The surface variation of small bodies across the solar system

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The Current Structure of the Solar System

It is often found with a large enough sample that there are no rigid boundaries between certain classes of objects, but instead there is a somewhat smooth gradient bridging all types of bodies. Creating boundaries and definitions, however, facilitate study and discussion. Outlined here are the main (non-solar) components of which the Solar System is composed. The definitions of a planet, dwarf planet, and small body stated here originate from the recently assigned definitions in Resolution 5A of the IAU 2006 General Assembly (Source: IAU Website).


A “planet” is a celestial body that: 1) is in orbit around the Sun, 2) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and 3) has cleared the neighborhood around its orbit.
The eight planets are thus: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. They are located roughly at 0.4, 0.7, 1.0, 1.52, 5.2, 9.5, 19.2, and 30.0 Astronomical Unit (AU). Note this official definition excludes extra-solar planets because it restricts the definition to bodies orbiting around our Sun. A planet must have cleared its orbit, meaning any body residing in the Main Asteroid Belt between Mars and Jupiter or the Kuiper Belt belt past Neptune is excluded from planet status.

Dwarf Planets

A “dwarf planet” is a celestial body that: 1) is in orbit around the Sun, 2) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, 3) has not cleared the neighbourhood around its orbit, and 4) is not a satellite.
Dwarf planets are large bodies in the Main Belt, the Kuiper Belt, or further and currently include (1) Ceres, (134340) Pluto, (136108) Haumea, (136472) Makemake, and (136199) Eris. Ceres is located in the asteroid belt, while all others are located past Neptune.


All other objects in the Solar System, except satellites, are considered “Small Solar-System Bodies.” There is a wealth of small bodies in the Solar System which include asteroids and comets. Dynamic and basic physical constraints that characterize each population are detailed for comets in this subsection and asteroids in the next two.
Comets are ice-rich bodies that sublimate volatiles during close approaches to the Sun. They are characterized by a nucleus, the inner core of the body; a coma, the outer spherical halo of sublimated material surrounding the nucleus; and two tails, a dust tail trailing opposite the comet’s trajectory and an ion tail in the anti-Sun direction. A neutral gas tail, was discovered on comet Hale-Bopp, however, it is typically not visible. If the nucleus contains species more volatile than water it can form a coma and tail at large distances. Sublimation of water typically begins at a distance of 2-3 AU from the Sun, although more volatile molecules sublimate at greater distances when exposed.
Comets are often described as “dirty snowballs”. Carbon and other dark materials are mixed with the ice substantially lowering the albedo. Comet nuclei are notoriously difficult to observe because the coma obscures it at close distances, but the dark surface is too dim to observe when farther away.
They are often discovered when a previously known asteroid is reobserved and the image appears “fuzzy” or blury because a coma is present. Comets are usually separated into these dynamical categories:
1) Long period comets have periods greater than 200 years and highly eccentric orbits and 2) Short period comets have periods less than 200 years. Among them are Halley Family Comets (P > 20 years) and Jupiter Family Comets (P < 20 years).
Recently discovered within the Main Asteroid Belt is a set of bodies known as either Activated Asteroids or Main-Belt Comets (MBCs). As their name implies, these objects have qualities attributed to both comets and asteroids: asteroid-like orbits within the Main Belt, but comet-like outgassing has been observed through imaging (Hsieh and Jewitt, 2006). MBCs include 133P/Elst-Pizarro, P/2005 U1 (Read), and 118401 (1999 RE70). These objects had all been discovered in the outer belt and two belong to the Themis asteroid family. P/2010 A2 (P/2008 R1 or P/Garradd) was just discovered in the middle part of the belt (a=2.73 AU) with “cometary” activity (Source: Minor Planet Electronic Circular 2010-A32), although it is unique. Throughout most of this body’s orbit, it experiences temperatures greater than the melting point of water, suggesting that this was a very recent impact and dust ejected from the surface is observed and not volatiles.


The term “asteroid” is a broad category including all small bodies that do not exhibit coma (i.e. not comets) and are not satellites of a planet. When an asteroid is discovered it is given a preliminary designation based on the date of discovery and how many objects were discovered in the same time period. The first asteroid discovered in the first half of January 2010 is labeled 2010 AA. The second is labeled 2010 AB. The first asteroid discovered in the second half of the month is labeled 2010 BA. Once the alphabet has been used it restarts with 2010 AA1, 2010 AB1 etc.
While they are all labeled in the same designation scheme, their compositions and size vary enor-mously. These range from the warm, rock-dominated bodies close to the Sun, even inside Earth’s orbit, to the cold, ice-rich bodies in the farthest reaches of the Solar System. Typically, the bodies past Jupiter are not referred to as asteroids, but instead as Centaurs and Transneptunian Objects. In this thesis, they are discussed separately from inner Solar System asteroids.
Main-Belt Asteroids: The Main Belt extends from ∼2.0 to ∼3.3 AU. The largest of these objects have diameters of around 1000 (Ceres, although technically a dwarf planet) and 500 (Pallas, Vesta) kilometers. There are estimated to be about 1 million asteroids with a diameter greater than 1 kilometer in the Main Belt (Tedesco et al., 2002). The structure of the belt is shaped in part by the Kirkwood gaps. These gaps occur at the mean-motion resonances (i.e. 3:1, 5:2, 7:3, and 2:1) with Jupiter. Gravitational perturbations from Jupiter create instabilities in these regions, therefore there is a deficit of bodies in these orbits compared with the rest of the Belt. These resonances are also expected to be a source for small bodies with Mars- and Earth-crossing orbits, because asteroids that fall into these resonances experience orbit excitation, increasing the eccentricity. The 3:1 and 5:2 resonances located near 2.5 and 2.82 AU, respectively create the boundaries defining the inner (2.0-2.5 AU), middle (2.5-2.82 AU), and outer (2.82-3.3 AU) portions of the belt.
Asteroid families (Hirayama, 1918; Zappala et al., 1995) provide important information about the asteroid belt and its formation and evolution. An asteroid family is a group of bodies with similar orbital elements that are thought to have originated from a single parent body that was collisionally disrupted. By integrating the orbits of family members back in time, it is possible to determine the approximate time of the collision, thus providing the opportunity to study the differences of surfaces based on age, as well as the frequency of collisions over time.
Near-Earth Objects (NEOs): NEOs include asteroids and comets that have orbits that are within or that cross near-Earth space (q ≤ 1.3 AU). There are an estimated 5000 to 6000 kilometer-sized Mars Crossing (q < 1.67 AU) and near-Earth objects (Bottke et al., 2002). NEO orbits are unstable for periods longer than 10 My (Gladman et al., 2000) years thus requiring resupply from various sources throughout the Solar System (e.g., Opik, 1963; Wetherill, 1976, 1979; Wisdom, 1985). While the primary source region is the Main Asteroid Belt (particularly the ν6 and 3:1 resonances and the outer belt; Bottke et al., 2002), about 8% of NEOs are consistent with a cometary origin (Jupiter Family Comets) based on both dynamical and physical criteria: their orbits, albedos, and spectra (DeMeo and Binzel, 2008).
Some NEOs require less propulsion (and therefore lower cost) to encounter by spacecraft than the moon, making them ideal mission targets. Indeed, numerous National Aeronautics and Space Admin-istration (NASA), European Space Agency (ESA) and Japan Aerospace Exploration Agency (JAXA) missions have been dedicated to exploring NEOs and Mars Crossers (or have passed by en route to more distant targets), including NEAR, Hyabusa, Deep Space and several proposed missions.
In 1998, NASA was given the objective to discover 90% of all NEOs with a diameter greater than 1 km by 2008. One kilometer is the approximate size of a body that could cause global disaster if it struck the Earth. More recently the objective was expanded to discover 90% of all asteroids greater than 140 meters in diameter by 2020. While these objects would likely not cause global disaster, they would certainly cause significant local destruction. There are 6792 known NEOs, 803 of which are greater than 1 kilometer (Source: NASA, Feb. 22, 2010). Figure 1.1 shows the rate of discovery of NEOs from 1980 to the present.
NEOs are subdivided into several dynamical categories. Figure 1.1 displays a typical orbit for these objects.
• Amors: Objects that satisfy 1.017 < q < 1.3 AU, where q is the perihelion. These objects approach Earth’s orbit but do not cross it.
• Apollos: Objects that satisfy a > 1 AU and q ≤ 1.017 AU, where a is the semi-major axis. These objects cross Earth’s orbit.
• Atens: Objects that satisfy a < 1 AU and Q > 0.983 AU, where Q is the aphelion. These objects cross Earth’s orbit.
• Atira: Objects that satisfy Q < 0.983 AU, meaning the orbit lies entirely inside that of Earth’s.
The class is named after the first object, (163693) Atira, discovered in 2003 (Source: NASA). Some consider these objects part of a subclass of Atens, and have also been called Apoheles.
Potentially Hazardous Asteroids (PHAs): PHAs are a subset of NEOs that are flagged because of their proximity to Earth’s orbit. An object is considered a Potentially Hazardous Asteroid (PHA), if its Minimum Orbit Intersection Distance (MOID) with respect to Earth is less than 0.05 AU and it has a diameter of 150 meters or greater. The size condition is satisfied by having an absolute magnitude (H) of 22.0 or less (with an assumed albedo of 0.13). There are 1103 PHAs known today (Source: NASA, Feb. 22, 2010). Continued tracking of these objects increases the accuracy of their orbits which allows us to better quantify the likeliness of impact. These objects are important to characterize because all objects that have impacted the Earth in the past or that will in the future come from this population. The most “famous” of known PHAs is 99942 Apophis which will have a very close approach (about 6 Earth radii, Chesley, 2005) in 2029 and could possibly impact the Earth in 2036 (1:43,000 impact probability, Source: NASA, Sep 8, 2009). Apophis’ orbit is shown in Figure 1.2.
Trojan Asteroids: There are almost 4,000 objects in the L4 (2,483 objects) and L5 (1,430 objects) Lagrange points of Jupiter’s orbit (Source: Minor Planet Center, Jan. 13, 2010). Jewitt et al. (2000) estimate that the number of L4 Jupiter Trojans with radius greater than 1 km is estimated to be around 1.6×105, which is on the order of the estimated population of the Main Belt. Several Mars and Neptune Trojans have also been discovered.

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Centaurs and TNOs

Centaurs: Centaurs are icy bodies in orbit between Jupiter and Neptune. There are 256 known Cen-taurs (including Scattered Disk Objects) as of May 16, 2010 (Source: Minor Planet Center). Diameters have been derived for over 20 Centaurs, ranging from tens to hundreds of kilometers (Stansberry et al., 2008), although this samples the brightest and therefore mostly likely the largest of the population. Their orbits are not stable over long time periods and are thus thought to have originated in the transneptunian region. (2060) Chiron was the first discovered Centaur in 1977, and it was later learned to have cometary activity and renamed 95P/Chiron. Most Centaurs, however, have been discovered within the past decade. The unique property of the Centaur population is its color bimodality. Their B-R colors divide into gray and red groups with 99.5% confidence (Tegler et al., 2008a). The gray Centaurs also have a lower mean albedo than the red ones, although dynamically, no differences in their orbits have been found (Tegler et al., 2008a).
TNOs: TNOs are objects that reside in and past the Kuiper Belt past Neptune’s orbit. The Kuiper belt (see Fig. 1.3) lies roughly between 30 and 55 AU. There are 1130 (as of May 16, 2010) known TNOs including Pluto (which is also a dwarf planet) and excluding Centaurs (Source: Minor Planet Center). Figure 1.3 shows the eight largest known TNOs. The current mass of the Kuiper Belt is estimated to be between 0.01 to 0.1 of Earth’s mass (Bernstein et al., 2004; Gladman et al., 2001), and is only 0.1% of the original mass of the Kuiper Belt (Morbidelli et al., 2008, and references therein). Diameters of measured TNOs range from hundreds to thousands of kilometers (Stansberry et al., 2008). The discovery of a serendipitous stellar occultation of a ∼500-meter body at 45 AU among archival data supports the current belief that there is a deficit of sub-kilometer TNOs (Schlichting et al., 2009).
Dynamical classifications summarized below are described in detail by Gladman et al. (2008). Fig-ure 1.4 is a plot of the dynamical regions of these classes from Gladman et al. (2008).
• Resonant: Resonant objects are in mean motion resonances with Neptune, meaning they complete a fixed number of orbits per orbit of Neptune. The 3:2 resonance is the most populous, and includes Pluto. These objects complete three orbits for every two Neptune orbits. Other prominent resonances include 5:3, 7:4, 2:1, and 5:2.
• Scattered Disk Objects: These objects are in unstable orbits. They have perihelions near Neptune and high eccentricities. Theories that would allow objects to reside in this region include a passing star, a rogue planet, or sweeping resonance, all of which are discussed further in Section 1.2.
• Detached Objects: These objects have perihelia decoupled from Neptune and include objects with large semi-major axes.
• Classical: Any object not within these outlier groups makes up part of the classical population, whose typical members have relatively circular orbits and low eccentricities. The densest region of objects is between about 42 to 48 AU. The classical objects have been proposed to be split into two populations, the hot and cold populations. The cold population has an inclination of less than 5 degrees and either formed in situ or was pushed outward during the planet migration phase, whereas the hot population has more excited orbits, with inclinations greater than 5 degrees. These bodies were thought to have originally been closer to the Sun and were then perturbed by Neptune and Uranus into their current orbits.

Table of contents :

I Introduction and Background 
1 Background 
1.1 The Current Structure of the Solar System
1.1.1 Planets
1.1.2 Dwarf Planets
1.1.3 Comets
1.1.4 Asteroids
1.1.5 Centaurs and TNOs
1.2 Solar System Evolution
1.2.1 Solar System Formation
1.2.2 Planet Migration: The Nice Model
1.2.3 Passing Star, Companion Star, and Rogue Planet Theories
1.2.4 The Late Heavy Bombardment
1.2.5 Effects currently shaping the Solar System
1.3 The surfaces of small bodies
1.3.1 Composition
1.3.2 Surface Evolution
2 Observational Data 
2.1 Methods of investigating surface composition
2.1.1 Photometry
2.1.2 Spectroscopy
2.2 Telescopes and Instruments
2.2.1 IRTF
2.2.2 VLT
2.3 Data Reduction
2.3.1 Calibration files
2.3.2 Photometry Reduction
2.3.3 Spectroscopy Reduction
2.4 Observational Programs
3 Methods of Analysis 
3.1 Classification Methods
3.1.1 G-mode analysis
3.1.2 Principal Component Analysis
3.2 Bidirectional Reflectance Models
3.2.1 Hapke Model
3.2.2 Shkuratov Model
3.3 Space Weathering Models
3.3.1 Hapke Model
3.3.2 Brunetto Model
II The Inner Solar System 
4 Taxonomy of Asteroids 
4.1 Need for a new taxonomy
4.2 The Data
4.3 The Taxonomy
4.3.1 The end members: A, V, R, O, Q
4.3.2 The S-complex: S, Sa, Sq, Sr, Sv
4.3.3 The w-notation
4.3.4 The end members: D, K, L, T
4.3.5 C- and X- Complexes: B, C, Cb, Cg, Cgh, Ch, X, Xc, Xe, Xk
4.4 Taxonomy Web Application
4.5 IR-only taxonomy
4.6 Limits of only visible or near-IR coverage
4.6.1 Visible: The 1-micron band uncertainty
4.6.2 Near-IR: S-complex and Q-types
4.6.3 Near-IR: C- and X- complexes
4.7 Albedo Distributions among Taxonomic Classes
4.8 Conclusion
III The Outer Solar System 
5 Photometric Analysis of TNOs and Centaurs 
5.1 State of Understanding
5.2 Taxonomy of TNOs
5.3 Results
5.4 Discussion
5.4.1 26375 (1999 DE9)
5.4.2 Ixion (29878)
5.4.3 Thereus (32532)
5.4.4 47932 (2000 GN171)
5.4.5 Bienor (54598)
5.5 Conclusion
5.6 Final Color Results from the second ESO Large Program
6 Spectroscopy of 3 Outer Solar System Small Bodies 
6.1 Introduction
6.2 Modeling
6.3 Discussion
6.3.1 (52872) Okyrhoe
6.3.2 (73480) 2002 PN34
6.3.3 (90482) Orcus
6.3.4 Limits on the presence of CH4 and CO2 on Orcus
6.4 Conclusion
7 A search for Ethane on Pluto and Triton 
7.1 Background on Pluto and Triton
7.2 Introduction
7.3 Modeling
7.4 Discussion
7.5 Conclusion
7.6 Mission to Pluto: New Horizons
IV Synthesis of Research and Conclusions 
8 The surface variation of small bodies across the solar system
8.1 The Early Solar System
8.2 Compositional trends in the Solar System today
8.2.1 Variation across the Main Asteroid Belt
8.2.2 Variation among Centaurs, in the Kuiper Belt and beyond
8.3 Water throughout the solar system
9 Comparison of systems around solar-like stars 
9.1 Evolution of Debris Disks
9.2 Formalhaut
9.3 Epsilon Eridani
9.4 Beta Pictoris
9.5 Composition of Dust Excess Emission
10 Conclusions and Perspectives


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