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All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

The Interior and Orbital Evolution of Charon as Preserved in Its Geologic Record

Pluto and its largest satellite, Charon, currently orbit in a mutually synchronous state; both bodies continuously show the same face to one another. This orbital configuration is a natural end-state for bodies that have undergone tidal dissipation. In order to achieve this state, both bodies would have experienced tidal heating and stress, with the extent of tidal activity controlled by the orbital evolution of Pluto and Charon and by the interior structure and rheology of each body. As the secondary, Charon would have experienced a larger tidal response than Pluto, which may have manifested as observable tectonism. Unfortunately, there are few constraints on the interiors of Pluto and Charon. In addition, the pathway by which Charon came to occupy its present orbital state is uncertain. If Charon's orbit experienced a high-eccentricity phase, as suggested by some orbital evolution models, tidal effects would have likely been more significant. Therefore, we determine the conditions under which Charon could have experienced tidally-driven geologic activity and the extent to which upcoming New Horizons spacecraft observations could be used to constrain Charon's internal structure and orbital evolution. Using plausible interior structure models that include an ocean layer, we find that tidally-driven tensile fractures would likely have formed on Charon if its eccentricity were on the order of 0.01, especially if Charon were orbiting closer to Pluto than at present. Such fractures could display a variety of azimuths near the equator and near the poles, with the range of azimuths in a given region dependent on longitude; east-west-trending fractures should dominate at mid-latitudes. The fracture patterns we predict indicate that Charon's surface geology could provide constraints on the thickness and viscosity of Charon's ice shell at the time of fracture formation.

Tectonics↗
NASA NTRS2014

Tidal Heating in Multilayered Terrestrial Exoplanets

The internal pattern and overall magnitude of tidal heating for spin-synchronous terrestrial exoplanets from 1 to 2.5 R(sub E) is investigated using a propagator matrix method for a variety of layer structures. Particular attention is paid to ice-silicate hybrid super-Earths, where a significant ice mantle is modeled to rest atop an iron-silicate core, and may or may not contain a liquid water ocean. We find multilayer modeling often increases tidal dissipation relative to a homogeneous model, across multiple orbital periods, due to the ability to include smaller volume low viscosity regions, and the added flexure allowed by liquid layers. Gradations in parameters with depth are explored, such as allowed by the Preliminary Earth Reference Model. For ice-silicate hybrid worlds, dramatically greater dissipation is possible beyond the case of a silicate mantle only, allowing non-negligible tidal activity to extend to greater orbital periods than previously predicted. Surface patterns of tidal heating are found to potentially be useful for distinguishing internal structure. The influence of ice mantle depth and water ocean size and position are shown for a range of forcing frequencies. Rates of orbital circularization are found to be 10-100 times faster than standard predictions for Earth-analog planets when interiors are moderately warmer than the modern Earth, as well as for a diverse range of ice-silicate hybrid super-Earths. Circularization rates are shown to be significantly longer for planets with layers equivalent to an ocean-free modern Earth, as well as for planets with high fractions of either ice or silicate melting.

celestial mechanics↗
NASA NTRS1974

Tides in the giant planets

Goldreich and Soter's (1966) discussion of tidal dissipation in the Jovian planets is reexamined for planetary models which possess an appreciable internal heat source. The tidal torque produced in a fully liquid planet is calculated as a function of the average viscosity in the interior. Turbulent viscosity, which is produced by the convection of internal heat to the surface, seems to be capable of producing small (about a few per cent) changes in the orbits of the innermost satellites of Jupiter over the age of the solar system. The basic regularity of many of the giant planet satellite systems is probably due to other, perhaps primordial, causes.

Hubbard, W. B.↗
NASA NTRS2004

Improved Estimate of Phobos Secular Acceleration from MOLA Observations

We report on new observations of the orbital position of Phobos, and use them to obtain a new and improved estimate of the rate of secular acceleration in longitude due to tidal dissipation within Mars. Phobos is the inner-most natural satellite of Mars, and one of the few natural satellites in the solar system with orbital period shorter than the rotation period of its primary. As a result, any departure from a perfect elastic response by Mars in the tides raised on it by Phobos will cause a transfer of angular momentum from the orbit of Phobos to the spin of Mars. Since its discovery in 1877, Phobos has completed over 145,500 orbits, and has one of the best studied orbits in the solar system, with over 6000 earth-based astrometric observations, and over 300 spacecraft observations. As early as 1945, Sharpless noted that there is a secular acceleration in mean longitude, with rate (1.88 + 0.25) 10(exp -3) degrees per square year. In preparation for the 1989 Russian spacecraft mission to Phobos, considerable work was done compiling past observations, and refining the orbital model. All of the published estimates from that era are in good agreement. A typical solution (Jacobson et al., 1989) yields (1.249 + 0.018) 10(exp -3) degrees per square year. The MOLA instrument on MGS is a laser altimeter, and was designed to measure the topography of Mars. However, it has also been used to make observations of the position of Phobos. In 1998, a direct range measurement was made, which indicated that Phobos was slightly ahead of the predicted position. The MOLA detector views the surface of Mars in a narrow field of view, at 1064 nanometer wavelength, and can detect shadows cast by Phobos on the surface of Mars. We have found 15 such serendipitous shadow transit events over the interval from xx to xx, and all of them show Phobos to be ahead of schedule, and getting progressively farther ahead of the predicted position. In contrast, the cross-track positions are quite close to the predicted values. Assuming that the along-track discrepancy is small enough that we can linearize the corrections, we model the mean orbital longitude as a quadratic function of time, and solve for corrections to the constant, linear, and quadratic terms. The time span of the recent observations is insufficient to properly resolve this issue alone, but when the 127 years of prior observations are added, we find a solution which reduces misfit to the new observations considerably, and makes no significant change to the fit to earlier observations. Our estimate for the secular acceleration term is (1.367 + 0.006) degrees per square year. The corresponding rate of energy dissipation is 3.34 MW. From a geophysical perspective, a more interesting parameter than the secular acceleration itself is the tidal lag angle, or tidal quality factor Q, for Mars. Unfortunately, the limiting error source in that determination is remaining uncertainty in the tidal Love numbers at harmonic degrees 2,3, and even 4. Until those parameters are better constrained, improvement in the orbital model of Phobos will not provide corresponding benefits for understanding the interior of Mars.

Bills, Bruce↗
NASA NTRS2014

The Tethered Moon

A reasonable initial condition on Earth after the Moonforming impact is that it begins as a hot global magma ocean1,2. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000- 4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down. A 2nd initial condition is a substantial atmosphere, 100-1000 bars of H2O and CO2, supplemented by smaller amounts of CO, H2, N2, various sulfur-containing gases, and a suite of geochemical volatiles evaporated from the magma. Third, we start the Moon with its current mass at the relevant Roche limit. The 4th initial condition is the angular momentum of the Earth-Moon system. Canonical models hold this constant, whilst some recent models begin with considerably more angular momentum than is present today. Here we present a ruthlessly simplified model of Earth's cooling magmasphere based on a full-featured atmosphere and including tidal heating by the newborn Moon. Thermal blanketing by H2O-CO2 atmospheres slows cooling of a magma ocean. Geochemical volatiles - chiefly S, Na, and Cl - raise the opacity of the magma ocean's atmosphere and slow cooling still more. We assume a uniform mantle with a single internal (potential) temperature and a global viscosity. The important "freezing point" is the sharp rheological transition between a fluid carrying suspended crystals and a solid matrix through which fluids percolate. Most tidal heating takes place at this "freezing point" in a gel that is both pliable and viscous. Parameterized convection links the cooling rate to the temperature and heat generation inside the Earth. Tidal heating is a major effect. Tidal dissipation in the magma ocean is described by viscosity. The Moon is entwined with Earth by the negative feedback between thermal blanketing and tidal heating that comes from the temperature-dependent viscosity of the magma ocean. Because of this feedback, the rate that the Moon's orbit evolves is limited by the modest radiative cooling rate of Earth's atmosphere, which in effect tethers the Moon to the Earth. Consequently the Moon's orbit evolves orders of magnitude more slowly than in conventional models. Slow orbital evolution promotes capture by orbital resonances that may have been important in the Earth-Moon system

Earth-Moon system↗
NASA NTRS1984

Physical Properties of Neptune and Triton Inferred from the Orbit of Triton

The orbital motion of Triton was redetermined from photographic data spanning the interval 1899-1981. The resulting ephemeris should provide Triton positions with respect to Neptune with an accuracy of plus or minus 500 km through the end of the century. The following physical results follow from the orbit solution. The inverse mass of Neptune + Triton is solar mass over (c sub N + m sub T) = 19490 plus or minus 40. No acceleration of the mean motion nor orbital eccentricity were detected, thus constraining the tidal dissipation factors of Neptune and Triton to O sub N less than or equal to 650 and QT less than or equal to 10,000. Tidal heating of Triton is presently insignificant. The gravitational harmonic J sub 2 of Neptune is 0.0043 plus or minus 0.0003 if Triton is as massive as m sub T/ M sub N = 0.00128, and if Neptune's spin is prograde with P approximately 18(h), or J sub 2 = 0.0037 plus or minus 0.0002 if Triton is much less massive. Triton undergoes extreme climatic variations due to the combined motion of it's orbit plane and Neptune's orbital motion. Approximately 10% of Triton's surface is presently hidden from diurnal insolation, which may provide a powerful cold trap for atmospheric voltatiles.

A W Harris↗
NASA NTRS1990

The coupled orbital and thermal evolution of Triton

The coupled orbital and thermal evolution of Triton is simulated with a model of the satellite having temperature-dependent k/Q (k is the second degree Love number and Q is the tidal dissipation factor). Large changes in orbital and interior properties occur in a short time span of less than 10 to the 8th years. The peak tidal heating rate exceeds the radioactive heating rate by a factor of at least 1000. The ability of tidal heating to overwhelm solid state convection and cause global melting is unequivocally demonstrated. Triton's initial thermal state and composition are shown to control the length of time that passes between capture from heliocentric orbit and the occurrene of swift and dramatic changes in orbital and internal properties. This time interval could have been several billion years.

Ross, Martin N.↗
NASA NTRS1988

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

Christodoulidis, D. C.↗
DOE OSTI2021

A Tidal Origin for a Three-body Resonance in Kepler-221

Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here, we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as a perturbative analysis, we demonstrate that this system likely began as a resonant chain and proceeded to undergo large-scale divergence away from resonance, under the action of tidal dissipation. Our results further indicate that obliquity tides, driven by a secular spin–orbit resonance and mutual inclination, are an excellent candidate for driving this orbital divergence, and that the high tidal luminosity may also explain the anomalous size of planet b, which lies within the Fulton radius gap.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

Seismic energy release of the moon

Lunar seismicity is investigated by calculating various source parameters for a number of shallow and deep-focus moonquakes. The seismic moment, seismic energy release, annual seismic energy release, stress drop, and body-wave magnitude are determined for the largest shallow moonquakes and for large deep-focus events. It is found that the shallow events dominate the lunar seismic energy release, that tidal dissipation may account for the energy release by the deep-focus events, and that the stress drops for the deep-focus events are comparable to or smaller than the calculated tidal stresses. A comparison of the results with terrestrial data indicates that the seismic characteristics of a planet are controlled more by tectonic style and state than by the relative magnitude of the driving forces.

Goins, N. R.↗
NASA NTRS1984

How fast do Galilean satellites spin?

Each of the Galilean satellites, as well as most other satellites whose initial rotations have been substantialy altered by tidal dissipation, has been widely assumed to rotate synchronously with its orbital mean motion. Such rotation would require a small permanent asymmetry in the mass distribution in order to overcome the small mean tidal torque. Since Io and Europa may be substantially fluid, they may not have the strength to support the required permanent asymmetry. Thus, each may rotate at the unknown but slightly nonsynchronous rate that corresponds to zero mean tidal torque. This behavior may be observable by Galileo spacecraft imaging. It may help explain the longitudinal variation of volcanism on Io and the cracking of Europa's crust.

Greenberg, R.↗
NASA NTRS1987

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.

Christodoulidis, D. C.↗
NASA NTRS2004

Jason 1 Investigation: Altimetric Studies of Ocean Tidal Dynamics

Two papers on tidal dissipation were completed and published. The first of these extended our earlier work, which focused on the dominant M2 constituent, to include 7 additional constituents. In addition to confirming a total deep water dissipation total very close to 1 TW, this study demonstrated significant differences in the distribution of dissipation between diurnal and semi-diurnal constituents. The second paper involved an extensive modeling study of tides in the present day and the last glacial maximum. In this study we showed that accuracy of tidal solutions for the present day Ocean were significantly improved by including a parameterization of internal tide drag over rough topography in the deep ocean. It was also demonstrated that a complete self-consistent treatment of Ocean self attraction and tidal loading was required for accurate solutions.

Egbert, Gary D.↗
NASA NTRS2000

Jet Propulsion Laboratory

Analyses of laser ranges to the Moon are utilized for a broad range of investigations: lunar science, gravitational physics, geodesy, geodynamics and astronomy. Unique contributions from LLR include: detection of a molten lunar core; measurement of tidal dissipation in the Moon; an accurate test of the principle of equivalence for massive bodies (strong equivalence principle); and detection of lunar free librations. LLR analysis has provided tests of relativity, measurements of the Moon's tidal acceleration and the Earth s precession, and has provided orders-of-magnitude improvements in the accuracies of the lunar ephemeris and three-dimensional rotation. JPL has been active in all of these various LLR applications and supplies lunar and planetary ephemerides and lunar physical librations to the community.

Williams, Jim↗
NASA NTRS1984

Origin and Evolution of the Uranian and Neptunian Satellites: Some Dynamical Considerations

The satellite system of Neptune is so irregular that some formation mechanism or subsequent dynamical evolution that sets it apart from the other, more regular, satellite systems is obviously indicated. McKinnon argued that satellite capture is the most likely possibility and has shown that tidal circularization of Triton's presumably highly eccentric initial orbit probably resulted in melting of the satellite's interior. The satellite system of Uranus, although somewhat bland, also has a number of special features that indicate an interesting dynamical history. These include the anomalously high orbital inclination of Miranda and the probable coexistence of small satellites and narrow rings inside the plant's Roche limit. The possibility that orbital evolution due to tidal dissipation is involved in both of these phenomena is discussed. Other topics discussed are: the origin of rings; the formation of coorbital satellites; the lack of stable orbit-orbit resonances in the Uranian satellite system; and chaos, tidal heating and the shapes of Miranda and Ariel.

Dermott, S. F.↗
DOE OSTI2020

Ultra-short-period Planets Are Stable against Tidal Inspiral

It has been unambiguously shown both in individual systems and at the population level that hot Jupiters experience tidal inspiral before the end of their host stars’ main-sequence lifetimes. Ultra-short-period (USP) planets have orbital periods P < 1 day, rocky compositions, and are expected to experience tidal decay on similar timescales to hot Jupiters if the efficiency of tidal dissipation inside their host stars parameterized as Q{sub ∗}{sup ′} is independent of P and/or secondary mass M {sub p}. Any difference between the two classes of systems would reveal that a model with constant Q{sub ∗}{sup ′} is insufficient. If USP planets experience tidal inspiral, then USP planet systems will be relatively young compared to similar stars without USP planets. Because it is a proxy for relative age, we calculate the Galactic velocity dispersions of USP planet candidate host and non-host stars using data from Gaia Data Release 2 supplemented with ground-based radial velocities. We find that main-sequence USP planet candidate host stars have kinematics consistent with similar stars in the Kepler field without observed USP planets. This indicates that USP planet hosts have similar ages to field stars and that USP planets do not experience tidal inspiral during the main-sequence lifetimes of their host stars. The survival of USP planets requires that Q{sub ∗}{sup ′} ≳ 10{sup 7} at P ≈ 0.7 day and M{sub p}≈2.6 M{sub ⊕}. This result demands that Q{sub ∗}{sup ′} depend on the orbital period and/or mass of the secondary in the range 0.5 day≲P≲5 days and 1 M{sub ⊕}≲M{sub p}≲1000 M{sub ⊕}.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2001

Three-Dimensional Simulations of Mantle Convection in Io

Io has very high surface heat flow and an abundance of volcanic activity, which are thought to be driven by nonuniform tidal heating in its interior. This nonuniform heat is transported to the base of the lithosphere by very vigorous convection in Io's silicate mantle, the form of which is presumably responsible for the distribution of surface features such as volcanoes and mountains. We here present three-dimensional spherical calculations of mantle convection in Io, in order to ascertain the likely form of this convection and the resulting distribution of heat flow at the surface and core-mantle boundary. Different models of tidal dissipation are considered: the endmember scenarios (identified by M. N. Ross and G. Schubert) of dissipation in the entire mantle, or dissipation in a thin (approximately 100-km-thick) asthenosphere, as well as the 'preferred' distribution of M. N. Ross et al. comprising 1/3 mantle and 2/3 asthenosphere heating. The thermal structure of Io's mantle and asthenosphere is found to be strongly dependent on tidal heating mode, as well as whether the mantle-asthenosphere boundary is permeable or impermeable. Results indicate a large-scale flow pattern dominated by the distribution of tidal heating, with superimposed small-scale asthenospheric instabilities that become more pronounced with increasing Rayleigh number. These small-scale instabilities spread out the surface heat flux, resulting in smaller heat flux variations with increasing Rayleigh number. Scaled to Io's Rayleigh number of O(10(exp 12)) variations of order a few percent are expected. This small but significant variation in surface heat flux may be compatible with the observed distributions of volcanic centers and mountains, which appear fairly uniform at first sight but display a discernible distribution when suitably processed. The observed distribution of volcanic centers is similar to the asthenosphere heating distribution, implying that most of the tidal heating in Io occurs in an asthenosphere.

Tackley, Paul J.↗
NASA NTRS1992

Tidal deceleration of the moon's mean motion

The secular change in the mean motion of the moon, n, caused by the tidal dissipation in the ocean and solid earth is due primarily to the effect of the diurnal and semidiurnal tides. The long-period ocean tides produce an increase in n, but the effects are only 1 percent of the diurnal and semidiurnal ocean tides. In this investigation, expressions for these effects are obtained by developing the tidal potential in the ecliptic reference system. The computation of the amplitude of equilibrium tide and the phase corrections is also discussed. The averaged tidal deceleration of the moon's mean motion, n, from the most recent satellite ocean tide solutions is -25.25 +/- 0.4 arcseconds/sq century. The value for n inferred from the satellite-determined ocean-tide solution is in good agreement with the value obtained from the analysis of 20 years of lunar laser-ranging observations.

Cheng, M. K.↗