to drive the

dynamo in the form of the latent heat of solidification and gravitational

potential energy. Solidification of the Earth’s inner core might play an

essential role in driving the geodynamo. It might also be that Venus’

core is simply not cooling fast enough to have a thermally driven

dynamo because the planet’s mantle cannot convect efficiently enough

to remove a lot of heat from the core. Venus has no plate tectonics, an

indication that its mantle convects sluggishly. Only when we can

determine the extent of solidification of Venus’ core through seismic

exploration of the planet will we be able to identify the reason for

the planet’s lack of a magnetic field.

Moment of inertia and interior of a planet, Mars and

the Moon

When we come to discuss Mars and the Moon we are fortunate to have

a crucial piece of information in addition to density that tells us a great

deal about the distribution of mass inside a body. This is the moment

of inertia C of the body about its rotation axis. The moment of inertia

of a point mass about a rotation axis is the product of the mass and the

square of the perpendicular distance of the mass to the axis. Planets

and moons are not point masses, so their moments of inertia represent

a summation or integral of contributions to the total moment of inertia

from all the elements of mass within the body. It is easy to calculate

the moments of inertia of idealized bodies. For example, the moment

of inertia of a constant density sphere of radius R and total mass M

is 0.4MR

. Since the actual moment of inertia of a planetary body is

some huge number, it is convenient to describe a planet’s moment of

inertia by scaling it to MR

. The moment of inertia factor of a constant

density sphere is then C=MR

¼ 0:4. The moment of inertia factors of

planets and moons are less than 0.4 because these bodies are denser

at depth than they are near the surface. The more a planet’s mass is

Figure I24 Normalized core density r

=r versus normalized core

radius r

=R for different values of normalized mantle density r

in a two-layer model of a planet.

INTERIORS OF PLANETS AND SATELLITES 441

concentrated near its center the smaller is its moment of inertia. Planets

and moons with metallic cores are obviously denser at their centers

since iron is much denser than rock. Density also increases with depth

in a planet because of the increase in pressure with depth. Extraordin-

ary pressures experienced deep within planets compress rock and

make it denser. The extreme pressures can even rearrange the minerals

of the rock to create denser phases of the minerals. The tendency of pres-

sure to increase density at depth in a planet occurs despite the effect of

enhanced temperature deep within a planet. Most materials including

rocks decrease in density with increasing temperature. Pressure over-

whelms temperature as far as density is concerned. The moment of iner-

tia factors of Earth, Moon, and Mars are given in Table I4 . These are the

only planets in the solar system for which we have direct measurements

of the moment of inertia.

Mome nt of iner tia and two -layer models, Mars

We will discuss how the moment of inertia of a planet can be deter-

mined, but let us first see how this property can be used to learn more

about a planet ’s internal distribution of mass than could be deduced

from density alone. The simple two-layer model of a planet provides

an illustrative tool for this purpose. As discussed above, the two-layer

model has three unknown quantities we would like to determine,

; r

, and r

= R. Equation (1) and the known density provide one con-

straint on the three unknowns. The equation for the moment of inertia

of a two-layer spherical body and the value of the moment of

inertia provide a second constraint. The equation is

¼ 0: 4

 r

ðÞ





(Eq. 2)

and the left-hand side is known. There are now two equations for three

unknowns, and we can construct a suite of models for a planet by con-

sidering, for example, a range of plausible values of r

= R. Figure I25

shows the results of using (Eqs. 1 and 2) together with the known

values of density and moment of inertia factor for the planet Mars

(Table I4 ). The figure plots core density against r

=R and represents

the equation

ð kg m

 3

Þ¼ 3 935: 0

0: 365

0 :4



1 





 1 þ







(Eq. 3)

For plausible core densities corresponding to densities of iron or iron

mixed with lighter elements like sulfur, values of r

= R range from

about 0.45 to 0.60. If the normalized core radius is about 0.45, then

the density of the core is about 8250 kg m

3

typical of the density of

a pure Fe core. If the normalized core radius is 0.60, then the density

of the core is about 5900 kg m

3

typica l of the density of a core con-

taining both iron and sulfur as FeS. While the cores of terrestrial pla-

nets are composed mainly of metals like iron and nickel, the cores

can also contain other lighter elements such as S or O. Indeed, based

on the seismically determined density of the Earth ’s core and the mea-

sured density of iron at high temperature and pressure, it is certain that

light elements are in the Earth ’s core in addition to Fe and Ni. The

density and moment of inertia of Mars leave no doubt that Mars has

a metallic core and rocky mantle (Figure I23/Plate 12). For plausible

core densities the core radius is between about 1530 (0.45R ) and

2040 km (0.6 R) depending on core composition; the more iron-rich

the core, the smaller it is. The mantle density is about 3400– 3500

kg m

–3

depending on core size; smaller mantle densities correspond to

larger cores. The results we find for Mars show that even simple two-

layer models can provide strong constraints on certain global properties

of planets and moons.

Measur ing moment of inerti a from a planet’s rotation

How do we determine the moment of inertia of a planet like Mars?

Basically, we must be able to observe how a planet ’s state of rotation

responds to external torques exerted on the planet. The rotation of a body

is determined by an equation analogous to Newton’s second law of

motion for the linear movement of a body. Newton’s second law states

that the force applied to a body equals the product of its mass and accel-

eration. The analogous principle for angular motion states that the tor-

que applied to a body equals the product of its moment of inertia and

angular acceleration. The torque about an axis is the product of a force

with the perpendicular distance between the force and the axis. Torques

on planets arise from the gravitational pull of the Sun or the gravita-

tional attraction of a planet’s satellite. The torque applied to the Earth

by the Moon significantly affects the Earth’s rotation. Mercury and

Venus have no satellites to influence their rotational states. Phobos

and Deimos exert torques on Mars, but their combined effect is much

less than the torque exerted on Mars by the Sun. The rotation or spin

axes of Earth and Mars are tilted about axes normal to their orbital

planes (the obliquities of Earth and Mars are 23:45



and 25: 19



, respec-

tively), and the gravitational torques on them cause their spin axes to

precess about the orbit normals. Measurement of the precession rate

together with knowledge of the forcing gravitational torque allows

the determination of the axial moment of inertia from the form of

Newton’s law for angular motion. Astronomical observations have

revealed the precession rate of the Earth’s spin axis and in turn the

Earth’s moment of inertia. Radio tracking of the Mars Pathfinder

Lander has yielded similar information for Mars. Laser ranging obser-

vations of the Moon made possible by reflectors placed on the lunar

surface during the Apollo program have determined the Moon’s rota-

tional state and its moment of inertia. Moments of inertia of planets

and satellites are summarized in Table I4. The table includes the direct

measurements and values inferred indirectly by other means as

discussed below.

Moment of inertia and interior of the Moon

The moment of inertia factor of the Moon (C=MR

¼ 0:3935, Table I4)

is sufficiently close to 0.4 that the interior could be rock with an almost

Figure I25 Core density as a function of normalized core

radius r

=R for a two-layer model of Mars constrained by the

values of average density and axial moment of inertia.

442 INTERIORS OF PLANETS AND SATELLITES

constant density. Density would increase slightly with depth in such a

body due to the increase of pressure with depth and the small increase

of density could account for the small decrease in the moment of inertia

factor below 0.4. Alternatively, the moment of inertia factor of the

Moon is also consistent with it having a small iron core a few hundred

kilometers in radius at its center (Figure I23/Plate 12). Though we do

have seismic data for the Moon, these data do not constrain the possible

existence of a metallic core. However, magnetic data for the Moon indi-

cate the likelihood that it has an iron core. Magnetometers were placed

on the lunar surface and in orbit around the Moon during the Apollo

exploration program, and these instruments showed that while the

Moon has no large-scale magnetic field at present, the lunar crust is

magnetized. It is generally believed that the crust was magnetized at

a time in the past when the Moon had an active dynamo, and the crustal

rocks cooled through the Curie temperature in the presence of a lunar

magnetic field. If the remanent magnetization of the Moon’s crust

was created in this way, then the Moon must have a metallic core that

supported a dynamo in the past. The lack of a magnetic field at present

could be due to the cooling of the Moon over geologic time, which has

left it with a nearly solidified core in which dynamo action can no

longer occur. Other explanations are also possible, but the cooling of

a relatively small body like the Moon is expected to have substantially

solidified its core. The lunar core may not be entirely solidified, or even

partially frozen, according to an interpretation of the lunar rotational

data from the laser ranging observations.

Mars crustal magnetization

A magnetometer on the Mars Global Surveyor spacecraft discovered

that the southern highlands crust of Mars is also magnetized, and, in

certain regions of Mars, even more strongly magnetized than Earth’s

most magnetic rocks (see Magnetic field of Mars). The southern high-

lands crust of Mars dates from the earliest phase of Martian evolution,

the so-called Noachian , and its magnetization suggests that Mars had a

magnetic field generated by an internal core dynamo in the distant

past. The existence of a metallic core in Mars, as deduced from its den-

sity and moment of inertia, is consistent with the inference of a core

from the magnetization of the Martian crust. The absence of a Martian

dynamo at present could be explained in ways similar to those that

offer explanations for the lack of present magnetic fields on Venus

and the Moon. These include solidification of the core to the point

where a dynamo cannot operate in the remaining liquid outer core or

the inability of the mantle to cool the core at a rate large enough to

drive a dynamo through thermal convection in the core. The detection

of the solar gravitational tide on Mars through radio tracking of the

orbiting Mars Global Surveyor has led to the conclusion that at least

some outer portion of the Martian core is not solidified.

Gravitational field and a planet’s interior

Much can be learned about a planet’s interior from measurements of

its external gravitational field since the gravitational field of a body

arises directly from the mass inside it. Each element of mass in a pla-

net or satellite contributes to the external gravitational field according

to Newton’s law of gravitation, which states that the gravitational force

exerted by an element of mass is directly proportional to the element’s

mass and inversely proportional to the square of the distance between

the mass element and the point at which the force acts. The net grav-

itational force at a point outside a planet is obtained by summing the

forces exerted by each mass element over the entire distribution of

mass inside the body, taking proper account of the directional nature

of the gravitational force. When a planet is in hydrostatic equilibrium

(see below), its moment of inertia and internal structure can be

deduced directly from the gravitational field measurements. The Earth

is reasonably close to this state, but Mars is not, due to the uncompen-

sated portion of the Tharsis uplift. The Moon is not in hydrostatic

equilibrium, and it is not known to what extent Mercury and Venus

might depart from this state. Thus, though we know the gravitational

field of Venus quite well, we cannot use this knowledge to determine

its moment of inertia and deep internal structure and, in particular, to

verify that it has a metallic core like Earth. There are other bodies in

the solar system that we think are in hydrostatic equilibrium. These

include the outer planets with fluidlike interiors and the Galilean

moons of Jupiter, Io, Europa, Ganymede, and Callisto. Measurements

of the gravitational fields of these moons by the Galileo spacecraft

have been used to deduce their internal structures.

The gravitational field of any planet is generally represented mathe-

matically by a function known as the gravitational potential V; the

gravitational force on a unit mass is the gradient or directional deriva-

tive of V. The potential is, in turn, given by a series of terms known as

a spherical harmonic expansion. Spherical harmonics (q.v.) are func-

tions of latitude and longitude that provide a basis for the representa-

tion of potential functions like the gravitational field external to a

distribution of mass. These potential fields are solutions of Laplace’s

equation. The terms in the spherical harmonic expansion of the exter-

nal gravitational field depend not only on latitude and longitude, but

they also include a dependence on the radial distance r to the center

of mass of the planet; the terms are inversely proportional to powers

of r. The leading term in the spherical harmonic expansion of the exter-

nal gravitational field is GM/r (where G is the universal gravitational

constant and M is the mass of the planet). This is the gravitational field

that would exist if all the mass of the planet were concentrated in a point

at its center of mass. The next terms, there are five of them, are all pro-

portional to r

3

. These terms can be thought of as arising from the ellip-

soidal distortion of the planet’s mass distribution. One of these terms,

GM=rðÞR=rðÞ

3 sin

f1=2



, is of particular importance because

the coefficient C

(sometimes denoted by  J

) can be used,

under certain circumstances, to determine the planet’s axial moment

of inertia. There is no term in the external gravitational potential

proportional to r

2

because the origin of the coordinate system is

fixed at the planet’s center of mass (the center of mass is the point

inside a mass distribution about which the mass distribution has no

net moment).

Hydrostatic equilibrium: determining C from the

gravitational field

The gravitational coefficient C

can be used to determine C/MR

when a planet is in a state of hydrostatic equilibrium. A planet in

hydrostatic equilibrium behaves like a fluid in response to forces

exerted on the planet. Over geologically long times, rocks can behave

like fluids and flow in response to forces exerted on them. The

motions are very slow, but over geologi c time the rocks in a planet

can deform and move over large distances. This is the process that

enables plate tectonics and mantle convection on Earth and allows

the Earth, for example, to adjust to changes in the mass loading of

its surface by postglacial rebound.. Fluidlike deformation of rock is

facilitated by high temperature so that subsolidus creep generally

occurs beneath a relatively cold and strong outer shell of a planet

called the lithosphere. If the lithosphere is thick enough and strong

enough to support the stresses associated with surface or subsurface

mass anomalies, then the planet will not be in hydrostatic equilibrium.

This is probably why the Moon is not in hydrostatic equilibrium, and a

similar explanation might apply to the small planet Mercury if we find

that it is also not in hydrostatic equilibrium. We are not safe in using

to determine C/MR

for Mercury or Venus, but the procedure

can be applied to the Galilean satellites of Jupiter.

For a body in hydrostatic equilibrium that is distorted by rotation

and tides, it can be shown that C/MR

is related to C

by the Radau

equation



4  k

1 þ k



1=2

(Eq. 4)

INTERIORS OF PLANETS AND SATELLITES 443

where k

is the fluid Love number of the planet, which depends on its

internal mass distribution and is given in terms of C

C

ðÞ (Eq. 5)

for a tidally and rotationally distorted satellite in synchronous rotation

about a planet (e.g., one of the Galilean moons orbiting Jupiter), or by

C

ðÞ (Eq. 6)

for a planet distorted by rotation only (e.g., Earth or Mars), where

(Eq. 7)

and o is the rotational angular velocity of the body.

For Earth and Mars it is unnecessary to try to estimate C/MR

from

using the Radau equation because C/MR

has been determined

directly from the observed rates of precession of the planets’ rotation

axes. However, it is useful to carry out the exercise to see how the

approach works for these planets and to assess how far these planets

are out of hydrostatic equilibrium. For bodies like the Galilean satel-

lites of Jupiter, the only way we can estimate C/MR

is to deduce it

from the gravitational fields (C

) measured by radio tracking the

Galileo spacecraft as it made multiple flybys of the moons. For Earth,

¼ 0:0034498 and C

¼0:0010826, and the Radau equation

yields C=MR

¼ 0:332, very close to the value of C=MR

¼ 0:3308

deduced from precession of the Earth’s rotation axis. For Mars,

¼ 0:0045702 and C

¼0:001964, and the Radau equation yields

C=MR

¼ 0:376, not close enough to the value of C=MR

¼ 0:365

deduced from observations of the precession rate of the rotation axis

of Mars (by radio tracking of the Mars Pathfinder Lander and Mars

Global Surveyor orbiter) to yield reliable models of the Martian inter-

ior. The reason, as noted above, is that Mars is not in hydrostatic equi-

librium because the Tharsis highland is a major mass load that is

partially supported by the strength of the Martian lithosphere.

Galilean moo ns of Jupiter

A strong case can be made that the Galilean moons of Jupiter, Io,

Europa, Ganymede, and Callisto are sufficiently close to hydrostatic

equilibrium for their axial moments of inertia and internal structures

to be inferred from their gravitational field coefficients C

. These

satellites are distorted by the tidal forces from the massive Jupiter

and by the centrifugal forces of their rotations. The Galilean moons

are in synchronous rotation about Jupiter (they keep the same face to

Jupiter as they rotate about it) with periods of days (Table I5); the

satellites are reasonably rapid rotators. Because they do not have the

strength to resist the large tidal and rotational forces over geological

time, their internal masses flow and adopt an equilibrium ellipsoidal

fluid shape. Rotation flattens the moons along their rotational axes

and produces equatorial bulges perpendicular to the axes of rotation.

Each moon is also elongated by tidal forces along an axis that passes

from its center of mass to the center of mass of Jupiter. The redistribu-

tion of mass into an ellipsoidal shape is the source of the contributions

to the gravitational field represented by coefficients like C

The gravitational fields of all the Galilean satellites have been mea-

sured by radio tracking the trajectory of the Galileo spacecraft as it

repeatedly orbited Jupiter and flew by the moons. The subtle deflec-

tion of the spacecraft trajectory as it passes close to a moon and feels

the pull of the moon’s gravitational field provides a direct measure of

the field. The Galileo spacecraft arrived at Jupiter in December of

1995 and explored the Jovian system until it was targeted to crash into

Jupiter on September 21, 2003. The many flybys of the Galilean

moons by the spacecraft over this nearly 8-year period provided all

the gravitational data on which present models of the satellite interiors

are based. Multiple flybys of Io were particularly useful in establishing

that it is in hydrostatic equilibrium. A polar flyby of Io at an altitude of

300 km and equatorial flybys at altitudes between 100 and 200 km

enabled independent determination of rotational and tidal contributions

to the gravitational field. These separately determined gravitational

field components are in a ratio consistent with the equilibrium ellipsoi-

dal distortion of Io under Jovian tidal forces and rotation of Io. Io’s

actual shape, as determined from spacecraft images of the satellite, is

also consistent with the equilibrium ellipsoid. Io is certainly in hydro-

static equilibrium, a condition expected for a body so hot in its interior

that its mantle might be substantially partially molten. Even without

melting, the rocks should be so hot that they should easily flow over

geologic time. Io’s high-temperature internal state is revealed by its

active volcanism; Io is the most volcanically active body in the solar

system. The energy for all this volcanic activity comes from the dissi-

pation of tidally forced distortions of the body. The time-varying tidal

distortions giving rise to heating are deformations in addition to the

steady tidal distortion that gives rise to Io’s quadrupole gravitational

field. These additional tidal deformations are caused by the eccentri-

city of Io’s orbit around Jupiter. There are no similar data to more

rigorously establish the hydrostaticity of the other Galilean satellites.

Table I4 summarizes the physical characteristics of the Galilean satel-

lites of Jupiter including, in particular, the densities and moments of

inertia that are used to construct models of the moons’ interiors. These

properties are based mainly on the data acquired by the Galileo space-

craft. Two- and three-layer models of the interiors of the moons, based

on these properties and the modeling approach discussed above, are

shown in Figure I23/Plate 12. Io, about the size of the Moon, is differ-

entiated into a metallic core and rocky mantle. If Io’s core is pure iron

with a density of about 8 090 kg m

3

then its radius is 650 km or about

36% of Io’s outer radius. The mass of this Fe core is about 10% of Io’s

total mass. If the core consists of a eutectic Fe-FeS alloy with a density

of about 5150 kg m

3

, then its radius is about 950 km or about 36%

of Io’s outer radius. The mass of this Fe-FeS core is about 20% of

Io’s total mass. The magnetometer on the Galileo spacecraft did not

detect an Ionian magnetic field on its flybys of the satellite. The lack

of an operative dynamo in Io’s metallic core might be explained by

the inability of the hot mantle to cool the core. If the heat flow from

the core is too small, the core would not convect and there would be

no core motions to drive a dynamo. It seems unlikely, given the volca-

nic activity of the satellite and the large amount of heat it radiates, that

Io’s core could have solidified to the point where dynamo action

would not be possible. It is more likely that Io’s core is completely

molten but not convecting.

Europa

Europa is somewhat smaller than Io and the Moon. Like Io, Europa has a

metallic core surrounded by a rocky mantle (Figure I23/Plate 12).

Table I5 Orbital parameters of moons

Body

Average distance

from planet (km)

Orbital period

(days)

Io 4:22  10

1.77

Europa 6:71  10

3.55

Ganymede 10:70 10

7.15

Callisto 18:83  10

16.7

Titan 1:222 10

15.94

Triton 3:55  10

5.88

444 INTERIORS OF PLANETS AND SATELLITES

In addition, it has a layer of water about 100 km thick that covers the

rock mantle. At the surface, the water is frozen, but beneath the surface

the water may be liquid, i.e., Europa might have an internal ocean. The

ocean could be extremely deep and extend all the way down to the sili-

cate mantle. The ocean could also be a relatively thin layer of liquid

water within a largely ice shell. The average density and the moment

of inertia of a planet or satellite provide information on the internal den-

sity distribution. We cannot infer from these data whether an iron core

is solid or liquid or whether a water shell is ice or liquid. This is

because the density changes associated with freezing of water or mol-

ten iron are too small to be distinguished in simple models of planetary

interiors based on only mean density and moment of inertia. Europa is

not volcanically active like Io, but its icy surface is disrupted by frac-

tures and ridges indicative of internal activity in the moon. In fact,

the appearance of the surface, with some regions so broken apart that

they resemble the tops of floating icebergs, is one of the reasons, it is

believed, that Europa has a liquid water ocean beneath its surface. A

second reason to suspect the existence of an internal liquid water ocean

in Europa is the detection of electrical currents inside Europa by the

magnetometer on the Galileo spacecraft. The currents are driven by

magnetic field changes felt in the moon as it orbits Jupiter and senses

the planet’s magnetic field. The currents in turn produce magnetic

fields that are detected by the Galileo spacecraft. Rocks and ice are

not good enough conductors of electricity to support the currents, but

salty water, like the Earth ’s ocean, is conductive enough. So, the evi-

dence for a subsurface ocean in Europa is all indirect, but the possibility

that the ocean really exists is so important (an internal ocean would pro-

vide an environment conducive to life) that Europa will undoubtedly be

a focus of future planetary exploration. The Galileo magnetometer did

not detect an Europan magnetic field (a steady global magnetic field

produced by a dynamo), so like Io, there is no dynamo operating in

Europa’s core. The reason for lack of dynamo action in Europa’s core

is probably different from the explanation for Io because Europa is

not intensely heated by tidal dissipation as is Io. Europa may not have

a dynamo for the same reason the Moon lacks a dynamo at present;

these small moons may have cooled sufficiently that their cores are lar-

gely solidified and unable to support a dynamo. Other explanations are

also possible. Europa’s core could vary in radius from about 13% to

45% of Europa’s full radius, depending on the composition of the core.

Ganymede

Ganymede is the largest moon in the solar system. It is even larger

than the planet Mercury (Tables I4 and I5). It is also the only moon

in the solar system known to have a magnetic field. Its magnetic field

is larger than Mercury’s magnetic field. Ganymede’s moment of iner-

tia is smaller than that of any of the terrestrial planets or other Galilean

satellites (Tables I4 and I5). Its density (about 2000 kg m

3

) is inter-

mediate between that of water (about 1000 kg m

3

) and rock (about

3000 kg m

3

), and accordingly it consists of about half rock (þ metal)

and half water by mass. Ganymede is therefore known as an icy satel-

lite. Like Europa, Ganymede consists of a metallic core surrounded by

a rock mantle and a water-ice shell (Figure I23/Plate 12). However,

unlike Europa, the outer ice shell is enormously thick (as thick as about

800 km). The small moment of inertia (C=MR

¼ 0:3115) requires a

large density difference between the core and the outer shell; this is pro-

vided by the density difference between water and iron. The detection

of induced magnetic fields by the Galileo magnetometer, similar to

the induced fields found around Europa, supports the possibility that

Ganymede, like Europa, has an internal liquid water ocean embedded

in its largely frozen outer shell of ice. The internal ocean on Ganymede

would be buried deeper below the surface than it is on Europa. Though

Ganymede’s surface has been modified by internal dynamical pro-

cesses (endogenic modification of the surface), it does not display the

features found on Europa that suggest an ocean just below the surface.

The core is the site of the dynamo that creates Ganymede’s magnetic

field; the existence of the magnetic field is indirect proof of the

existence of Ganymede’s metallic core. Moreover, we know that

Ganymede’s core is either entirely molten or liquid in an outer shell

thick enough to sustain a convectively-driven dynamo. The possibility

that Ganymede’s magnetic field is produced by the global magnetiza-

tion of a shell of rock in its interior cannot be completely ruled out,

but it is considered less likely than a core dynamo. Even in this case,

Ganymede would have to have had a dynamo operating in a metallic

core in the past to create the magnetic field in which the crust was mag-

netized. Curiously, perhaps, the interior of Ganymede looks very much

like Io with the addition of a thick ice shell. However, tidal dissipation

does not presently heat the interior of Ganymede.

Callisto

Callisto is another icy satellite, just slightly smaller and slightly less

dense than Ganymede. However, both its interior and surface are very

different from Ganymede. Though Callisto is also about half rock

and half water by mass, its C/MR

is only slightly smaller than 0.4

(Table I4), implying that its interior is not too different from a uniform

mixture of ice and rock with nearly constant density. The reduction of

C/MR

from 0.4 is due in part to the densification of ice with depth

inside Callisto (ice transforms to higher density phases at sufficiently

high pressures) and the partial separation of rock from ice in the rela-

tively shallow subsurface layers of Callisto. However, in the bulk of

Callisto at depth, ice and rock are still intimately mixed as they are

in the material which accreted to form Callisto (Figure I23/Plate 12).

In particular, Callisto does not have a metallic core as do the other

Galilean satellites. The lack of a magnetic field associated with Callisto

(based on observations by the Galileo spacecraft) is consistent with the

absence of a core. Callisto is said to be only partially differentiated,

where in this context, differentiation is the process that separates ice

from rock and usually would involve the melting of the ice of an

ice-rock mixture. Ganymede is differentiated not only in the sense that

its ice and rock have separated, but its metal and rock have also sepa-

rated through the melting of the primordial rock component early in

the formation of the satellite. The term differentiation, as traditionally

applied to terrestrial planets, usually refers to the melting of rock and

the separation of molten iron into a central core. Why Ganymede got

hot enough inside to fully differentiate and separate ice from rock

and also form a metal core while similarly sized Callisto failed to

get hot enough to even melt most of the ice in the primordial ice-rock

mixture from which it formed is still an unsolved problem. The answer

might lie in the orbital-dynamical history of the satellites; Ganymede

might have been intensely tidally heated in the past, while Callisto

would have escaped such a fate since Callisto is much farther from

Jupiter and not involved in orbital resonances with the other Galilean

satellites. Electromagnetic induction signals have been detected in

several flybys of Callisto by the Galileo spacecraft, indicating that

Callisto, like Europa and Ganymede, has an internal liquid water ocean

buried deep beneath its surface. How such a global ocean could exist

in a largely undifferentiated satellite is not understood.

Titan

Saturn’s large satellite Titan is an icy satellite with a density of about

1880 kg m

3

(Table I4). It is in synchronous rotation about Saturn

at an average orbital distance of about 1.2 million km (Table I5).

There are no rotational or gravitational data to constrain interior

models of Titan, so present ideas about the moon are based on its den-

sity. It is generally thought that ice and rock are separated in Titan as

they are in Ganymede. However, unlike Ganymede, Titan does not have

a magnetic field, a fact confirmed by magnetometer data from a recent

flyby of Titan by the Cassini spacecraft. The absence of a magnetic field

is only a weak constraint on whether or not Titan has a metallic core;

either Titan does not have an iron core, or it has a core, but not an opera-

tive dynamo in the core. Future flybys of Titan by the Cassini spacecraft

should provide information about Titan’s gravitational field that will

INTERIORS OF PLANETS AND SATELLITES 445