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In order to clarify the relationship between microscopic and macroscopic magnetic features of a rock, we applied magnetic force microscopy (MFM) as a local probe on a sample with an intense natural remanent magnetisation, a norite from Heskestad, Norway. We studied in detail seven magnetite (Fe3O4) exsolution lamellae, five of them were about 30 μm long and a few micrometers wide, two were significantly shorter; all were located in their natural host, a grain of clinopyroxene. By combining MFM images of surface magnetisation with information about shape observed with optical microscopy (OM), the internal domain structure was determined for individual grains. In general, the lamellae were pseudo-single-domain grains with open-flux domain magnetisations parallel to their long axes. The domain sizes were, in cross-section, on the order of a micrometer for the longer lamellae and about 300 nm for the short lamellae. By increasing the separation between the MFM probe and the exposed end of the lamellae, information could be obtained about the decrease in stray fields for the individual grains. Close to the lamellae, stray fields were significant even for grains with multiple domains. The largest fields were found above the largest domains. A separation of approximately one domain width was found to be a characteristic distance, where stray fields from adjacent domains begin to cancel one another.

The Mars Polar Lander carries an instrument package called the Magnetic Properties Experiments. This package consists of one magnet array, one tip-plate magnet, and three Thermal and Evolved Gas Analyzer (TEGA) magnets. The magnet array and the tip-plate magnet are identical to those flown on Mars Pathfinder and will be passively exposed to airborne dust. The TEGA magnets are a new addition to the package designed to study actively sampled material collected from three different depths in the trench that will be dug by the robotic arm soil sampler.

The Mars Pathfinder lander carried two magnet arrays, each containing five small permanent magnets of varying strength. The magnet arrays were passively exposed to the wind borne dust on Mars. By the end of the Mars Pathfinder mission a bull's-eye pattern was visible on the four strongest magnets of the arrays showing the presence of magnetic dust particles. From the images we conclude that the dust suspended in the atmosphere is not solely single phase particles of hematite (α-Fe2O3) and that single phase particles of the ferrimagnetic minerals maghemite (γ-Fe2O3) or magnetite (Fe3O4) are not present as free particles in any appreciable amount. The material on the strongest magnets seems to be indistinguishable from the bright surface material around the lander. From X-ray fluorescence it is known that the soil consists mainly of silicates. The element iron constitutes about 13% of the soil. The particles in the airborne dust seem to be composite, containing a few percent of a strongly magnetic component. We conclude that the magnetic phase present in the airborne dust particles is most likely maghemite. The particles thus appear to consist of silicate aggregates stained or cemented by ferric oxides, some of the stain and cement being maghemite. These results imply that Fe2+ ions were leached from the bedrock, and after passing through a state as free Fe2+ ions in liquid water, the Fe2+ was oxidized to Fe3+ and then precipitated. It cannot, however, be ruled out that the magnetic particles are titanomagnetite (or titanomaghemite) occurring in palagonite, having been inherited directly from the bedrock.

The soil on Mars is known to contain a ferrimagnetic mineral, the unequivocal identification of which mineral will contribute to understanding the origin of the Martian soil. Mossbauer spectroscopy of magnetically separated dust can give essential information on the iron mineralogy and magnetic properties of the dust. The Mars Surveyor missions in 2001 and 2003 will carry a Mossbauer spectrometer and several permanent magnets, which together should be able to achieve these goals.

The paper gives a description of two instruments, the Magnet Array (MA) and the Tip Plate Magnet (TPM), that are part of the Magnetic Properties Experiments on board the U.S. Mars Pathfinder spacecraft, which was launched 4 December 1996, and is expected to land on Mars 4 July 1997. Both instruments consist of permanent magnets of varying strength that are designed to capture airborne dust. The instruments will be imaged by the Lander camera and the pictures transmitted to Earth. The pictures are the data on which conclusions about the magnetic properties of the Martian dust will be based. As an addition to the description of the construction of the instruments, we give a brief discussion of the background for the interpretation of the results of the Magnetic Properties experiment.

The imager for Mars Pathfinder (IMP), a stereoscopic, multispectral camera, is described in terms of its capabilities for studying the Martian environment. The camera's two eyes, separated by 15.0 cm, provide the camera with range-finding ability. Each eye illuminates half of a single CCD detector with a field of view of 14.4×14.0° and has 12 selectable filters. The ƒ/18 optics have a large depth of field, and no focussing mechanism is required; a mechanical shutter is avoided by using the frame transfer capability of the 512×512 CCD. The resolving power of the camera, 0.98 mrad/pixel, is approximately the same as the Viking Lander cameras; however, the signal-to-noise ratio for IMP greatly exceeds Viking, approaching 350. This feature along with the stable calibration of the filters between 440 and 1000 nm distinguishes IMP from Viking. Specially designed targets are positioned on the Lander; they provide information on the magnetic properties of wind-blown dust, measure the wind vectors, and provide radiometric standard reflectors for calibration. Also, eight low-transmission filters are included for imaging the Sun directly at multiple wavelengths, giving IMP the ability to measure dust opacity and potentially the water vapor content. Several experiments beyond the requisite color panorama are described in detail: contour mapping of the local terrain, multispectral imaging of the surrounding rock and soil to study local mineralogy, viewing of three wind socks, measuring atmospheric opacity and water vapor content, and estimating the magnetic properties of wind-blown dust. This paper is intended to serve as a guide to understanding the scientific integrity of the IMP data that will be returned from Mars starting on July 4, 1997.

The significance of the element titanium for the study of the magnetic mineral in the surface dust of Mars is described.

The iron mineralogy of samples of the Monturaqui impactite has been studied by Mossbauer spectroscopy. Magnetite, maghemite, goethite and a ferrous glass phase were identified. In a magnetic separate a bcc-structured iron-nickel alloy was identified in addition to the oxide phases. The oxides have formed by weathering of iron-nickel alloys.

A Mossbauer spectrometer is included in the preliminary payload of a rover to be placed on the surface of Mars in the Soviet mission to the planct in 1996/1,2/. In counection with the American planctary program it has also been suggested to construct a Mossbauer spectrometer to be landed on Mars /3, 4/. The objective is to study the iron compounds of the Martian soil and rocks by backscattering Mossbauer spectroscopy. The paper describes the significance of the element iron in the study of the evolution of the planetary system and what we might expect to learn from Mossbauer spectroscopy of the surface materials of Mars. The study of Mars is expected to expand substantially in the coming decades, probably culminating with a manned flight to the planet. The international Mossbauer community may contribute significantly to the preparation of these events.

Both the USSR and US have plans of performing rover missions and sample return missions to the planet Mars in the coming decade. There may be possibilities of performingin situ Mossbauer spectroscopy on Mars or on fresh samples returned to a space station.

[1] The Mars Exploration Rovers each carry a set of Magnetic Properties Experiments designed with the following objectives in mind: (1) to identify the magnetic mineral(s) in the dust, soil and rocks on Mars, (2) to establish if the magnetic material is present in the form of nanosized (d < 10 nm) superparamagnetic crystallites embedded in the micrometer sized airborne dust particles, and (3) to establish if the magnets are culling a subset of strongly magnetic particles or if essentially all particles of the airborne dust are sufficiently magnetic to be attracted by the magnets. To accomplish these goals, the Mars Exploration Rovers each carry a set of permanent magnets of several different strengths and sizes. Each magnet has its own specific objective. The dust collected from the atmosphere by the Capture magnet and the Filter magnet (placed on the front of each rover) will be studied by the Mossbauer spectrometer and the Alpha Particle X-ray Spectrometer, both of which are instruments located on the rover's Instrument Deployment Device. The captured dust particles will also be imaged by the Pancam and Microscopic Imager. The Sweep magnet will be imaged by Pancam and is placed near the Pancam calibration target. The four magnets in the Rock Abrasion Tool (RAT) are designed to capture magnetic particles originating from the grinding of Martian surface rocks. The magnetic particles captured by the RAT magnets will be imaged by Pancam.

The previous chapters have dealt with problems of translational motion. We now begin an investigation of motions where rotation is an important ingredient. We start by associating with one particle the so-called angular momentum, defined with respect to some reference point often taken to be at rest in an inertial frame. These considerations will then be extended to a system of particles. Forming the angular momentum for a system of particles with respect to the center of mass (CM), we shall see that the equation of motion for this angular momentum has a simple form, even if CM is accelerating.

In the previous chapters we have considered rotations of rigid bodies possessing a high degree of symmetry. We have seen that the rotational motion of such a body around an axis fixed in inertial space and fixed relative to the body is as simple to describe as the motion of a single particle moving along a straight line. The same equations govern the motion in these two cases, when p is substituted for L, and v is substituted for ω, etc.

As mentioned, we will here assume some knowledge of elementary mechanics and the concepts within that theory. As the reader progresses through the book, he or she will find these concepts treated in substantial detail.

In this chapter we investigate the motion of the center of mass for a system of particles, acted upon by external forces. As an important special case we shall consider the motion of the center of mass of the system of particles when no external forces act on the system.

The magnetic properties experiments on the Viking missions and the Pathfinder mission indicate that the Martian soil and airborne dust are somewhat magnetic (average saturation magnetization, σS ∼ 4 A m2kg-1). While hematite, superparamagnetic or macrocrystalline, is not sufficiently magnetic to yield the results obtained, pyrogenetic titaniferous magnetite (TiMt) might conceivably be the cause. However, the σS of the dust is considerably higher than that in any of the known Martian meteorites, some of which may be representative of the bedrock from which the Mars soil formed. Furthermore if the reported TiO2 content of Mars soil (∼1% by weight) was entirely present as TiMt of composition Usp 60 (that typical of terrestrial ocean floor basalts), the calculated abundance (S of only 1.2 A m2kg-1. As the Pathfinder magnetic properties experiment results pertain only to the airborne dust particles on Mars, the likelihood of aeolian concentration of such TiMt grains is minimal. Ferrous iron in the bedrock silicates must have been converted to maghemite (γ-Fe2O3) by some unknown oxidative mechanism; this "magnetic enhancement" should be incorporated in any process envisioned for the origin of Martian soil.

This section contains substantial mathematical derivations. The results - not the derivations - are crucial to an insight into fundamental aspects of the Newtonian theory of motion. The main result can be expressed in a simple and elegant manner, and the physical content of this important result is quite transparent (see Equation (6.36)).

Mars Pathfinder successfully landed at Ares Vallis on July 4, 1997, deployed and navigated a small rover about 100 m clockwise around the lander, and collected data from three science instruments and ten technology experiments. The mission operated for three months and returned 2.3 Gbits of data, including over 16,500 lander and 550 rover images, 16 chemical analyses of rocks and soil, and 8.5 million individual temperature, pressure and wind measurements. Path-finder is the best known location on Mars, having been clearly identified with respect to other features on the surface by correlating five prominent horizon features and two small craters in lander images with those in high-resolution orbiter images and in inertial space from two-way ranging and Doppler tracking. Tracking of the lander has fixed the spin pole of Mars, determined the precession rate since Viking 20 years ago, and indicates a polar moment of inertia, which constrains a central metallic core to be between 1300 and ∼2000 km in radius. Dark rocks appear to be high in silica and geochemically similar to anorogenic andesites; lighter rocks are richer in sulfur and lower in silica, consistent with being coated with various amounts of dust. Rover and lander images show rocks with a variety of morphologies, fabrics and textures, suggesting a variety of rock types are present. Rounded pebbles and cobbles on the surface as well as rounded bumps and pits on some rocks indicate these rocks may be conglomerates (although other explanations are also possible), which almost definitely require liquid water to form and a warmer and wetter past. Air-borne dust is composed of composite silicate particles with a small fraction of a highly magnetic mineral, interpreted to be most likely maghemite; explanations suggest iron was dissolved from crustal materials during an active hydrologic cycle with maghemite freeze dried onto silicate dust grains. Remote sensing data at a scale of a kilometer or greater and an Earth analog correctly predicted a rocky plain safe for landing and roving with a variety of rocks deposited by catstrophic floods, which are relatively dust free. The surface appears to have changed little since it formed billions of years ago, with the exception that eolian activity may have deflated the surface by ∼3–7 cm, sculpted wind tails, collected sand into dunes, and eroded ventifacts (fluted and grooved rocks). Pathfinder found a dusty lower atmosphere, early morning water ice clouds, and morning near-surface air temperatures that changed abruptly with time and height. Small scale vortices, interpreted to be dust devils, were observed repeatedly in the afternoon by the meteorology instruments and have been imaged.

Chemical analyses returned by Mars Pathfinder indicate that some rocks may be high in silica, implying differentiated parent materials. Rounded pebbles and cobbles and a possible conglomerate suggest fluvial processes that imply liquid water in equilibrium with the atmosphere and thus a warmer and wetter past. The moment of inertia indicates a central metallic core of 1300 to 2000 kilometers in radius. Composite airborne dust particles appear magnetized by freeze-dried maghemite stain or cement that may have been leached from crustal materials by an active hydrologic cycle. Remote-sensing data at a scale of generally greater than ∼1 kilometer and an Earth analog correctly predicted a rocky plain safe for landing and roving with a variety of rocks deposited by catastrophic floods that are relatively dust-free.

Our own galaxy is called the Milky Way. The galaxy closest to us is the Andromeda Galaxy. Light from the Andromeda reaching us today initiated out there some 2 000 000 years ago. About this time man was at the beginning of his long journey through evolution.

In Newtonian mechanics, dynamical systems are described by differential equations which, if supplied with initial conditions, can be integrated to a unique solution at any future time t. A unique solution means that for each set of initial conditions there exists only one solution. A set of initial conditions determines exactly one solution. Dynamical systems having this property are called deterministic. See Example 12.8.

It was an important event in the history of physics when Sir Isaac Newton in 1687 published his book Philosophiae Naturalis Principia Mathematica.

Since the time of Galileo’s famous experiments with freely falling bodies it has been known that all material bodies, at the same place on Earth, fall with the same acceleration when air resistance is disregarded. Through many experiments this has become a well documented experimental fact.

This chapter contains nothing new. Through a series of examples we wish to illustrate the application of the basic theorems of mechanics. We start by reviewing classical mechanics in the form of ten “laws” or theorems.

The general treatment of the motion of a rigid body is rather involved and we shall in this book consider only certain special cases. The insights to be gained can be applied in virtually all of theoretical physics, and have important technological ramifications. Applications of the theorems derived stretch from studies of the spin of the electron and rotating atomic nuclei, to investigations of the motion of planets and galaxies.

As a preparation for later chapters we shall now review the description of the motion of the Earth relative to the fixed stars.

In this chapter we will try to summarize some of the ideas and opinions on which Newtonian physics rests. These views have been substantially revised in the 20th century, largely due to the works of Einstein in his special and general theory of relativity.

The achondrite Nakhla, belonging to the group of SNC meteorites, is more oxidized than the ordinary achondrites, e.g. Nakhla contains titanomagnetite (≈2%). Besides the Fe3+ in the titanomagnetite, Nakhla includes other compounds carrying Fe3+. By means of Mossbauer spectroscopy we demonstrate that in some of the pyroxenes separated from Nakhla the Fe3+ is distributed throughout the crystals, i.e. the oxidation of the pyroxenes in Nakhla is not only a surface phenomenon.

The Martian moons Phobos and Deimos are relatively small (r ∼ 104 m) irregularly shaped objects that represent a large class of small Solar System Bodies. Based on spectral reflectance measurements and comparison with meteorites the Martian moons are believed to be of Carbonaceous Chondrite composition /1/. The Carbonaceous Chondrites are characterized by a very high average oxidation state of the iron in them compared to that of all other types of meteorites. By use of Mossbauer Spectroscopy Carbonaceous Chondrites of the classes CI, CM, CV and CO are easily distinguished from each other and from other classes of meteorites. The possibility of identifying the Martian moons as distinct types of Carbonaceous Chondrites based on Mossbauer spectra of the surface is investigated.

Locating a rock on the surface of Mars that bears unambiguous evidence of the existence—prior or present—of life on that planet is, understandably, the “Holy Grail” of NASAs sample return missions. Remote recognition of such a rock on Mars will not be easy. We do know, however, that present in the Martian crust—especially in the “Southern highlands”—is rock carrying strong natural remanent magnetization (NRM). Characterization of such magnetized rock has profound implications for adding to our knowledge about the origin and early evolution of the Martian interior, lithosphere, atmosphere, and possibly even Martian life forms [Ward and Brownlee, 2000]. Moreover, it should be possible to recognize such rocks by use of a simple magnetic compass mounted on a Rover.

JSC Mars-1 is a recently announced simulant for the Mars soil “available for scientific, educational study” [Allen et al., 1998]. It is a somewhat altered volcanic ash from a Mauna Kea, Hawaii, cinder cone that yields a reflectance spectrum remarkably similar to the Olympus-Amazonis bright region on Mars [see Allen et al., 1998,Figure 1].The comparability in terms of other chemical and physical properties of the simulant to what is considered to be known of the properties of Mars soil is outlined, and an acceptable similarity is implied. We wish, however, to point out several shortcomings in this Martian analog, to caution researchers and teachers that “looks can be deceiving,” and that they should not conclude that because of the spectral similarity, Mars soil must necessarily be “altered volcanic ash.” It may well prove to be ash in some form but this sample is not the answer.

Viking mission soil analyses and the constitution of the SNC group of meteorites have indicated that the Martian regolith is derived from basalt. On Earth such material often weathers to yield a highly magnetic soil (spontaneous magnetization σS ≥ 1 J T−1 kg−1), the magnetic constituent of which is fully oxidized titanomaghemite. We propose that titanomaghemite is likewise responsible for the magnetism of the soils on Mars.

The meteorite Orgueil is a carbonaceous chondrite of type CI. Carbonaceous chondrites contain Fe(III), Fe(II) and in some cases metallic iron, indicating that they are in a state far from thermodynamic equilibrium. In Orgueil about 40% of the iron is present in magnetite (Fe3O4). In this work a sample of magnetite grains extracted from Orgueil has been studied by Mossbauer spectroscopy. It has been found that the magnetic phase contains about 11% of maghemite and that the remaining magnetite has a vacancy concentration smaller than 0.006, corresponding to the formula Fe2.994O4.

Banded iron formations are rocks of sedimentary origin, formed 2-4 billion years ago. They consist of alternating layers of iron oxides and silicates. In the oxide layers the iron is often in the Fe3+ state while in the silicate layers the iron is mainly in the Fe2+ state. The conditions under which banded iron formations formed are not understood, but the varying oxidation states of iron reflect somehow the evolution of the terrestrial atmosphere. The oxidation state of iron in selected banded iron formations has been determined by Mossbauer spectroscopy. It is found that the youngest rocks are the most oxidized.

The article starts with a brief review of ideas on the origin of the solar system, with emphasis on the cosmic history of the element iron. Some examples of the application of Mossbauer spectroscopy to the study of iron compounds from various types of meteorites, which represent different stages of the evolution of the planetary system, then follow.

Mossbauer investigations of three meteorites of the type SNC-achondrites are reported. The results are compared with Mossbauer spectra of other meteorites, and selected terrestrial and lunar rocks. Through the oxidation state of iron in the pyroxenes and magnetic oxides studied, the work confirms that the mantle of the Earth is highly oxidized compared with the mantle of asteroidal bodies and lunar basalts. The investigations show that at least one of the SNC meteorites (Nakhla) comes from a highly oxidized parent body, believed to be the planet Mars. Based on the results obtained, a somewhat general conclusion about the oxidation state of iron in planetary bodies is proposed.

Samples from the two Ni-rich iron meteorites Santa Catharina and Twin City have been investigated by conventional Mossbauer spectroscopy and by conversion electron Mossbauer spectroscopy. The spectra obtained show that the major components of these two meteorites are an ordered FeNi (∼50%, ∼50%) phase and a paramagnetic Fe−Ni phase with ≤28% Ni.

The meteorites called carbonaceous chondrites are the least altered samples we have of the material which formed our solar system. Using57Fe Mossbauer spectroscopy we show that the carbonaceous chondrite Murchison contains a compound exhibiting superparamagnetic relaxation below 80 K.

It is generally believed that liquid water was once stable on the surface of Mars. In the rather thin and nearly oxygenfree atmosphere of Mars UV-radiation from the Sun reaches the martian surface, and in aqueous environment UV-light is a source of oxidation of Fe2+ (aq). As a Mars simulation experiment, we have studied the precipitates forming from the photochemical oxidation of Fe2+ (aq) in the laboratory by means of Mossbauer spectroscopy. Our results show that α-FeOOH (goethite) must have precipitated in martian aqueous environments as a result of photostimulated oxidation of Fe2+ (aq).

Mars Pathfinder obtained multispectral, elemental, magnetic, and physical measurements of soil and dust at the Sagan Memorial Station during the course of its 83 sol mission. We describe initial results from these measurements, concentrating on multispectral and elemental data, and use these data, along with previous Viking, SNC meteorite, and telescopic results, to help constrain the origin and evolution of Martian soil and dust. We find that soils and dust can be divided into at least eight distinct spectral units, based on parameterization of Imager for Mars Pathfinder (IMP) 400 to 1000 nm multispectral images. The most distinctive spectral parameters for soils and dust are the reflectivity in the red, the red/blue reflectivity ratio, the near-IR spectral slope, and the strength of the 800 to 1000 nm absorption feature. Most of the Pathfinder spectra are consistent with the presence of poorly crystalline or nanophase ferric oxide(s), sometimes mixed with small but varying degrees of well-crystalline ferric and ferrous phases. Darker soil units appear to be coarser-grained, compacted, and/or mixed with a larger amount of dark ferrous materials relative to bright soils. Nanophase goethite, akaganeite, schwertmannite, and maghemite are leading candidates for the origin of the absorption centered near 900 nm in IMP spectra. The ferrous component in the soil cannot be well-constrained based on IMP data. Alpha proton X-ray spectrometer (APXS) measurements of six soil units show little variability within the landing site and show remarkable overall similarity to the average Viking-derived soil elemental composition. Differences exist between Viking and Pathfinder soils, however, including significantly higher S and Cl abundances and lower Si abundances in Viking soils and the lack of a correlation between Ti and Fe in Pathfinder soils. No significant linear correlations were observed between IMP spectral properties and APXS elemental chemistry. Attempts at constraining the mineralogy of soils and dust using normative calculations involving mixtures of smectites and silicate and oxide minerals did not yield physically acceptable solutions. We attempted to use the Pathfinder results to constrain a number of putative soil and dust formation scenarios, including palagonitization and acid-fog weathering. While the Pathfinder soils cannot be chemically linked to the Pathfinder rocks by palagonitization, this study and McSween et al. [1999] suggest that palagonitic alteration of a Martian basaltic rock, plus mixture with a minor component of locally derived andesitic rock fragments, could be consistent with the observed soil APXS and IMP properties.