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Gravity Science With the Uranus Orbiter

The Cassini and Juno missions have considerably expanded our understanding of Saturn, Jupiter, and their moons. The spacecraft radio tracking data acquired by the NASA Deep Space Network (DSN) have enabled the accurate measurement of gravitational perturbations of these planetary bodies on the spacecraft trajectory. The inferred static zonal gravity fields have been key in understanding the interior structure and dynamics within Jupiter and Saturn. Repeated flybys of moons such as Titan and Enceladus can also constrain their interior properties, putting constraints on their formation and evolution, and potential habitability. The exploration of the Uranus system by NASA’s future flagship mission (Uranus Orbiter and Probe, UOP) holds the promise of making similar gains for Uranus and its moons. Here we address the gravity science that may be possible with UOP.

Erwan Mazarico↗

NASA NTRS2000

Planet Formation and the Characteristics of Extrasolar Planets

An overview of current theories of planetary growth, emphasizing the formation of extrasolar planets, is presented. Models of planet formation are based upon observations of the Solar System, extrasolar planets, and young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but if they become massive enough before the protoplanetary disk dissipates, then they are able to accumulate substantial amounts of gas. These models predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. A potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed.

Lissauer, Jack J.↗

NASA NTRS1997

On the Diversity of Planetary Systems

Models of planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. Modern theories of star and planet formation, which are based upon observations of the Solar System and of young stars and their environments, predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. A potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed.

Lissauer, Jack J.↗

NASA NTRS1999

Formation and Detection of Planetary Systems

Modern theories of star and planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. The most detailed models of planetary growth are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. These models predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. A potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed, and the methods that are being used and planned for detecting and characterizing extrasolar planets are reviewed.

Lissauer, Jack J.↗

NASA NTRS2002

Planet Formation

Lissauer, Jack J.↗

NASA NTRS2005

Planet Formation - Overview

Modern theories of star and planet formation are based upon observations of planets and smaller bodies within our own Solar System, exoplanets &round normal stars and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. These models predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large enough to gravitationally trap substantial quantities of gas. A potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path.

Lissauer, Jack J.↗

NASA NTRS1997

The Birth of Planetary Systems

Models of planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. Modern theories of star and planet formation, which are based upon observations of the Solar System and of young stars and their environments, predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large- enough to gravitationally trap substantial quantities of gas. Another potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed.

Lissauer, Jack J.↗

NASA NTRS1997

Impact Cratering Calculations

Understanding the physical processes of impact cratering on planetary surfaces and atmospheres as well as collisions of finite-size self-gravitating objects is vitally important to planetary science. The observation has often been made that craters are the most ubiquitous landform on the solid planets and the satellites. The density of craters is used to date surfaces on planets and satellites. For large ringed basin craters (e.g. Chicxulub), the issue of identification of exactly what 'diameter' transient crater is associated with this structure is exemplified by the arguments of Sharpton et al. (1993) versus those of Hildebrand et al. (1995). The size of a transient crater, such as the K/T extinction crater at Yucatan, Mexico, which is thought to be the source of SO,-induced sulfuric acid aerosol that globally acidified surface waters as the result of massive vaporization of CASO, in the target rock, is addressed by our present project. The impact process excavates samples of planetary interiors. The degree to which this occurs (e.g. how deeply does excavation occur for a given crater diameter) has been of interest, both with regard to exposing mantle rocks in crater floors, as well as launching samples into space which become part of the terrestrial meteorite collection (e.g. lunar meteorites, SNC's from Mars). Only in the case of the Earth can we test calculations in the laboratory and field. Previous calculations predict, independent of diameter, that the depth of excavation, normalized by crater diameter, is d(sub ex)/D = 0.085 (O'Keefe and Ahrens, 1993). For Comet Shoemaker-Levy 9 (SL9) fragments impacting Jupiter, predicted excavation depths of different gas-rich layers in the atmosphere, were much larger. The trajectory and fate of highly shocked material from a large impact on the Earth, such as the K/T bolide is of interest. Melosh et al. (1990) proposed that the condensed material from the impact upon reentering the Earth's atmosphere induced. radiative heating, and producing global firestorms. The observed reentry splash of the SL-9 impact-induced plumes that reimpact Jupiter (Boslough et al., 1994) supported Melosh's K/T model. The fate of early primitive planetary atmospheres during the latter stages of planetary accretion, resulting from impactors in the 100 to 103 km diameter require modeling, e.g. Newman et al. (1997). Ahrens (1990; 1993) and Chen and Ahrens (1997) found that upon delivery of most of the impact energy to the solid planet, very large ground motions arise, which couple sufficient kinetic energy to the atmosphere to cause substantial atmospheric escape. The trade-off of this model with that of Cameron (1997) who suggests that atmospheric blow-off occurs as a result of the massive impact-induced heating of the atmosphere and Pepin (1997) who uses this heating event to model differential hydrodynamic loss of lighter atmospheric gases, requires further research.

Ahrens, Thomas J.↗

NASA NTRS1992

Minimum impulse trajectories for Mars round trip missions

Data are presented for minimum-impulse earth-Mars round-trip trajectories for the 2010 to 2027 Mars launch opportunities. Round-trip mission times from 120 to 600 days, including a 30-day rendezvous at Mars, for direct trajectories and trajectories utilizing a Venus gravitational assist are considered. Optimal planetary launch and arrival dates and total impulse requirements are based on all maneuvers being performed propulsively with no finite burn or other losses. Direct trajectories have the lowest impulse requirements for shorter mission times and Venus gravitational assist trajectories have the lowest impulse requirements for longer mission times. It is shown that one can depart on trajectories to Mars, beginning with lower energy trajectories to the moon. The fuel savings varies, depending on the final energy level required and on the swingby procedure used. Procedures discussed include single lunar swingbys, double-powered or unpowered lunar swingbys, third lunar flybys a year later, and gravity assists by Venus and earth after the final lunar swingby.

Horvat, Glen M.↗

NASA NTRS1985

Accumulation of the Terrestrial Planets

The validity of the two body approximation in calculations of planetary growth is examined. Use of this approximation is essential to practical 3 dimensional simulations of planetary growth. With regard to gravitational perturbations, the changes in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 A.U.) out to 10 Tisserand sphere of influence radii were calculated by two and three dimensional numerical integration. These were compared with the results of treating the encounter as a two body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of (V/V sub e) approx. 0.35 (V = relative velocity, V = escape velocity of largest body), the two body approximation fails to describe the outcome of individual encounters. In this low velocity region, the two body gravitational focusing cross section is no longer valid.

Wetherill, G. W.↗

NASA NTRS1972

Evidence on the deeper planetary interiors

Various theories are evaluated that have arisen in attempts at determining the physics of planetary interiors by observations from the gravitational field and radiation from the surface. It is concluded that there appears great scope in obtaining data from planetary fields which will provide not only evidence of static structure but also of dynamic behavior and which will produce parameters of the solid state properties of their deep interiors.

Runcorn, S. K.↗

NASA NTRS1981

Accuracy of gravitational physics tests using ranges to the inner planets

A number of different types of deviations from Kepler's laws for planetary orbits can occur in nonNewtonian metric gravitational theories. These include secular changes in all of the orbital elements and in the mean motion, plus additional periodic perturbations in the coordinates. The first order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post Newtonian theory parameters were calculated as well as the corrections due to the solar quadrupole moment and a possible secular change in the gravitational constant. The results were applied to the case of proposed high accuracy ranging experiments from the Earth to a Mercury orbiting spacecraft in order to see how well the various parameters can be determined.

Ashby, N.↗

NASA NTRS1977

Flight with lift modulation inside a planetary atmosphere

A set of dimensionless variables is introduced to derive the equations for flight with lift and bank modulation inside a planetary atmosphere in a Newtonian gravitational field. Flight subject to constraints on state variables is discussed and a general approach is presented. Two examples are analyzed in detail: flight at constant speed, and flight at constant sinking speed.

Vinh, N. X.↗

NASA NTRS1984

Viking radio science data analysis and synthesis

The rotational motion of Mars and its geophysical ramifications were investigated. Solar system dynamics and the laws of gravitation were also studied. The planetary ephemeris program, which was the central element in data analysis for this project, is described in brief. Viking Lander data were used in the investigation.

Shapiro, I. I.↗

NASA NTRS1986

The rotation period of Uranus

On 24 January 1986 the spacecraft Voyager 2 transversed the innermost magnetosphere of the planet Uranus, coming as close as 4.2 Uranus radii to the planet. It is pointed out that the magnetic field data provide a direct measure of the rotation period of the planet's interior, where the field is generated. Two period determinations are reported. A combination of the obtained values provides a weighted mean value of P = 17.24 + or - 0.01 h. It is concluded that the 17.24-h rotation period has important consequences for studies of atmospheric dynamics and the internal structure and composition of Uranus. Thus, inferences regarding the internal structure can be drawn from the relationship between the observed planetary oblateness, rotation period, and gravitational moment.

Desch, M. D.↗

NASA NTRS1990

Formation of the earth

The origin of the earth is discussed in the context of the formation of the sun and the planets, and a standard model for such a formation assuming gravitational instability in a dense interstellar molecular cloud is outlined, along with the most significant variant of the model in which the loss of the nebular gas occurred after the formation of the earth. The formation of the sun and solar nebulae is addressed, and the coagulation of grains and the formation of small planetesimals are covered, along with the gravitational accumulation of planetesimals into planetary embryos and final stages of accumulation - embryos of planets. It is pointed out that the final stage of accumulation consists of the collision of these embryos; because of their large size, particularly after their further growth, these collisions represent giant impacts. It is concluded that the earth was initially an extremely hot and melted planet, surrounded by a fragile atmosphere and subject to violent impacts by bodies of the size of Ceres and even the moon.

Wetherill, George W.↗

NASA NTRS1974

Hydrodynamic instability of the solar nebula in the presence of a planetary core

When a planetary core composed of condensed matter accumulates in the primitive solar nebula, the gas in the nebula becomes gravitationally concentrated as an envelope about the planetary core. An analysis of models of such gaseous envelopes indicates that giant planets (such as Jupiter and Saturn) formed in a massive primitive solar nebula of the type constructed by Cameron and Pine (1973). When the mass of the accumulating planetary core becomes sufficiently great, the surrounding gaseous envelope will become hydrodynamically unstable against collapse onto the planetary core. Much of the surrounding gas also may be compressed onto the core by the background pressure of the gas.

Perri, F.↗

NASA NTRS1994

Preliminary solutions for the lunar gravity field from analysis of lunar orbiter tracking data

Knowledge of the gravitation field, in combination with surface topography, provides one of the principal means of inferring the internal structure of a planetary body. Previous analyses of the lunar gravitational field have been based on data from the Lunar Orbiters, the Apollo subsatellites, and the low altitude passes of the Apollo spacecraft. Recently, Konopliv et al. have reanalyzed all available Lunar Orbiter and Apollo subsatellite tracking data, producing a 60th degree and order solution. In preparation for the Clementine Mission to the Moon, we have also initiated a reanalysis of the Lunar Orbiter and Apollo subsatellite data. Our reanalysis takes advantage of advanced force and measurement modeling techniques as well as modern computational facilities. We applied the least squares collocation technique which stabilizes the behavior of the solution and high degree and order. The extension of the size of the field reduces the aliasing coming from the omitted portion of the gravitational field. This is especially important for the analysis of the tracking data from the Lunar Orbiters, as the periapse heights frequently ranged from 50 to 100 km.

Lemoine, F. G.↗