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NASA NTRS1977

On the early scattering processes of the outer planets

The gradual scattering of small bodies by the Jovian planets in the late stage of their accretion is simulated by Monte Carlo calculation. The effects of collisional interaction of the scattered planetesimals with the inner planets and asteroidal belt are estimated. The total mass influx injected into the terrestrial zones from the outer planetary zone could be appreciable; however, if the damping effects due to the mutual inelastic or catastrophic collisions among the small bodies were significant, the total mass influx would be greatly reduced. The origin of the cometary Oort cloud in relation to these scattering processes is also discussed. The calculation indicates that, in addition to Jupiter, Uranus and Neptune were likely to be the major contributors to the population of long-period comets if they originated from such scattering processes.

Ip, W. H.↗

NASA NTRS1995

Properties of ultra low frequency upstream waves at Venus and Saturn: A comparison

The upstream regions of all planets, except Pluto, have been investigated, using in situ spacecraft measurements and a variety of analysis techniques. The detailed studies at Earth indicate that these waves are generated locally in the magnetically connected solar wind by the interaction with ions backstreaming from the shock. However, since the properties of the solar wind vary with heliocentric distance and since properties of planetary shocks depend on plasma beta, interplanetary magnetic field (IMF) spiral angle and Mach number, the amount of heating, acceleration efficiencies, etc. significantly change with heliocentric distance. In turn the waves seen at each planet propagate not in the same but different (physical) propagation modes. In this paper we compare the ULF wave observations at an outer and an inner planet. We use the results of the ratio, quantites easily derivable with sufficient accuracy at each planet. We use the full electromagnetic dispersion relation for comparison with theoretical predictions.

Orlowski, D. S.↗

DOE OSTI2020

EXPRES. I. HD 3651 as an Ideal RV Benchmark

The next generation of exoplanet-hunting spectrographs should deliver up to an order of magnitude improvement in radial velocity (RV) precision over the standard 1 m s{sup −1} state-of-the-art spectrographs. This advance is critical for enabling the detection of Earth-mass planets around Sun-like stars. New calibration techniques such as laser frequency combs and stabilized etalons ensure that the instrumental stability is well characterized. However, additional sources of error include stellar noise, undetected short-period planets, and telluric contamination. To understand and ultimately mitigate error sources, the contributing terms in the error budget must be isolated to the greatest extent possible. Here, we introduce a new high-cadence RV program, the Extreme Precision Spectrograph (EXPRES) 100 Earths Survey, which aims to identify rocky planets around bright, nearby G and K dwarfs. We also present a benchmark case: the 62 day orbit of a Saturn-mass planet orbiting the chromospherically quiet star, HD 3651. The combination of high eccentricity (0.6) and a moderately long orbital period ensures significant dynamical clearing of any inner planets. Our Keplerian model for this planetary orbit has a residual rms of 58 cm s{sup −1} over a ∼6 month time baseline. By eliminating significant contributors to the RV error budget, HD 3651 serves as a standard for evaluating the long-term precision of extreme precision RV programs.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Imaging Asteroid 4 Vesta Using the Framing Camera

The Framing Camera (FC) onboard the Dawn spacecraft serves a dual purpose. Next to its central role as a prime science instrument it is also used for the complex navigation of the ion drive spacecraft. The CCD detector with 1024 by 1024 pixels provides the stability for a multiyear mission and its high requirements of photometric accuracy over the wavelength band from 400 to 1000 nm covered by 7 band-pass filters. Vesta will be observed from 3 orbit stages with image scales of 227, 63, and 17 m/px, respectively. The mapping of Vesta s surface with medium resolution will be only completed during the exit phase when the north pole will be illuminated. A detailed pointing strategy will cover the surface at least twice at similar phase angles to provide stereo views for reconstruction of the topography. During approach the phase function of Vesta was determined over a range of angles not accessible from earth. This is the first step in deriving the photometric function of the surface. Combining the topography based on stereo tie points with the photometry in an iterative procedure will disclose details of the surface morphology at considerably smaller scales than the pixel scale. The 7 color filters are well positioned to provide information on the spectral slope in the visible, the depth of the strong pyroxene absorption band, and their variability over the surface. Cross calibration with the VIR spectrometer that extends into the near IR will provide detailed maps of Vesta s surface mineralogy and physical properties. Georeferencing all these observation will result in a coherent and unique data set. During Dawn s approach and capture FC has already demonstrated its performance. The strong variation observed by the Hubble Space Telescope can now be correlated with surface units and features. We will report on results obtained from images taken during survey mode covering the whole illuminated surface. Vesta is a planet-like differentiated body, but its surface gravity and escape velocity are comparable to those of other asteroids and hence much smaller than those of the inner planets or

Keller, H. Uwe↗

NASA NTRS2000

Delivery of Volatiles to Habitable Planets in Extrasolar Planetary Systems

The Earth can support life because: (1) its orbit lies in the Sun's habitable zone', and (2) it contains enough volatile material (e.g. water and organics) for life to flourish. However, it seems likely that the Earth was drier when it formed because it accreted in a part of the Sun's protoplanetary nebula that was too hot for volatiles to condense. If this is correct, water and organics must have been delivered to the habitable zone, after dissipation of the solar nebula, from a 'wet zone' in the asteroid belt or the outer solar system, where the nebula was cool enough for volatiles to condense. Material from the wet zone would have been delivered to the Earth by Jupiter and Saturn. Gravitational perturbations from these giant planets made much of the wet zone unstable, scattering volatile-rich planetesimals and protoplanets across the Solar System. Some of these objects ultimately collided with the inner Planets which themselves lie in a stable part of the Solar System. Giant planets are now being discovered orbiting other sunlike stars. To date, these planets have orbits and masses very different from Jupiter and Saturn, such that few if any of these systems is likely to have terrestrial planets in the star's habitable zone. However, new discoveries are anticipated due to improved detector sensitivity and the increase in the timespan of observations. Here we present numerical experiments examining the range of giant-planet characteristics that: (1) allow stable terrestrial Planets to exist in a star's habitable zone, and (2) make a large part of the star's wet zone weakly unstable, thus delivering volatiles to the terrestrial planets over an extended period of time after the dissipation of the solar nebula.

Chambers, John E.↗

NASA NTRS1972

Planetary resonances, bi-stable oscillation modes, and solar activity cycles

The natural resonance structure of the planets in the solar system yields resonance periods of 11.08 and 180 years. The 11.08 year period is due to resonance of the sidereal periods of the three inner planets. The 180-year period is due to synodic resonances of the four major planets. These periods are also observed in the sunspot time series. The 11-year sunspot cycles from 1 to 19 are separated into categories of positive and negative cycles, Mode 1 and Mode 2 cycles, and typical and anomalous cycles. Each category has a characteristic shape, magnitude, or duration, so that statistical prediction techniques are improved when a cycle can be classified in a given category. These categories provide evidence for bistable modes of solar oscillation. The next minimum is expected in 1977 and the next maximum in 1981 or later. These epoch values are 2.5 years later than those based on typical cycle characteristics.

Sleeper, H. P., Jr.↗

NASA NTRS1976

Solar electric propulsion combined with earth gravity assist - A new potential for planetary exploration

The need to shorten mission time (travel time to target planet) in missions to the outer planets prompts a search for alternatives to one-way minimum-energy transfers while continuing to minimize on-power thrusts. Gravity assists via swing-bys of inner planets are examined, with emphasis on a projected Venus-earth gravity assist (VEGA) and a combined solar electric propulsion and earth gravity assist (SEEGA). Gravity assists are also examined as essential for missions with sample returns back to earth. Possible use of such techniques in the Shuttle Interim Upper Stage (IUS) program is considered. Various SEEGA and VEGA trajectories are discussed and charted, and time lost in the launch orbit to earth re-encounter time is weighed against time gained by faster speed toward the mission destination.

Atkins, K. L.↗

NASA NTRS1975

Surface history of Mercury - Implications for terrestrial planets

A plausible surface history of Mercury is presented which is suggested by Mariner 10 television pictures. Five periods are postulated which are delineated by successive variations in the modification of the surface by external and internal processes: accretion and differentiation, terminal heavy bombardment, formation of the Caloris basin, flooding of that basin and other areas, and light cratering accumulated on the smooth plains. Each period is described in detail; the overall history is compared with the surface histories of Venus, Mars, and the moon; and the implications of this history for earth are discussed. It is tentatively concluded that: Mercury is a differentiated planet most likely composed of a large iron core enclosed by a relatively thin silicate layer; heavy surface bombardment occurred about four billion years ago, which probably affected all the inner planets, and was followed by a period of volcanic activity; no surface modifications caused by tectonic, volcanic, or atmospheric processes took place after the volcanic period.

Murray, B. C.↗

NASA NTRS2010

Generating an Atmosphere

The presence of water ice on most of the large satellites of the outer planets was established many years ago through near-infrared observations with ground-based telescopes. Frozen carbon dioxide, sulfur dioxide, methane, nitrogen, and other molecular ices are also found in various combinations on inner planets such as Mars to bodies far beyond Pluto. Recent discoveries of ice varieties on some asteroids and sequestered in protected regions on Mercury and the Moon point to the near-universal distribution of frozen volatiles throughout the solar system.

Cruikshank, Dale P.↗

NASA NTRS1995

Contributions of Planetary Science to Studies of Early Biosphere Evolution

The history of impact cratering on the Moon, and extrapolations of crater chronologies to the inner planets, suggests that the late accretionary history of the Earth overlapped with other crucial events in the its history, including the origin of terrestrial life. This evidence, acquired from studies of other planetary bodies in the inner solar system, has profoundly affected how we view the early history of the Earth and evolution of the biosphere. Pre-biotic chemical evolution and the origin of life would have been delayed by the probable existence of a global magma ocean until -4.2 Ga. The early crust was largely destroyed by recycling, thus accounting for the sparse Archean record on Earth. Once life had developed, large impacts may have extinguished it several times before it finally gained a foothold. Potentially sterilizing impacts could have occurred as late as 3.7 Ga. At the very least, large impacts would have forced the biosphere through major environmental "bottlenecks" thereby canalizing its subsequent evolution. One legacy of these early events may be the structure of the present RNA-tree which indicates that extreme thermophiles are primitive within the Archaea, and may be the last common ancestors of life. By 3.5 Ga, marine sedimentary sequences contain unequivocal microbial fossils that attest to the presence of a terrestrial biosphere. The diversity of microbial forms present in these earliest fossil assemblages implies a preceding interval of evolution during which major evolutionary advances (e.g. photosynthesis) could have taken place. Evidence cited above places the origin of life within the interval 3.5 and 4.2 Ga, a period of 700 Ma. Thus, it appears that terrestrial life not only evolved rapidly, but perhaps more than once. This expands the possibilities that life may have also developed elsewhere. Of the other planets in our solar system, Mars holds the greatest chance of having developed life. But, the present surface of Mars is hostile to life. Liquid water, regarded as essential for living systems, is unstable on the surface of Mars due to the low atmospheric pressure. The results of the Viking Lander biology experiments established that organic molecules are not present in the regolith of Mars, forcing the exobiological community to consider new ways of exploring for Martian life. Older, heavily cratered terranes on Mars show geomorphic evidence for abundant water between 3.0- 4.0 Ga. It is quite possible that life developed on Mars during this time, as it did on the Earth. The present focus for Mars Exobiology lies in the search for a fossil record. Archean-aged crust, while mostly missing on Earth, appears to be widespread in ancient cratered highlands of Mars, and aqueous mineral deposits within such sequences may hold crucial fossil evidence for an early Martian biosphere.

Farmer, Jack D.↗

NASA NTRS2013

Prospecting for Polar Volatiles: Results from the Resolve Field

Both the Moon and Mercury evidently host ice and other volatile compounds in cold traps at the planets poles. Determining the form, spatial distribution, and abundance of these volatiles at the lunar poles can help us understand how and when they were delivered and emplaced. This bears directly on the delivery of water and prebiotic compounds to the inner planets over the solar system s history, and also informs plans for utilizing the volatiles as resources for sustained human exploration as well as the commercial development of space. Temperature models and orbital data suggest near-surface volatile concentrations may exist at polar locations not strictly in permanent shadow. Remote operation of a robotic lunar rover mission for the 7-10 days of available sunlight would permit key questions to be answered. But such a short, quick-tempo mission has unique challenges and requires a new concept of operations. Both science and rover operations decisionmaking must be done in real time, requiring immediate situational awareness, data analysis, and decision support tools.

Elphic, Richard C.↗

NASA NTRS1993

Space Biology and Medicine: Space and Its Exploration - Volume I

Perhaps one of the greatest gifts that has been given to the people of the world in the last few hundred years has been an emerging sense of the place of our planet and its inhabitants within the context of the vast universe. Our knowledge of the rest of the universe has not come quickly, nor was the process of attaining it only recently begun; however, the unprecedented acceleration of that process has benefitted from a fundamental new aspect of our species that has only manifested itself in the last 30 years or so, the ability to travel in space. Before the space age, the Universe was studied only through observations from the Earth. All that has changed with the beginning of the space age. Machines built by humans have flown to all but one of the nine planets that revolve around our Sun, have ventured billions of miles from the Earth and looked back, and have landed on three other worlds. Spacecraft in orbit around the Earth have viewed the sky at a vast number of electromagnetic wavelengths, detecting the shape of the galaxy and the universe, and even measuring the remnants of the universe's beginning. Human explorers have ventured forth, first for short stays in orbit, then, later, walking upon the Moon and living for long periods in space. As they did so, billions of people on the Earth came to view the Earth in a fundamentally different way, not just as the familiar day to- day backdrop for their lives, but as a small oasis suspended in the night sky above an alien landscape. It is this new view of the Earth that is the true gift of space exploration. Space exploration has at once given us a new perspective on the value of our world, and a new perspective from which to understand how it operates. It has shown us that the Earth is by far the most precious place in the solar system in terms of supporting human life, while revealing that other destinations may still be compelling. The exploration of space has at once become a challenge for humanity to overcome and a path to our common future. But for humanity to embark on this path, we need to understand ourselves in a new environment. As such, an understanding of the biological consequences of and opportunities in space flight is essential. In this, the first volume of a joint U.S./Russian series on space biology and medicine, we describe the current status of our understanding of space and present general information that will prove useful when reading subsequent volumes. Since we are witnesses to the beginning of a new era of interplanetary travel, a significant portion of the first volume will concentrate on the physical and ecological conditions that exist in near and outer space, as well as heavenly bodies from the smallest ones to the giant planets and stars. While space exploration is a comparatively recent endeavor, its foundations were laid much more than 30 years ago, and its history has been an eventful one. In the first part of this volume, Rauschenbach, Sokolskiy, and Gurjian address the "Historical Aspects of Space Exploration" from its beginnings to a present-day view of the events of the space age. The nature of space itself and its features is the focus of the second section of the volume. In the first chapter of the part, "Stars and Interstellar Space," the origin and evolution of stars, and the nature of the portions of space most distant from Earth are described by Galeev and Marochnik. In Chapter 2, Pisarenko, Logachev, and Kurt in "The Sun and Interplanetary Space" bring us to the vicinity of our own solar system and provide a description and discussion of the nearest star and its influence on the space environment that our Earth and the other planets inhabit. In our solar system there are many fascinating objects, remnants of the formation of a rather ordinary star in a rather obscure portion of the galaxy. Historical accident has caused us to be much more curious (and knowledgeable) about "The Inner Planets of the Solar System" than about any of these other objects. In Chapter 3, Marov describes the planets Mercury, Venus, Earth, and Mars, their history and origin, and their environmental conditions, and in Chapter 4 Owen provides similar information about Jupiter, Saturn, Uranus, Neptune, and Pluto, "The Outer Planets of the Solar System." Morrison provides a thorough discussion of "Asteroids, Comets, and Other Small Bodies" in Chapter 5. The understanding of these relics of the formation of the solar system may form the center of our ability to understand the origin of solar systems in general, and of the critical role that the beginning of the solar system had on the prospects for the origin of life and its continued survival and evolution in the face of their recurrent impacts on Earth. In Chapter 6, the first chapter of the third part, Rummel describes the area of "Exobiology," the study of the origin, evolution, and distribution of life in the context of the origin and evolution of the universe. The same processes that have given rise to life on Earth may have given rise to life elsewhere. In Chapter 7, the "Earth and the Biosphere," the nature and function of the Earth are discussed as a specific instance of planetary and biological evolution. The effects of biological processes on the Earth under the influence of human activities are also addressed by Moore and Bartlett in Chapter 7. The final chapter in this section concerns the prospects that life in the universe may be widespread; "SETI," the Search for Extraterrestrial Intelligence, by Billingham and Tarter, presents the arguments for conducting a search for evidence of life elsewhere in the galaxy, and describes the various methods proposed for conducting such a search. While SETI has a distinctly exploration al character, more direct means are available for exploring the solar system around us. The fourth part of the volume addresses this subject of space exploration. Considering the prospects for research on space biology and medicine, the means of providing "Access to Space" are described by Feoktistov and Briggs in Chapter 9. This chapter addresses carriers and launch systems, the unmanned and manned spacecraft that they loft into space, and the task of mission operations by which these precious vessels are monitored, navigated, and controlled. Despite the successes of the past and the capabilities of the present, it is clear that the study of space biology and medicine will be even more rewarding in the future than it has been to date. The work of the next few years that will be undertaken by the U.S. and Russia, both independently and jointly, will focus first on enabling greater capabilities in the exploration of space, and then on using the unique characteristics of the space environment to provide insight and greater understanding into biological systems, their behavior, development, and origin. The chapters of the first volume were written by leaders in their fields from the U.S. and Russia. The material presented summarizes our current understanding of space and its exploration. We understand that the first volume will be of interest not only to medical personnel and biologists, but also to general readers who want information about space beyond their own particular fields of expertise.

Nicogossian, Arnauld E.↗

NASA NTRS2016

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of jn(sub 2) - ( j - 2)n(sub 1), where j ≽ 3 is an integer characterizing the resonance and n(sub 2) and n(sub 1) are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of ϕ and ≈ϕ + π, where the phase ϕ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs.

Celestial mechanics↗

NASA NTRS2021

TESS and HARPS reveal two sub-Neptunes around TOI 1062

The Transiting Exoplanet Survey Satellite (TESS) mission was designed to perform an all-sky search of planets around bright and nearby stars. Here we report the discovery of two sub-Neptunes orbiting around TOI 1062 (TIC 299799658), a V = 10.25 G9V star observed in the TESS Sectors 1, 13, 27, and 28. We use precise radial velocity observations from HARPS to confirm and characterize these two planets. TOI 1062b has a radius of 2.265(-0.091,+0.096) Rꚛ, a mass of 10.15 ± 0.8 Mꚛ, and an orbital period of 4.1130 ± 0.0015 days. The second planet is not transiting, has a minimum mass of 9.78(−1.18,+1.26) Mꚛ and is near the 2:1 mean motion resonance with the innermost planet with an orbital period of 7.972(−0.024,+0.018) days. We performed a dynamical analysis to explore the proximity of the system to this resonance, and to attempt further constraining the orbital parameters. The transiting planet has a mean density of 4.85(−0.74,+0.84) g/cu. cm and an analysis of its internal structure reveals that it is expected to have a small volatile envelope accounting for 0.35% of the mass at most. The star’s brightness and the proximity of the inner planet to what is know as the radius gap make it an interesting candidate for transmission spectroscopy, which could further constrain the composition and internal structure of TOI 1062b.

J. F. Otegi↗

NASA NTRS1978

Physical properties of the planets and satellites from radar observations

The radar cross section of a planetary target is defined as the area of an isotropic scatterer, normal to the illumination, that would yield the observed echo intensity, if it were placed at the target's location. Attention is given to the angular scattering law, surface imagery, and topography. The observational results are discussed, taking into account the moon and the inner planets, the asteroids, the Galilean satellites, and the rings of Saturn. It is pointed out that the reach of radar astronomy has maintained nearly an exponential growth over the past three decades, as the sensitivity of available radar systems has on average more than doubled each year. There are, however, limits to this growth set by the large costs required for a new generation of observing facilities. Only modest increases in radar system sensitivity are, therefore, expected for the next decade.

Pettengill, G. H.↗

NASA NTRS2012

Gravity, Topography, and Magnetic Field of Mercury from Messenger

On 18 March 2011, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft was inserted into a 12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapse latitude of 60 deg N, and apoapsis at approximately 15,200 km altitude in the southern hemisphere. This orbit has permitted the mapping of regional gravitational structure in the northern hemisphere, and laser altimetry from the MESSENGER spacecraft has yielded a geodetically controlled elevation model for the same hemisphere. The shape of a planet combined with gravity provides fundamental information regarding its internal structure and geologic and thermal evolution. Elevations in the northern hemisphere exhibit a unimodal distribution with a dynamic range of 9.63 km, less than that of the Moon (19.9 km), but consistent with Mercury's higher surface gravitational acceleration. After one Earth-year in orbit, refined models of gravity and topography have revealed several large positive gravity anomalies that coincide with major impact basins. These candidate mascons have anomalies that exceed 100 mGal and indicate substantial crustal thinning and superisostatic uplift of underlying mantle. An additional uncompensated 1000-km-diameter gravity and topographic high at 68 deg N, 33 deg E lies within Mercury's northern volcanic plains. Mercury's northern hemisphere crust is generally thicker at low latitudes than in the polar region. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 +/- 0.017, where M=3.30 x 10(exp 23) kg and R=2440 km are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of Cm/C = 0.452 +/- 0.035. One proposed model for Mercury's radial density distribution consistent with these results includes silicate crust and mantle layers overlying a dense solid (possibly Fe-S) layer, a liquid Fe-rich outer core of radius 2030 +/- 37 km, and an assumed solid inner core. Magnetic field measurements indicate a northward offset of Mercury's axial magnetic dipole from the geographic equator by 479 +/-3 km and provide evidence for a regional-scale magnetic field approximately collocated with the northern volcanic plains of possible crustal origin. These results from MESSENGER indicate a complex and asymmetric evolution of internal structure and dynamics in this end-member inner planet.

Neumann, Gregory A.↗

NASA NTRS1967

The rotation of the planet Mercury

Radar observations of Mercury have disclosed that the sidereal period of the planet's axial rotation is 59 + 3 days (Pettengill and Dyce, 1965; Dyce et al., 1966), rather than the previously accepted period of 88 days (see, for example, Dollfus, 1953). The purpose of our investigation is to discover the implications for our theories of the solar system (and of the inner planets in particular) which this new result may require.

ROTATION↗

NASA NTRS2015

Mercury-T: A New Code to Study Tidally Evolving Multi-Planet Systems. Applications to Kepler-62

A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass 0:1 M(sub ⨀), Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water..

Dynamical evolution and stability↗