Download The role of Jupiter in driving Earth`s orbital evolution: An update

The role of Jupiter in driving Earth’s orbital evolution: An
update
Jonathan Horner1,2, James B. Gilmore2, and Dave Waltham3
Computational Engineering and Science Research Centre, University of Southern
Queensland, West St, Toowoomba QLD 4350, Australia
2
Australian Centre for Astrobiology, UNSW Australia, Sydney, NSW 2052, Australia
3
Department of Earth Sciences, Royal Holloway, University of London
1
Published in the peer-reviewed proceedings of the 14th Australian Space Research
Conference, University of South Australia, Adelaide, 29th September – 1st October 2014.
Proceedings ISBN: 13: 978-0-9775740-8-7; Editors: Wayne Short & Iver Cairns.
Summary: In the coming decades, the discovery of the first truly Earth-like exoplanets is
anticipated. The characterisation of those planets will play a vital role in determining which
are chosen as targets for the search for life beyond the Solar system. One of the many
variables that will be considered in that characterisation and selection process is the nature of
the potential climatic variability of the exoEarths in question.
In our own Solar system, the Earth’s long-term climate is driven by several factors –
including the modifying influence of life on our atmosphere, and the temporal evolution of
Solar luminosity. The gravitational influence of the other planets in our Solar system add an
extra complication – driving the Milankovitch cycles that are thought to have caused the ongoing series of glacial and interglacial periods that have dominated Earth’s climate for the
past few million years.
Here, we present the results of a large suite of dynamical simulations that investigate the
influence of the giant planet Jupiter on the Earth’s Milankovitch cycles. If Jupiter was located
on a different orbit, we find that the long-term variability of Earth’s orbit would be
significantly different. Our results illustrate how small differences in the architecture of
planetary systems can result in marked changes in the potential habitability of the planets
therein, and are an important first step in developing a means to characterise the nature of
climate variability on planets beyond our Solar system.
Keywords: Astrobiology, Exoplanets, Exo-Earths, Habitability, Jupiter, Milankovitch cycles
Introduction
The question of whether we are alone in the universe is one that has long fascinated mankind.
In the past twenty years, we have made the first steps toward being able to answer that
question. In 1995, astronomers announced the discovery of 51 Pegasi b [1] – the first planet
found orbiting a sun-like star. In the first years after that discovery, news of new exoplanets
came infrequently, as planets very different to those in our own Solar system were discovered
(e.g. [2][3][4]). As time has passed, the techniques by which we detect exoplanets have been
refined (as detailed in [11]), and the temporal baseline over which observations have been
carried out has expanded. As a result, astronomers are now beginning to discover planetary
systems that more closely resemble our own – such as those hosting “Jupiter Analogues”,
giant planets moving on near-circular orbits that take of order a decade to complete (e.g.
[5][6][7]). At the same time, improvements in the our ability to monitor the minute variations
in a star’s brightness that reveal the transit of an unseen planet across its host star have
resulted in the detection of ever smaller planets. A thorough analysis of the data obtained by
the Kepler spacecraft ([8][9]) has already resulted in the discovery of just over 1,000 planets1,
including several that are significantly smaller than the Earth (e.g. [10]).
It is now increasingly apparent that small planets are far more common than larger ones. This
result is clearly seen in data taken by Kepler (e.g. [9][46][47]) and that obtained by radialvelocity search programs (e.g. [48][49]). Building on this work, a number of new exoplanet
search programs will soon begin that should further bolster the number of small exoplanets
known. These feature both ground-based programs (including dedicated facilities such as
MINERVA [50] and NRES [51]) and space-based surveys (the Kepler K2 mission [52], TESS
[53] and PLATO [54]).
With the rate at which new planets are being detected, and given the exciting new detection
programs due to begin in coming years, it is likely that the first truly Earth-like planets
(exoEarths) will soon be discovered. At that point, the search for life beyond the Solar system
will become a key focus of astronomical research. However, the observations needed to
characterise those planets, and search for any signs of life, will be incredibly challenging. The
recent detection of water vapour in the atmosphere of a Neptune-sized exoplanet, HAT-P-11b
[12] is a case in point. Despite the fact the planet is ~4 times the radius of Earth, and orbits its
host star at around 1/20th the Earth-Sun distance, the detection still required the combination
of 212 observations, totalling approximately 7 hours of integration time, using the Hubble
Space Telescope’s WFC3 G141 grism spectrometer. To gather spectroscopic evidence for life
in the atmosphere of an exoEarth will be a significantly greater challenge, and would require
more detailed and lengthy observations – making it a costly and time consuming process2. For
that reason, it is imperative that astronomers select the most promising targets for the search
for life before beginning their observations. But how will those targets be selected?
It is now thought that there are many factors that come together to render a given planet more
or less habitable (e.g. [14], and references therein). One of the key factors to be considered is
the stability of the climate of the planets in question. If all else were equal, it is reasonable to
assume that the planet with the most stable climate would be the most promising target to
search for life. It seems likely that otherwise ideal candidates could be rendered uninhabitable,
should their climates vary too dramatically or rapidly for life to adjust and survive.
In our Solar system, the Earth's orbit is perturbed by the gravitational interaction with the
other planets. This interaction results in Earth's eccentricity, inclination, and tilt varying over
time. These orbital changes cause the radiation received at Earth’s polar regions to vary over
astronomical timescales, with periods of ~20 kyr and ~100 kyr. These cycles are known as
Milankovitch cycles (e.g. [15][16][17]), and are thought to drive the glaciation/degalciation
cycles observed over the last few million years (e.g. [18][19]).
1
As of 18 Feb 2015, the number of confirmed planets discovered by the Kepler spacecraft
stands at 1013 (http://kepler.nasa.gov), with a further 4,175 candidates awaiting confirmation.
2
To illustrate the difficulty performing such observations, we note that recent simulations (as
2
To illustrate the difficulty performing such observations, we note that recent simulations (as
detailed in [13]), suggest that even the James Webb Space Telescope, due to be launched in
2018, will find it ‘nearly impossible to measure spectra of terrestrial analogs’ (section 2.1.3).
Despite the role played by the Milankovitch cycles in driving Earth’s climate and recent
glaciations, the scale of the variations in Earth’s orbital elements is actually relatively small.
The same is not true elsewhere in the Solar system, however. For example, Mercury exhibits
Milankovitch cycles with far greater amplitude than those of the Earth – with an orbital
eccentricity (currently ~0.21) that can reach values as high as 0.45 (e.g. [20][21]). Were the
Milankovitch cycles on the Earth equally extreme, it would sometimes move on an orbit that
brought it closer to the Sun than Venus, at perihelion, and take it out to almost the orbit of
Mars, at aphelion. The effects on Earth’s climate might prove to be catastrophic, and it seems
questionable whether life could survive, let alone thrive, on the surface of such a world.
In this paper, we present the preliminary results of a new study that aims to bring together nbody dynamical methods and climate modelling to assess the influence of planetary
architecture on the climate of Earth-like planets. Here, we study the influence of the orbit of
the planet Jupiter on the amplitude and frequency of Earth’s orbital oscillations. Our work
builds on that presented at the 13th Australian Space Science Conference [22] by using a
greatly expanded suite of dynamical integrations (both in terms of number and duration), and
using a corrected and improved methodology to perform the relativistic corrections required
to model the orbit of the planet Mercury.
In the next section, we detail our methods, before presenting our preliminary results, and then
conclude with a discussion of our plans for future work.
Method
In order to study how the architecture of the Solar system influences Earth’s orbital evolution,
we use a modified version of the Hybrid integrator within the n-body dynamics package
MERCURY ([23]). The standard version of the package models the dynamical interaction of
test particles (both massive and massless) in a purely Newtonian sense. In addition, the
modified version, developed for this work through the implementation of an additional userdefined force, takes account of the first-order post-Newtonian relativistic corrections [24].
This allows the code to accurately model the evolution of the orbit of the planet Mercury,
when using a solely Newtonian method would yield erroneous results (e.g. [25][26]).
Using our modified version of MERCURY, we performed 159,201 simulations following the
dynamical interaction of the eight planets in our Solar system for a period of 10 Myr. The
initial orbits of all planets, except Jupiter, were held fixed throughout the suite of simulations,
using the NASA DE431 [26] ephemeris to provide their current best-fit orbits. The simulation
start epoch was taken as JD2450985.5, which corresponds to 00:00 21st June 1998, UT.
In each of the simulations, we placed the giant planet Jupiter on a different orbit. The
inclination and rotation angles of Jupiter’s orbit were identical in all cases, taken from the
DE431 ephemeris. The semi-major axis and eccentricity of Jupiter’s orbit, however, were
varied from one run to the next. 399 unique values of semi-major axis were simulated, evenly
spread across a 4 au region, centred on Jupiter’s best-fit orbit (i.e. spanning the range
5.203102 ± 2.000000 au). At each of the semi-major axes tested, 399 discrete values of
initial orbital eccentricity were considered. These ranged from a circular orbit (i.e. e = 0.0) to
one with moderate eccentricity (e = 0.4), again in even steps. As such, the tested Jovian orbits
spanned a 399 x 399 grid in a-e space, giving us our 159,021 simulations.
To maximise the accuracy of the orbital solution, a time-step of 1 day is used in each
simulation. The orbital elements of each of the planets were output at 1,000-year intervals
throughout the integrations. As a result of the large range of orbital elements considered for
Jupiter, it was anticipated that at least some of the systems considered would prove
dynamically unfeasible (as has often been observed when examining the dynamics of recently
proposed exoplanetary systems – e.g. [27][28][29][30]). If any of the planets collided with
one another, or with the central body, the simulation was stopped, and the time at which the
collision occurred was recorded. Similarly, if any planet reached a barycentric distance of 40
au, that planet was considered ejected from the Solar system, and that integration was
stopped, with the time recorded3.
The results were used to create maps of the variability of the Earth’s orbital elements as a
function of Jupiter’s initial semi-major axis and eccentricity. These maps, which build on
earlier work studying the stability of proposed exoplanetary systems (e.g. [31][32]), give a
quick visual guide to the degree to which the Earth’s Milankovitch cycles are influenced by
small changes in the orbit of Jupiter, and we present a number of examples of such plots in the
next section. We are currently in the process of taking the numerical results of our simulations
(the orbital elements for the Earth across the various runs) and using them as input for simple
climate models (e.g. [33]), to examine how the observed variability in Earth’s orbit might
affect its climate. We anticipate that this analysis will be complete in the coming year.
Preliminary Results
Figure 1 shows the variation in the Earth’s orbital eccentricity (top panels, in red) and
inclination (lower panels, in blue) for two exemplar simulations. The only difference between
the two scenarios plotted was the initial semi-major axis chosen for Jupiter’s orbit. In the left
hand plots, Jupiter began the simulations at its true location in the Solar system, based on
NASA’s DE431 ephemeris (a = 5.203102 au). By contrast, the right hand plots show the
scenario where Jupiter began the simulations at a = 3.203102 au. All other initial conditions
were identical between these two simulations. It is immediately apparent that the amplitude of
both the eccentricity and inclination excursions experienced by the Earth are broadly similar
between the two runs. The maximum eccentricity in the scenario more closely resembling our
own Solar system (left) was slightly higher than when Jupiter was closer to the Sun, but
remained relatively small in both cases. However, the frequency of the cyclical behaviour in
both eccentricity and inclination was much greater when Jupiter was placed closer to the Sun
than when it began on its true orbit. Simply moving Jupiter inwards has had a significant
effect on the Milankovitch cycles experienced by the Earth in these runs.
3
A barycentric distance of 40 au was chosen for the ‘ejection’ distance as a reasonable
compromise that allowed us to determine when the Solar system had destabilised. For any of
the planets to reach 40 au would require a major re-arrangement of the system’s architecture.
0.06
0.06
0.04
0.04
0.02
0.02
0
0
0
0
Time (yr)
Time (yr)
5
5
4
4
3
3
2
2
1
1
0
0
0
0
Time (yr)
Time (yr)
Fig. 1: The variation in the Earth’s orbital eccentricity (top, red) and inclination (bottom,
blue), for two of the versions of our Solar system studied in this work. The left hand data is
from the system that most closely resembled our own, whilst the right is for the scenario
where Jupiter was shifted inwards by a distance of 2 au. All other initial conditions were
identical between the two runs. It is clear that, though the amplitude of the variations in
eccentricity and inclination were broadly the same between these two runs, the speed at which
the variations occurred was greater for the scenario where Jupiter was closer to the Sun.
The exemplar cases shown in Figure 1 clearly demonstrate how changing Jupiter’s orbit can
influence the Earth’s Milankovitch cycles. However, changes to Jupiter’s orbit can also have a
much more dramatic effect – they can cause the Solar system to become unstable on very
short timescales. As a result of the wide range of orbital architectures tested in this work, we
found that a significant fraction of the Solar systems we created proved to be dynamically
unstable, falling apart long before the end of our 10 Myr integrations. The stability of the
Solar system as a function of Jupiter’s initial semi-major axis and orbital eccentricity can be
seen in Figure 2. Of the 159,021 versions of our Solar system we tested, almost 74% (117,549
systems) proved dynamically unstable within the ten million years of our simulations. The
great majority of these featured Jupiters that were initially placed on orbits more eccentric
than that displayed by our own Jupiter. However, there were values of initial Jovian semimajor axis where the Solar system was rendered unstable even for circular initial Jupiter
orbits (such as those at around 4.25 and 4.95 au, where Jupiter and Saturn start in mutual 10:3
and 8:3 mean motion resonance, respectively). Similarly, there are two regions where the
Solar system would remain stable even for moderately eccentric Jupiters – around 4.6 and 6
au. Once again, these are locations where Jupiter and Saturn would move on mutually
resonant orbits – namely the 3:1 and 2:1 mean motion resonances, respectively.
Fig. 2: The stability of the Solar system as a function of the initial semi-major axis, a, and
eccentricity, e, of Jupiter’s orbit. In these integrations, the initial orbits of the other planets
were held at their DE431 ephemeris values, and their evolution was followed for 10 Myr
under the influence of their mutual gravitation. The left plot shows the lifetime of each system
on a linear scale, whilst the right shows the same information on a logarithmic scale. It is
clear that the majority of systems were unstable, even on the short timescales considered.
The resonant features described above are clearly seen in the left panels of Figure 3, which
shows the fraction of unstable simulations (top) and mean lifetime (bottom) of the Solar
system as a function of Jupiter’s initial semi-major axis and eccentricity. Both unstable and
stable resonant features can be seen as troughs and peaks overlaid on a gradual trend to lower
stability the closer Jupiter moves toward Saturn. The situation is more clear-cut when one
considers the influence of eccentricity on the system’s stability. Even scenarios featuring
Jupiter on an initially circular orbit can prove unstable – but away from the destabilising
influence of resonances (as seen in Fig. 2), the great majority of low-eccentricity solutions
prove stable on the timescales considered in this work. Aside from those resonant regions, it is
generally the case that scenarios where Jupiter has an initial orbital eccentricity less than
~0.125 prove dynamically stable – although this critical value is somewhat higher at low
semi-major axes, and lower at greater semi-major axes. This transition region is evidenced in
the right-hand panels of Figure 3 by the shoulder visible at e ~ 0.1, where the unstable fraction
begins to climb more rapidly, and the mean lifetime begins to fall off more steeply.
For those regions where the system survived for the full 10 Myr of integration time, we have
mapped the variability of the Earth’s orbital elements as a function of time. In Figure 4, we
show the variability of the Earth’s orbital eccentricity over the integration period. In the left
hand panel of that plot, we show the rms time variability of Earth’s eccentricity, plotted on a
logarithmic scale. In general, the closer to the Sun the initial orbit of Jupiter, the more rapidly
the Earth’s orbital eccentricity is driven to vary. As a second-order effect, the more eccentric
the initial orbit of Jupiter, the more rapid are Earth’s eccentricity excursions. This effect is
particularly apparent in the strips of stability located at location of the 2:1 and 3:1 meanmotion resonances between Jupiter and Saturn.
Fig. 3: The fraction of our simulations that proved dynamically unstable (top) and the mean
lifetime of those integrations (bottom), as a function of the initial semi-major axis (left) and
orbital eccentricity (right) of Jupiter. The increasing instability of the systems tested as a
function of orbital eccentricity can be clearly seen in the right hand panels, whilst the
influence of mean-motion resonances (such as the 3:1 and 2:1 MMRs between Jupiter and
Saturn, at ~4.6 and 6.0 au respectively) can be clearly seen in the left hand panels.
The right-hand panel of Figure 4 shows the maximum eccentricity obtained by the Earth over
the course of our integrations, again for those simulations where the Solar system survived
intact for the full simulation time. In contrast to the rate at which Earth’s eccentricity is driven
to change, the scale of its maximum excursions seems unrelated to the initial orbital semimajor axis of Jupiter. Instead, it seems to be a function of the degree of stability of that
planet’s orbit. In general, towards the centre of the broad regions of stability, the maximum
eccentricity obtained by the Earth’s orbit is low, with it rising towards the edges of the stable
regions – an indication that the Solar system is in the process of transitioning between a more
stable and a less stable regime in those areas.
Figure 5 shows the variation of the Earth’s orbital inclination over the course of our 10 Myr
simulations. As with Figure 4, the left-hand panel shows the rms rate of change of Earth’s
orbital inclination, plotted on a logarithmic scale, whilst the right hand plot shows instead the
maximum excursions seen in orbital inclination. As was the case with the rate at which
Earth’s orbital eccentricity was driven, it is clear from the left-hand panel of Figure 5 that the
rate of inclination change is a strong function of Jupiter’s initial semi-major axis. The closer
that Jupiter orbits, the more rapidly the Earth’s orbital inclination is driven. When taken in
concert with the results shown in the left-hand panel of Figure 4, this is an indication that the
frequency of the Milankovitch cycles might be a strong function of Jupiter’s initial orbital
location – the greater the Earth-Jupiter separation, the more slowly the cycles progress. Future
work is necessary, however, before this conclusion can be confirmed.
Fig. 4: The variation of the Earth’s orbital eccentricity, as a function of Jupiter’s initial
orbital semi-major axis and eccentricity. The left hand panel shows the variation in the rootmean-squared value of the rate of change of Earth’s orbital eccentricity with time, whilst the
right shows the maximum value that eccentricity obtained over the 10 Myr of our integrations.
The red square in the plots shows the location of Jupiter in our own Solar system.
The right hand panel of Figure 5 shows the maximum inclinations obtained by the Earth
across the stable 10 Myr integrations we performed. The great majority of stable solutions
show only very small excursions in inclination. There are, however, three bands (located at
~4.1, 4.7 and 6.3 au) where Earth’s orbital inclination varies over a larger range. The band of
values around ~15 degrees, at ~4.1, may well be the result of the 7:2 mean-motion resonance
between Jupiter and Saturn, which would occur at ~4.14 AU. That narrow band at around 6.3
au is somewhat more mysterious, but given the apparent curved nature of the band (with an
extension potentially visible at a ~6 au, e ~0.2) suggests that it may be the result of a secular
resonance between the three planets in question (Jupiter, Saturn, and the Earth). Again, further
work is needed to confirm or deny our suspicions in this case.
Fig. 5: The variation of the Earth’s orbital inclination, as a function of Jupiter’s initial semimajor axis and eccentricity. Left: The RMS value of the rate of change of the Earth’s orbital
inclination with time. Right: The maximum inclination attained by the orbit of the Earth’s
over the 10 Myr of our integrations. The red square in the left-hand plot shows the location of
Jupiter’s orbit within our own Solar system.
Future Work
We are currently in the process of taking the orbital elements output for the many Earths in
our integrations and using them as the input for detailed climate modelling, to determine how
the changes in Earth’s orbital variability (as illustrated in Fig. 2 and Fig. 4) would influence
the climate of our planet. It is not necessarily the case that large excursions in orbital
eccentricity and inclination would render the climate less clement for the development of life
– clearly the rate at which variations occur will play an important role in determining the
climatic response to the Milankovitch cycles themselves (e.g. [34]).
Once we have a firm handle on the interaction between the Solar system’s architecture and the
Earth’s climate variability, we will look to extend our modelling to consider planets in the
habitable zone of known exoplanetary systems. Our long term goal is to construct a
systematic approach by which the potential habitability of such planets can be quickly
assessed, so that the best possible candidates can be selected for the search for life elsewhere.
Such studies will form a critical component of the search for life beyond the Solar system, and
will complement studies of the other factors that can influence planetary habitability – ranging
from stellar activity (e.g. [35][36][37]) to the impact regimes (e.g. [38][39][40][41]) and
delivery of volatiles (e.g. [42][43]) that might be experienced by potential targets, and even
the presence (or lack) of giant satellites (e.g. [44][45]).
Taken in concert, these studies will eventually provide a vital resource that will help observers
to target those exoplanets that offer the greatest likelihood of hosting life like that seen on the
Earth (e.g. [14]). Since studying the Milankovitch cycles will provide important information
about potential exoEarth climate variability, we anticipate that astronomers will want to
obtain as much information as possible prior to committing the extremely complicated
observations that will be necessary to look for biomarkers on newly discovered planets.
Acknowledgements
The work was supported by iVEC through the use of advanced computing resources located
at the Murdoch University, in Western Australia.
References
1. Mayor, M. and Queloz, D., “A Jupiter-mass companion to a solar-type star”, Nature, Vol.
378, 1995, pp. 355 - 359
2. Mary, G. W. and Butler, R. P., “A Planetary Companion to 70 Virginis”, Astrophysical
Journal Letters, Vol. 464, 1996, L147
3. Butler, R. P., Marcy, G. W., Williams, E., Hauser, H. and Shirts, P., “Three New ’51
Pegasi-Type’ Planets”, The Astrophysical Journal, Vol. 474, 1997, L115 – L118
4. Cochran, W. D., Hatzes, A. P., Butler, R. P. and Marcy, G. W., “The Discovery of a
Planetary Companion to 16 Cygni B”, The Astrophysical Journal, Vol. 483, 1997, pp.
457-364
5. Howard, A. W., Johnson, J. A., Marcy, G. W., Fischer, D. A., Wright, J. T., Bernat, D.,
Henry, G. W., Peck, K. M. G., Isaacson, H., Apps, K., Endl, M., Cochran, W. D., Valenti,
J. A., Anderson, J. and Piskunov, N. E., “The California Planet Survey. I. Four New Giant
Exoplanets”, The Astrophysical Journal, Vol. 731, 2010, pp. 1467 - 1481
6. Wittenmyer, R. A., Horner, J., Tuomi, M., Salter, G. S., Tinney, C. G., Butler, R. P.,
Jones, H. R. A., O’Toole, S. J., Bailey, J., Carter, B. D., Jenkins, J. S., Zhang, Z., Vogt, S.
S. and Rivera, E. J., “The Anglo-Australian Planet Search. XXII. Two New Multi-planet
Systems”, The Astrophysical Journal, Vol. 453, 2012, id. 169
7. Robertson, P., Horner, J., Wittenmyer, R. A., Endl, M., Cochran, W. D., MacQueen, P. J.,
Brugamyer, E. J., Simon, A. E., Barnes, S. I. and Caldwell, C., “A Second Giant Planet in
3:2 Mean-motion Resonance in the HD 204313 System”, The Astrophysical Journal, Vol.
754, 2012, id. 50
8. Borucki, W. J., Koch, D., Basri, G. et al., “Kepler Planet-Detection Mission: Introduction
and First Results”, Science, Vol. 327, 2010, pp. 977 - 980
9. Borucki, W. J., Koch, D., Basri, G. et al., “Characteristics of Planetary Candidates
Observed by Kepler. II. Analysis of the First Four Months of Data”, The Astrophysical
Journal, Vol. 736, 2011, id. 19
10. Barclay, T., Rowe, J. F., Lissauer, J. J. et al., “A sub-Mercury-sized exoplanets”, Nature,
Vol. 494, 2013, pp. 452-454
11. Perryman, M., “The Exoplanet Handbook”, by Michael Perryman, Cambridge, UK:
Cambridge University Press, 2014
12. Fraine, J., Deming, D., Benneke, B., Knutson, H., Jordán, A., Espinoza, N.,
Madhusudhan, N., Wilkins, A. and Todorov, K., “Water Vapor in the Clear Atompshere
of an exo-Neptune”, Nature, Vol. 513, 2014, pp. 526 – 529
13. Beichman, C., Benneke, B., Knutson, H. et al., “Observations of Transiting Exoplanets
with the James Webb Space Telescope (JWST)”, Publications of the Astronomical Society
of the Pacific, Vol. 126, 2014, pp. 1134 - 1173
14. Horner, J. and Jones, B. W., “Determining habitability: which exoEarths should we search
for life?”, International Journal of Astrobiology, 9, 2010, pp. 273-291
15. Croll, J., 1875, “Climate and time in their geological relations, a theory of secular changes
of the earth’s climate”, Published by Daldy, Tsbister & co., London
16. Köppen, W., Wegener, A., 1924, “Die Klimate der Geologischen Vorzeit”, Gebrüder
Borntraeger, Berlin.
17. Milankovitch, M., 1941, “Kanon der Erdbestrahlung und seine Andwendung auf das
Eiszeiten-problem”, R. Serbian Acad., Belgrade
18. Roe, G., 2006, “In defense of Milankovitch”, Geophysical Review Letters, 33, L24703
19. Hays, J. D., Imbrie, J. and Shackleton, N. J., 1976, “Variations in the Earth’s Orbit:
Pacemaker of the Ice Ages”, Science, 194, 1121-1132
20. Strom, R. G., Sprague, A. L., “Exploring Mercury: the iron planet”, eds. Strom, R. G.,
Sprague, A. L., Springer-Praxis Books in Astronomy and Space Sciences, London (UK):
Springer, Chichester (UK): Praxis Publishing. ISBN 1-85233-731-1, 2003
21. Correia, A. C. M., Laskar, J., , “Mercury's capture into the 3/2 spin–orbit resonance
including the effect of core–mantle friction”, Icarus, Vol. 201, 2009, 1-11
22. Horner, J., Waltham, D. and Koch, F. E., “The role of Jupiter in driving Earth’s orbital
evolution”, Proceedings of the 13th annual Australian Space Science Conference, ISBN
13: 978-0-9775740-7-0, eds. Wayne Short and Iver Cairns, 2014, pp. 117 - 128
23. Chambers, J. E., “A hybrid symplectic integrator that permits close encounters between
massive bodies”, Monthly Notices of the Royal Astronomical Society, Volume 304, 1999,
pp. 793 – 799
24. Gilmore, J. B. and Ross, A., “Effective field theory calculation of second post-Newtonian
binary dynamics”, Physical Review D, Vol. 78, 2008, 124021
25. Clemence, G. M., “The Relativity Effect in Planetary Motions”, Reviews of Modern
Physics, Vol. 19, 1947, pp. 361-364
26. Nobili, A. M., Will, C. M., “The real value of Mercury’s perihelion advance”, Nature,
Vol. 320, 1986, pp. 39 - 41
26. Folker, W. M., Williams, J. G., Boggs, D. H., Park, R. S. and Kuchynka, P., “The
Planetary and Lunar Ephemerides DE430 and DE431”, The Interplanetary Network
Progress Report, Volume 42, pp. 1-81
27. Horner, J., Marshall, J. P., Wittenmyer, R. A. and Tinney, C. G., “A dynamical analysis of
the proposed HU Aquarii planetary system”, Monthly Notices of the Royal Astronomical
Society, Volume 416, 2011, pp. 11 - 15
28. Horner, J., Hinse, T. C., Wittenmyer, R. A., Marshall, J. P. and Tinney, C. G., “A
dynamical analysis of the proposed circumbinary HW Virginis planetary system”,
Monthly Notices of the Royal Astronomical Society, Volume 427, 2012, pp. 2812 - 2823
29. Wittenmyer, R. A., Horner, J. and Marshall, J. P., “On the dynamical stability of the
proposed planetary system orbiting NSVS 14256825”, Monthly Notices of the Royal
Astronomical Society, Volume 431, 2013, pp. 2150 - 2154
30. Horner, J., Wittenmyer, R. A., Hinse, T. C., Marshall, J. P., Mustill, A. J. and Tinney, C.
G., “A detailed dynamical investigation of the proposed QS Virginis planetary system”,
Monthly Notices of the Royal Astronomical Society, 435, 2013, pp. 2033 - 2039
31. Horner, J., Lykawka, P. S., 2010, “2001 QR322: a dynamically unstable Neptune
Trojan?”, Monthly Notices of the Royal Astronomical Society, 405, 49-56
32. Horner, J., Wittenmyer, R. A., Hinse, T. C., Tinney, C. G., “A detailed investigation of the
proposed NN Serpentis planetary system”, Monthly Notices of the Royal Astronomical
Society, 425, 2012, 749-756
33. Gilmore, J. B., “How reliable are latitudinal energy balance models for habitability
calculations when using Earth’s radiative properties?”, Monthly Notices of the Royal
Astronomical Society, Vol. 440, 2014, pp. 1435 – 1445
34. Waltham, D., “Testing Anthropic Selection: A Climate Change Example”, Astrobiology,
Vol. 11, 2011, pp. 105-114
35. Dehant, V., Lammer, H., Kulikov, Y. N., Grießmeier, J.-M., Breuer, D., Verhoeven, O.,
Karatekin, Ó., vanHoolst, T., Korablev, O. and Lognonné , P., “Planetary Magnetic
Dynamo Effect on Atmospheric Protection of Early Earth and Mars”, Space Science
Reviews, vol. 129, 2007, pp. 279–300
36. Lundin, R., Lammer, H. and Ribas, I., “Planetary Magnetic Fields and Solar Forcing:
Implications for Atmospheric Evolution”, Space Science Reviews, Vol. 129, 2007, pp.
245-278
37. Nicholson, B., Mengel, M., Brookshaw, L., Vidotto, A. A., Carter, B., Marsden, S.,
Soutter, J., Waite, I. and Horner, J., “Winds Of Planet Hosting Stars”, Proceedings of the
14th Australian Space Research Conference, 2015, ISBN: 13: 978-0-9775740-8-7;
Editors: Wayne Short & Iver Cairns; arXiv:1503.05624
38. Horner, J. and Jones, B. W., “Jupiter friend or foe? I: The asteroids”, International
Journal of Astrobiology, 7, 2009, pp. 251-261
39. Horner, J. and Jones, B. W., “Jupiter - friend or foe? II: the Centaurs”, International
Journal of Astrobiology, 8, 2009, pp. 75-80
40. Horner, J., Jones, B. W. and Chambers, J., “Jupiter - friend or foe? III: the Oort cloud
comets”, International Journal of Astrobiology, 9, 2010, pp. 1-10
41. Horner, J. and Jones, B. W., “Jupiter - friend or foe? IV: the influence of orbital
eccentricity and inclination”, International Journal of Astrobiology, 11, 2012, pp.147-156
42. Horner, J., Mousis, O., Petit, J.-M. and Jones, B. W., “Differences between the impact
regimes of the terrestrial planets: Implications for primordial D:H ratios”, Planetary and
Space Science, 57, 2009, pp. 1338-1345
43. Contro, B., Wittenmyer, R. A., Horner, J. and Marshall, J. P., “Towards a dynamics-based
estimate of the extent of HR 8799’s unresolved warm debris belt”, Proceedings of the 14th
Australian Space Research Conference, 2015, ISBN: 13: 978-0-9775740-8-7; Editors:
Wayne Short & Iver Cairns; arXiv:1505.03198
44. Waltham, D., “Anthropic Selection for the Moon’s Mass”, Astrobiology, Vol. 4, 2004, pp.
460-468
45. Waltham, D., “The large-moon hypothesis: can it be tested?”, International Journal of
Astrobiology, Vol. 5, 2006, pp. 327-331
46. Fressin, F., Torres, G., Charbonneau, D., Bryson, S. T., Christiansen, J., Dressing, C. D.,
Jenkins, J. M., Walkowicz, L. M. and Batalha, N. M., “The False Positive Rate of Kepler
and the Occurrence of Planets”, The Astrophysical Journal, Volume 766, 2013, article id.
81
47. Howard, A. W., Marcy, G. W., Bryson, S. T., Jenkins, J. M., Rowe, J. F., Batalha, N. M.,
Borucki, W. J., Koch, D. G., Dunham, E. W., Gautier, T. N., III, Van Cleve, J., Cochran,
W. D., Latham, D. W., Lissauer, J. J., Torres, G., Brown, T. M., Gilliland, R. L.,
Buchhave, L. A., Caldwell, D. A., Christensen-Dalsgaard, J., Ciardi, D., Fressin, F., Haas,
M. R., Howell, S. B., Kjeldsen, H., Seager, S., Rogers, L., Sasselov, D. D., Steffen, J. H.,
Basri, G. S., Charbonneau, D., Christiansen, J., Clarke, B., Dupree, A., Fabrycky, D. C.,
Fischer, D. A., Ford, E. B., Fortney, J. J., Tarter, J., Girouard, F. R., Holman, M. J.,
Johnson, J. A., Klaus, T. C., Machalek, P., Moorhead, A. V., Morehead, R. C., Ragozzine,
D., Tenenbaum, P., Twicken, J. D., Quinn, S. N., Isaacson, H., Shporer, A., Lucas, P. W.,
Walkowicz, L. M., Welsh, W. F., Boss, A., Devore, E., Gould, A., Smith, J. C., Morris, R.
L., Prsa, A., Morton, T. D., Still, M., Thompson, S. E., Mullally, F., Endl, M., and
MacQueen, P. J., “Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler”,
The Astrophysical Journal Supplement, Volume 201, 2012, article id. 15
48. Howard A. W., Marcy, G. W., Johnson, J. A., Fischer, D. A., Wright, J. T., Isaacson, H.,
Valenti, J. A., Anderson, J., Lin, D. N. C. and Ida, S., “The Occurrence and Mass
Distribution of Close-in Super-Earths, Neptunes, and Jupiters”, Science, Volume 330,
2010, pp. 653
49. Wittenmyer, R. A., Tinney, C. G., Butler, R. P., O’Toole, S. J., Jones, H. R. A., Carter, B.
D., Bailey, J. and Horner, J., “The Frequency of Low-mass Exoplanets. III. Toward η⊕ at
Short Periods”, The Astrophysical Journal, Volume 738, 2011, article id. 81
50. Swift, J. J., Bottom, M., Johnson, J. A., Wright, J. T., McCrady, N., Wittenmyer, R. A.,
Plavchan, P., Riddle, R., Muirhead, P. S., Herzig, E., Myles, J., Blake, C. H., Eastman, J.,
Beatty, T. G., Lin, B., Zhao, M., Gardner, P., Falco, E., Criswell, S., Nava, C., Robinson,
C., Sliski, D. H., Hedrick, R., Ivarsen, K., Hjelstrom, A., de Vera, J. and Szentgyorgyi, A.,
“Miniature Exoplanet Radial Velocity Array (MINERVA) I. Design, Commissioning, and
First Science Results”, SPIE, Astronomical Telescopes + Instrumentation, in press, 2015,
arXiv:1411.3724
51. Eastman, J. D., Brown, T. M., Hygelund, J., van Eyken, J., Tufts, J. R. and Barnes, S.,
“NRES: the network of robotic Echelle spectrographs”, Proceedings of the SPIE, Volume
9147, 2014, id. 914716 pp. 15
52. Howell, S. B., Sobeck, C., Haas, M., Still, M., Barclay, T., Mullully, F., Troeltzsch, J.,
Aigrain, S., Bryson, S. T., Caldwell, D., Chaplin, W. J., Cochran, W. D., Huber, D.,
Marcy, G. W., Miglio, A., Najita, J. R., Smith, M., Twicken, J. D. and Fortney, J. J., “The
K2 Mission: Characterization and Early Results”, Publications of the Astronomical
Society of the Pacific, Volume 126, Issue 938, 2014, pp. 398-408
53. Ricker, G. R., Winn, J. N., Vanderspek, R., Latham, D. W., Bakos, G. Á., Bean, J. L.,
Berta-Thompson, Z. K., Brown, T. M., Buchhave, L., Butler, N. R., Butler, R. P., Chaplin,
W. J., Charbonneau, D., Christensen-Dalsgaard, J., Clampin, M., Deming, D., Doty, J., De
Lee, N., Dressing, C., Dunham, E. W., Endl, M., Fressin, F., Ge, J., Henning, T., Holman,
M. J., Howard, A. W., Ida, S., Jenkins, J., Jernigan, G., Johnson, J. A., Kaltenegger, L.,
Kawai, N., Kjeldsen, H., Laughlin, G., Levine, A. M., Lin, D., Lissauer, J. J., MacQueen,
P., Marcy, G., McCullough, P. R., Morton, T. D., Narita, N., Paegert, M., Palle, E., Pepe,
F., Pepper, J., Quirrenbach, A., Rinehart, S. A., Sasselov, D., Sato, B., Seager, S.,
Sozzetti, A., Stassun, K. G., Sullivan, P., Szentgyorgyi, A., Torres, G., Udry, S. and
Villasenor, J., “Transiting Exoplanet Survey Satellite (TESS)”, Proceedings of the SPIE,
Volume 9143, 2014, id. 914320
54. Rauer, H., Catala, C., Aerts, C., Appourchaux, T., Benz, W., Brandeker, A., ChristensenDalsgaard, J., Deleuil, M., Gizon, L., Goupil, M.-J., Güdel, M., Janot-Pacheco, E., MasHesse, M., Pagano, I., Piotto, G., Pollacco, D., Santos, Ċ., Smith, A., Suárez, J.-C., Szabó,
R., Udry, S., Adibekyan, V., Alibert, Y., Almenara, J.-M., Amaro-Seoane, P., Eiff, M.
Ammler-von, Asplund, M., Antonello, E., Barnes, S., Baudin, F., Belkacem, K.,
Bergemann, M., Bihain, G., Birch, A. C., Bonfils, X., Boisse, I., Bonomo, A. S., Borsa, F.,
Brandão, I. M., Brocato, E., Brun, S., Burleigh, M., Burston, R., Cabrera, J., Cassisi, S.,
Chaplin, W., Charpinet, S., Chiappini, C., Church, R. P., Csizmadia, Sz., Cunha, M.,
Damasso, M., Davies, M. B., Deeg, H. J., Díaz, R. F., Dreizler, S., Dreyer, C.,
Eggenberger, P., Ehrenreich, D., Eigmüller, P., Erikson, A., Farmer, R., Feltzing, S., de
Oliveira Fialho, F., Figueira, P., Forveille, T., Fridlund, M., García, R. A., Giommi, P.,
Giuffrida, G., Godolt, M., Gomes da Silva, J., Granzer, T., Grenfell, J. L., Grotsch-Noels,
A., Günther, E., Haswell, C. A., Hatzes, A. P., Hébrard, G., Hekker, S., Helled, R., Heng,
K., Jenkins, J. M., Johansen, A., Khodachenko, M. L., Kislyakova, K. G., Kley, W., Kolb,
U., Krivova, N., Kupka, F., Lammer, H., Lanza, A. F., Lebreton, Y., Magrin, D., MarcosArenal, P., Marrese, P. M., Marques, J. P., Martins, J., Mathis, S., Mathur, S., Messina, S.,
Miglio, A., Montalban, J., Montalto, M., Monteiro, M. J. P. F. G., Moradi, H., Moravveji,
E., Mordasini, C., Morel, T., Mortier, A., Nascimbeni, V., Nelson, R. P., Nielsen, M. B.,
Noack, L., Norton, A. J., Ofir, A., Oshagh, M., Ouazzani, R.-M., Pápics, P., Parro, V. C.,
Petit, P., Plez, B., Poretti, E., Quirrenbach, A., Ragazzoni, R., Raimondo, G., Rainer, M.,
Reese, D. R., Redmer, R., Reffert, S., Rojas-Ayala, B., Roxburgh, I. W., Salmon, S.,
Santerne, A., Schneider, J., Schou, J., Schuh, S., Schunker, H., Silva-Valio, A., Silvotti,
R., Skillen, I., Snellen, I., Sohl, F., Sousa, S. G., Sozzetti, A., Stello, D., Strassmeier, K.
G., Švanda, M., Szabó, Gy. M., Tkachenko, A., Valencia, D., Van Grootel, V., Vauclair,
S. D., Ventura, P., Wagner, F. W., Walton, N. A., Weingrill, J., Werner, S. C., Wheatley,
P. J. and Zwintz, K., “The PLATO 2.0 mission”, Experimental Astronomy, Volume 38,
Issue 1-2, 2014, pp. 249-330