Dynamics of Extrasolar Planetary Systems by Ricky Leon Murphy:
Back to Exoplanets
The Solar Nebula Hypothesis and the Core Accretion Model
The Transit Method
Types of Systems
Exoplanetary System Formation
Core Accretion Model Revisited
Dynamics of Extrasolar Planetary Systems
There are two competing theories of
planet formation in a system of planets: the Core Accretion Model and the Disk
Instability Model (sometimes called the Gravity Instability Model). Because we
are able to study our own Solar System, we are reasonably certain the formation
of it occurred via the Solar Nebula Hypothesis with the Core Accretion Model
responsible for planet formation. The cores of the planets, the delineation
between terrestrial and gas giant planets and the ingredients of chondrites
serve as evidence to support this theory; however, the discovery of numerous
exoplanetary system have some astronomers
favoring the Disk Instability Model
over the Core Accretion Model. Could this be due to massive planets forming
close to their host star or due to inward migration of Jupiter-sized planets? Could
the sampling of large planets be the result of instrument sensitivity? While it is difficult to create a
unified theory of solar system formation, it may be possible that planetary systems form
with a combination of both theories. In
addition to discussing planetary formation, I will also introduce the methods in
detecting extrasolar planets and the possibility of detecting Earth-like
planets. The advantages and disadvantages of detection methods are also covered
as this can also give important information to the known dynamics of extrasolar
planetary systems. A note to the reader: the terms exoplanet and extrasolar
planet are used interchangeably.
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Nebula Hypothesis and the Core Accretion Model:
To understand planetary systems (also
known as exoplanetary systems), we must first understand our own system of
planets. This may sound simple, but we are still learning about our Solar System
– however, there are some things we do know. For example, we are reasonably
certain that our own Sun and the planets that orbit the Sun formed from a cloud
of gas and dust – or molecular cloud. This is the basis of the Solar Nebula Hypothesis –
that from a cloud of dust and gas, our Solar System formed to what we see today:
a Sun, four rocky terrestrial planets, an asteroid belt, four “gas-giant”
planets, Pluto and the other Kuiper Belt Objects, and the Oort cloud (and the
variety of debris within).
While many pages can be
written to describe the process of
our Solar System formation, the basic
steps are as follows
and Kaufmann, 2005):
Within the arms of our
Milky Way Galaxy exist clumps of dust clouds that contain molecular hydrogen
causes one of these clouds to collapse – perhaps a nearby supernova
or spiraling density waves within the arms of the galaxy.
As the cloud
collapses, it begins to rotate and flatten out.
Gravity and pressure
begin to increase their influence – gravity wants to collapse the cloud
while pressure tries to balance the force to prevent collapse.
Eventually gravity wins
(in this case) – pressure is exerted on the center of the cloud and by the
Kelvin-Helmholtz contraction the center of the cloud heats up.
Continual heating and
cloud spinning results in a central proto-star – that is a star that has not
begun the fusion process – forms while dust in the newly formed disk begins
The proto-star continues to
gain mass, with increasing heat and pressure while planetesimals form with
the accreted dust particles.
Continued accretion of
material form even larger planetesimals while the heat from the proto-star
cause the ices in the inner portion of the disk to melt away – the line that
separates the temperature differential between the inner and outer disk is
called the “snow-line.”
form within the inner disk. The same occurs in the outer disk but these
protoplanets have more gaseous material available to collect huge
atmospheres. The planetesimals differentiate – that is due to heat, pressure
and added mass, heavier elements sink towards the core.
At this time, the
proto-star gets enough mass and pressure to initiate fusion – the star
ignites and a T Tauri wind blows away any non-accreted material within the
What remains are a newly
formed star and a system of planets.
The collection of dust particles to
form planetesimals to protoplanets to full fledged planets is the crux of the
Core Accretion model. Primitive refractory material has been found in Chondrites
that support this theory (Beatty
et al., 1999). The fact that planets have cores – which formed by
differentiation – also support this theory.
There are two issues with the Core
Accretion model, and they have to do with the gas giant planets (Jupiter-like
planets). Given the time
it takes to form a terrestrial planet prior to the T Tauri phase, it is believed
there was not enough time to form the outer massive planets. In addition, the mass of
Jupiter would have prevented the formation of Uranus and Neptune in their
current positions. The Disk Instability Models explains how such large planets
can form so rapidly – and given that formation occurs so fast, the all the
material is available for planet formation (i.e. Uranus and Neptune) prior to
the T Tauri Phase. In other words, the gas giant planets formed directly from
the solar nebula (Freedman
and Kaufmann, 2005) and not by accretion. For the large planets to form, the
material accretes by a process called “runaway accretion” – a process that does
not allow time enough for a core to form. However, there are four major flaws
with the Disk Instability Model:
- This model does not
explain the cores of Jupiter, Saturn, Uranus and Neptune – each of these
planets have a core even though the model suggests they should not have one.
- If Jupiter (being the
largest, most massive planet in or Solar System) formed directly from the
solar nebula, it should have the same composition as the Sun – it does not.
- The Disk Instability
Model should have formed much larger gas giant planets.
- This model does not
explain why the terrestrial planets exist.
These issues are still being worked
out – and with the data collected regarding exoplanetary systems it is hoped
that the issue of Core Accretion versus Disk Instability will be worked out.
Planetary formation via the Solar
Nebula Hypothesis has been demonstrated by three phenomena:
Proplyds (proto-planetary disks)
discovered in the Orion Nebula
Image of individual orbital rings
around Beta Pictoris
– shown on the left – are a system of planets in the making. Much of the
material here has been “blown away” by the surrounding hot O and B type stars, which
is why the T Tauri star is visible. The dense region surrounding the T
Tauri star is the circumstellar disk that has accreted to a disk shape.
Planets will form here (we are actually uncertain if planets will form
within these proplyds as there may not be enough material).
More information on this image
and the Proplyds can be found on the
Hubble Space Telescope website.
Herbig-Haro objects are a T
Tauri star (or proto-star) surrounded by the “correct” amount of
material that emits visible jets (Freedman
and Kaufmann, 2005). In other words, there is enough disk material
to stimulate continued system evolution with the presence of the jets
– seen here 90 degrees from the plane of the disk
- while the T Tauri Star itself is not visible.
According to the
Hubble Space Telescope website, the action
and morphology of these disks
demonstrates the circumstellar disk material is still falling onto the
The most dramatic image of a solar
system in progress is the circumstellar orbits image around Beta Pictoris. This
image appears to demonstrate the sweeping up of debris to accrete planets - a
good example of the Core Accretion Model.
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Images of Proplyds, Herbig-Haro
objects and circumstellar disks suggest our theory on the formation of our Solar
System by the Solar Nebula Hypothesis is correct, but it says nothing on how the
planets formed (although the Beta Pictoris image does demonstrate possible
accretion). In fact, these three remarkable images show no planets.
The only image we have of an
extrasolar planet is the remarkable image from the European Southern
Observatory. As the caption in the image states – it is the planetary companion
to Brown Dwarf 2M1207. The distance of the planet is twice as far as the
Sun-Neptune distance and was imaged using a variety of infrared wavelengths.
More detail is available on the
ESO Press Release 12/05 webpage.
Exoplanet research is one of the
hottest new fields in Astronomy – and its one that both amateurs and
professionals can participate. These images are very dramatic and
prove all of the efforts of the various projects that search for these planets,
imaging a random star will not guarantee
an image of a planet. We need to know where to look, and
this is where detection takes place.
There are two main methods of
detection with a third and fourth method gaining momentum.
- Radial Velocity
- The Transit Method
Radial Velocity and the Transit Method are, at the moment, the primary methods
of detection. Astrometry is also used to detect
planets, but this method is most useful in long term follow up of known
exoplanetary systems – it also detects a wobble (discussed in the radial
velocity section below) but without using a spectrometer
- instead, it uses lots of math. In addition, the
number of planets detected with the astrometric method is very low, and accuracy is
at best equal to Doppler
2005). Astrometry does have its strong points. For one, the mass of the
detected planet is measured accurately compared to the radial velocity method.
In addition, planets with larger orbits can be detected, but this can take years
– even decades – to complete a study.
Microlensing also deserves a brief
introduction, but only a handful of planets have been detected using this method. At best,
microlensing serves more as a survey to determine
how many Earth-sized
planets there are. The distances to these stars – at least the distance to allow
for microlensing events – are too far away for continued study (Lunine,
2005). How microlensing works is by detecting a gravity lens, however a star
is not capable of bending the image of another star (like those wonderful galaxy
lenses seen in Hubble images) – due to its low mass relative to galaxies.
Instead, the brightness of the star increases a bit. If the lensing star has a
planet, the brightness of the lensed star will increase a bit more for a short
period of time. It is safe to say that not much information about the planet can
be gleaned from this data – only that a planet is present.
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The first exoplanets were discovered
by what is called the “wobble.” This sounds low tech, but this is very
significant (the “wobble”
is also associated with astrometric detection). When two objects orbiting each other contain any mass, they will
have an affect on each other resulting in an inertial center - called the barycenter (Mayor
and Frei, 2003). Using our own solar system as an example, Saturn and
Jupiter have enough mass that the effect is a wobble of the Sun (Marcy
and Butler, 1997). The net affect of both planets produce a wobble of around
13 m/s and if Jupiter were the only planet, a wobble of around 12 m/s would be
A spectrometer detects shifting in the
absorption lines of the stars spectra. This shift can be measured using simple
mathematics that compares a reference object containing identical spectra to
the shifted object. With this information, it is possible to determine the
velocity of the object.
Determining Doppler redshift and blue
z = redshift
∆λ = shift in wavelength
λ = wavelength of stationary object
λο = stationary wavelength – reference
v = velocity
c = speed of light (300,000 km/s)
It is important to state that:
Equation 1 is the basis of determining the orbital velocity of the object
orbiting the affected star or determining the radial velocity of the affected
star. Once the orbital velocity is determined, simple usage of Kepler’s Third
Law will determine the distance the planet is to the host star.
Kepler’s Third Law:
P2 = a3
P = object’s rotation period in years
a = object’s distance to star in
By using a high resolution
spectrometer, standard Doppler measurements are around 15 m/s; however, a method
of introducing iodine gas near the slit entrance has allowed for precision
measurements of up to 3 m/s (Butler
et al, 1996). The iodine is used to create a composite spectrum to overlay
the spectra of the analyzed star and enhances our view of the absorption lines while acting
like a ruler. By eliminating any uncertainty between stellar absorption lines
with a laboratory standard, precision measurements are attained.
There are some disadvantages to using the
Doppler shift to measure radial velocities: the star must be as close to the
host star are possible. For example, one of the first exoplanets discovered –
the companion to 51 Pegasi – is only 0.05 AU’s
and Frei, 2003). That means the planet, which is 0.5 times the mass of
Jupiter, is much closer than the orbit of Mercury is about our Sun. For planets
that orbit at a larger distance from the star, more precise astrometry
measurements are desired – mostly because larger orbits require many years to
study versus days of a closer orbiting planet.
In addition, the mass of the planet is
determined by m sin i - which varies based on the angle of the system
relative to the observer (m = mass, i - inclination). If the system is face on
(God's eye view), the determination of mass is not accurate at all; however, if a system is
closer to an edge on view, the determination of mass is more accurate. This is
often called the "m sin i problem."
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Another important method of detection
is by measuring the transit of a planet over the face of the host star. By
performing careful photometric plots of the host star, drops in stellar
brightness as a planet moves across the face of the star can be measured. The
first ever measurement of a stellar transit was made by the Elodie group
(discoverers of the companion to 51 Pegasi) and the David Latham group (Mayor
and Frei, 2003) - also known as project
STARE. Currently this method is used to study known
With the m sin i problem discussed above, the transit detection allows
astronomers to determine the value for i in order to determine planet mass more
accurately. Once the mass is determined by Doppler, diameter of the planet can
clue us in to density and even infer an atmosphere.
The transit method can only be used
for a planetary system that
is directly in our line of sight. An additional limitation is the
size of the planet. A planet 0.64 times the mass of Jupiter will decrease the
brightness of its host star by about 0.0011 magnitudes – this is a small change
in brightness (Mayor
and Frei, 2003). Determining the transit of an exoplanet is not as difficult as
performing radial velocity measurements. While determining the radial velocity
requires carefully calibrated equipment, specialized spectroscopes, and lots of
patience, determining the transit only requires the skill of photometry,
a telescope and CCD camera, and a
personal computer. Quite simply, photometry is the study of stellar brightness.
While there is a danger that a transiting planet can be confused by other
phenomenon like variable stars, proper measurements will rule this out as
variable stars and transiting binary stars have specific patterns of photometric
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The majority of exoplanets discovered
have been around metal rich main sequence stars (with a few exceptions) –
specifically stars with a spectral class of F, G and H (Butler
et al, 2000). The reasons are twofold:
- F, G, and K type stars
are “normal” sized stars like our Sun, and will more than likely exist long
enough for planets to form. Larger, hotter burning stars end their lives
much sooner so the possibility of mature planets to form is highly unlikely;
although planets have been found to orbit stellar remnants such as pulsars.
- Metal rich stars contain
heavier elements in their atmospheres as a result of enriched molecular
clouds from which they have formed. This results in more absorption lines to
It is much more likely that a planet
capable of having a substantial atmosphere will require a metal-rich host because
this will require silicate and carbonate materials - material from a metal-rich
molecular cloud from which the system formed.
This image, from the
Extrasolar Planet Encyclopedia website, demonstrates the metallicities and
masses of the stars hosting planets thus far. This coincides with the data from
Butler et al., 2000.
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Exoplanetary System Formation:
As of April 16, 2006 there are 188
detected exoplanets. The vast majority (176 of them) have been detected using
the Radial Velocity method. 4 planets have been detected by direct imaging, 4
planets orbiting pulsars have been detected and 4 planets detected by microlensing (http://vo.obspm.fr/exoplanetes/encyclo/catalog.php).
Since the much publicized discovery of 51 Peg
companion in 1995, the field of
exoplanetary study has grown rapidly. For the initial years of exoplanet
detection, spectrometer resolution (for the radial velocity searches) was
limited to a 13 m/s detection capability. With this level of sensitivity, the
majority of planets discovered were massive planets very near the host star. By
using a technique of introducing an iodine gas into a spectrometer, it was found
that the spectral resolution increased to an incredible 3 m/s (Butler
et al., 1996).
Since the introduction of the higher
resolution spectrometer, more planets have been discovered but with the same
parameters as the earlier planets – high mass “hot-Jupiters” orbiting very near
the host star. The number of these high-mass, close orbit planets was initially thought to be
a sampling issue, but higher resolution spectroscopy is detecting more of these
high mass planets. There are two possible explanations as to why these bodies
are so close to their host: either they formed close to the host star, or they
migrated inward. In both cases, the Core Accretion Model does not apply (Boss,
Transiting planets, like HD 209458b,
can have a significant atmosphere (Arribas
et al., 2006). This is thought to be the result of the planet being so close
to the host star; the planet “swells up” to appear much larger
than it would had the planet been allowed to condense. This could be one reason
why there are so many Jupiter-sized bodies in such tight orbits. This type of
planet, so easily “puffed up,” coincides with formation via Disk Instability
as there is no definitive core keeping
the planet together.
Two major issues confront astronomers
when studying exoplanetary systems:
- Prevalence of high-mass
planets in close orbits
- Highly eccentric orbits
As briefly mentioned, the presence of
high-mass planets in close proximity to the host star does not fit the Core
Accretion Model. For such a high mass planet to form so rapidly requires
immediate formation – the crux of the Disk Instability Model. Migration of the
newly-formed planet also requires a proto-planetary disk of higher density. This
provides the material for formation as well as the “drag” required to cause the
planet to migrate (Boss,
2000) - which is believed to be the
primary reason for the existence of tight orbit, high mass planets.
Planets are not believed to form
close to the star as the star itself would grab up any debris that would have
created the planet.
While simulations by
Boss, 2000 indicate Disk Instability can occur with a proto-planetary nebula
of 0.1 solar mass (believed to be the mass of our own solar nebula prior to Solar
Goldreich et al., 2004 states the disk
material required for Disk Instability to work
must be optically thick (thicker than our own Solar Nebula). In addition, disk
clean-up (the material not accreted to create planets) is a poorly understood
process. Any significant debris left in the proto-planetary disk could
provide the necessary drag to force planetary migration – especially if there
are few bodies on the system.
The high eccentricity of many
discovered exoplanets caused some concern for the Core Accretion Model as this
feature of exoplanetary systems seems to offer additional evidence to the Disk
Instability Model – the sudden creation of a planet that migrated as a result of
disk debris and interactions with other rapidly accreting bodies. However,
Innanen et al, 1998 of our own Solar System demonstrate that without the
Earth-Moon system, the inner planets – Mercury, Venus and Mars - would evolve
into highly elliptical orbits. In some simulations, Mercury was completely
ejected. This results in an important (and new) system dynamic called orbital resonance - a key part
in planetary system stability. In a project I did for a previous class, I
determined the stability component of the inner planet of the Gliese 876 system
to the other two massive planets. The result is that the eccentric orbits of
Gliese 876b (1.9 Mjup) and Gliese 876c (0.6 Mjup) are the results of
interactions with each other and Gliese 876d (0.023 Mjup) is the stabilizing
factor that keeps the eccentric orbits stable (Murphy,
2005). This inner planet has also prevented further migration of the larger
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Core Accretion Model Revisited:
The Disk Instability Model does
present some compelling data in the present condition
of exoplanetary systems, but
even now smaller planets are being discovered
in several of these existing systems. This can be attributed to better,
more sensitive equipment and continued study and simulations of current systems.
Some very interesting data plots are available from the
Extrasolar Planets Encyclopedia website. For example, the following plots
show trends of planet mass versus discovery date, planet count by discovery date,
semi-major axis (S.M.A.) versus discovery date and S.M.A. count by discovery
These images show that as time reaches
the present, we are able to detect more lower-mass planets at greater orbits as
well as more balanced overall system.
With orbital resonance as a factor, this greatly affects the overall system
evolution when considering Disk Instability.
These plots demonstrate that smaller
planets as well as larger orbits are being discovered. These are certain to
provide the necessary data to help re-introduce the Core Accretion Model as far
as exoplanetary formation. The reasons are:
- Larger planets found at
- Increased number of
planets to explain orbital resonance and ecliptic orbits
Only with the collection of more data
can we solidify either theory, or as
Boss, 2000 suggests: the formation of planetary systems could be the
marriage of both the Core Accretion Model for terrestrial, high density planets
and the Disk Instability Model for gaseous, lower density planets. But it's
clear that the bias towards high mass planets is due to current detection
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Detecting an Earth-like planet is the
absolute Holy Grail of exoplanet research. What is exciting is that observations
are well under way that will pave the way for this detection. Currently, the
favored mechanism for detecting an atmosphere is using spectroscopy coupled with
a transit of the planet around the host star. The methodology is rather simple:
with the spectra of the star
identified, simply subtract this known spectrum with the spectra of the planet. Any gaseous atmosphere will be detected. This sounds rather simple and
in a way it is with the only limitation being equipment sensitivity.
Using a technique called Integral
Field Spectroscopy (which is a combination of high resolution spectroscopy and
wide field detection spectroscopy), sodium was detected in the atmosphere is
planet HD 209458b (Arribas
et al., 2006). This technique is planned to be used in the future DARWIN and
TPF missions, but the detection of sodium using a terrestrial based
telescope demonstrates that results can also be shown with the Hubble Space Telescope
or the future James Webb Space Telescope.
One experiment that was set to detect
and explore Earth-like worlds was NASA’s Terrestrial Planet Finder (TPF). Using
a similar layout to DARWIN, this would have been able to detect Earth-like
atmospheres. Unfortunately, budget cuts have forced NASA to send the TPF to the
2006). However, lets consider the search as if the TPF were still in the
wings; what would the TPF look for? The spectra of the atmosphere would need to
be captured; however, the difficulty is in the optical wavelengths – that is
contamination by the host star. To get around this, the spectra would be
captured in the infrared.
In the infrared, water and
ozone will be more prominent (Lunine,
2005). Since water is required for
life, the presence of water in the spectrum of the detected planet is a
good indicator that life is possible. The presence of Ozone will
demonstrate than some biological process is occurring as oxygenation of
the atmosphere can occur through natural biological processes.
drawback is that the spectrometer on the TPF will be unable to detect liquid
water – which is required for life to evolve. Water detected in an atmosphere
does not mean that liquid water exists on the surface – but the detection of any
water in an atmosphere of an extrasolar planet is significant.
While the TPF project has been scrapped, the DARWIN is still underway. With a
predicted launch date of 2015, the
DARWIN will contain four free-flying 3-meter infrared telescopes. The
purpose is to be a nulling interferometer to directly detect and image planets by “nulling
out” the host star. Because the telescope operates in the infrared, the
orbit of the spacecraft will be at L2 with a distance of 1.5 million
kilometers opposite the Sun in order to shield the telescope from the
“heat” of the Earth and
While direct detection of Earth-sized
bodies as well as detection of an Earth-like atmosphere is no guarantee we will
find life, it does provide us with definitive proof that Earth-like bodies do
exist in the Universe. This certainly does have some impact on the social and
religious environments on Earth, but that is another story!
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There is a lot of information here
that covers a broad spectrum of the exoplanet phenomenon. To recap, exoplanets
have been discovered using the venerable radial velocity method. While this
method has discovered the most planets – and will not doubt continue to do so –
the transit method and astrometry method are better at nailing down the actual
mass of the discovered planet,
supplementing important data to support the radial velocity measurements;
however, currently the radial velocity is biased towards high massed planets due
to its current sensitivity.
The transit method is unfortunately limited to
close orbiting bodies of high mass that are directly in our line of site while
astrometry is limited to planets with larger orbits and therefore require long
bits of time to observe. Microlensing is a method to give a survey of
Earth-sized worlds but cannot help with any additional data beyond detection. Direct
detection has not been covered with the exception of the first ever detection
from the ESO. The reason is not only space constraints on this paper, but there
are only 4 planets credited to direct detection.
The future of direct detection
is very interesting indeed, and one project deserves mention: PLANETPOL (http://www.ing.iac.es/PR/wht_info/whtplanetpol.html).
While in its infant stages, the goal is to directly detect planets by detecting
the polarized light reflected by the planet emanating from the host star (which
is not polarized).
While we are reasonable certain of our
own Solar System formation through the Core Accretion Model, the discovery of
exoplanets with high masses in close orbits along with high elliptical orbits
have the Disk Instability Model preferred in the formation of these systems.
While this has some ramifications on our Core Accretion Model theory, the issue
may simply be sampling as more sensitive instrumentation are finding smaller
bodies. In addition, the result of ellipsis could also be interactions with
other planets – simply a consequence of planetary system formation. Planetary
migration due to the density of the protoplanetary disk may also play a role in
the presence of the “hot-Jupiters.” It is possible that planet formation is a
combination of the Core Accretion and Disk Instability Models.
Detection of an atmosphere around a
high-mass planet has been detected, but detection of an Earth-like atmosphere –
as well as directly detecting an Earth-sized planet – will require infrared
detection with a space-based telescope. The DARWIN mission will provide the
necessary resources to detect these bodies as well as look for the tell-tale
sign of a life bearing atmosphere.
Exoplanet research is an exciting
field in Astronomy. Since 1995 when the first planet was detected, the field
shows no sign of slowing down. While the models of exoplanetary solar systems
seem to fit the Disk Instability Model – an unfavorable model of planet
formation – further data collection seems to point to a combined Core Accretion
Model and Disk Instability Model in the creation of a planetary system. It is
hoped that missions like DARWIN as well as continued follow-up using methods
like astrometry and transit studies will provide the data to solidify these theories.
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Santiago et al. “Exploring the Potential of Integral Field Spectroscopy for
Observing Extrasolar Planet Transits: Ground-based Observations of the
Atmospheric Na in HD 209458b.” PASP, 118:21-36. January 2006.
Beatty, Kelly J.;
Petersen, Carolyn C. and Andrew Chaikin. The New Solar System. Fourth
Edition. Cambridge University Press, 1999.
et al. “Evidence for Solar-Like Oscillations in ß Hydri.” The Astrophysical
Journal, 549: L105-L108, March 1, 2001.
Boss, Alan P.
“Possible Rapid Gas Giant Planet Formation in the Solar Nebula and Other
Protoplanetary Disks.” The Astrophysical Journal, 536:L101-104, June 20, 2000.
Butler, Paul, et al. “Attaining
Doppler Precision of 3 m s -1.” Publications of the Astronomical Society of the
Pacific, v 108: 500-509, June 1996.
“A precision Velocity Study of Photometrically Stable Stars in the Cepheid
Instability Strip.” The Astrophysical Journal, 494: 342-365, February 10, 1998.
Butler, Paul et al. “Planetary
Companions to the Metal-Rich Stars BD -10o 3166 and HD 52265.” The
Astrophysical Journal, 545: 504 – 511, December 10, 2000.
A. and William J. Kaufmann III. Universe. Seventh Edition. W.H. Freeman
and Company, New York. 2005.
Peter; Lithwick, Yoram and Re’em Sari. “Final Stages of Planet Formation.” The
Astrophysical Journal, 614:497-507, October 10, 2004.
Mikkola, Seppo and Paul Wiegert. “The Earth-Moon System and the Dynamical
Stability of the Inner Solar System.” The Astrophysical Journal, 116:2055-2057.
Kitchin, C. R.
Astrophysical Techniques 3rd Edition. Institute of Physics
Publishing. Bristol, 1998.
Astrobiology. A Multidisciplinary Approach. Pearson Addison Wesley, San
Marcy, G. W. and
Paul Butler. “Characteristics of Observed Extrasolar Planets.” The Tenth
Cambridge Workshop on Cool Stars, Stellar Systems and the Sun. Cambridge,
Massachusetts. July 16-20, 1997.
Mayor, Michael and
Pierre-Yves Frei. New World in the Cosmos. The Discovery of Exoplanets.
Cambridge University Press, 2003.
Jonathan. “NASA Science in Free Fall.” Sky and Telescope Magazine, pg 16-17.
“On the Stability of the Gliese 876 System of Planets and the Importance of the
Inner Planet.” HET617 Project, November 2005.
Alessandro. “Astrometric Methods and Instrumentations to Identify and
Characterize Extrasolar Planets: A Review.” PASP, 117:1021-1048. October, 2005.
Practical Amateur Spectroscopy. Springer. London, 2003.
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