Roche Limit Research Articles

Motion of blocks on the surface of Phobos: New constraints for the formation of grooves

Although grooves are common on asteroids, on Phobos the grooves have been the subject of various formation hypotheses for two reasons: the fact that Phobos is orbiting around Mars close to the Roche limit, implies an unusual gravity environment as well as the presence of the huge crater impact, Stickney, which seems to be related at least to a family of grooves. Among many hypotheses, it has been suggested that the grooves could have been dug by rolling Stickney ejecta, but this hypothesis was questioned using two main arguments: no block was observed at the end of the grooves, nor do they run downslope. Thus, the study of surface and near surface dynamics on Phobos can clarify the soundness of these controversial arguments.The present study explores this idea by computing the trajectory of a test mass gliding on the surface of Phobos for any initial position and velocity. An ellipsoidal model of Phobos is used for both the gravity and surface geometry, and several orbiting distances from Mars are considered. It is shown that, due to the Phobos rotation, the trajectories generally do not run downslope even for velocities as low as ∼1m/s. In consequence the corresponding argument against the rolling blocks hypothesis is not applicable. This hypothesis, however, is clearly ruled out for the sets of parallel grooves in the polar regions because of the curvature of the computed trajectories. On the contrary the trajectories issued from the rim of Stickney close to the equator, with velocities of a few m/s, show similitude with the corresponding groove patterns, in particular for the east–west asymmetry. In some conditions the trajectories leave the surface, which may account for regions free of grooves and for trails without blocks at the end. Consequently, the rolling block hypothesis cannot be rejected outright until further analysis is carried out. Damping of the motion on the regolith is simulated introducing a solid damping coefficient in the equations. A relatively small but not unrealistic coefficient of ∼0.1 accounts for the length of the long main western hypothetic block trails. The simulations with damping confirm that the trajectories turn downslope only at the very end for velocities ⪡1m/s, but valuable comparison with the observations requires a better model.

The recent formation of Saturn's moonlets from viscous spreading of the main rings

The regular satellites of the giant planets are believed to have finished their accretion concurrent with the planets, about 4.5 Gyr ago. A population of Saturn's small moons orbiting just outside the main rings are dynamically young (less than 10(7) yr old), which is inconsistent with the formation timescale for the regular satellites. They are also underdense ( approximately 600 kg m(-3)) and show spectral characteristics similar to those of the main rings. It has been suggested that they accreted at the rings' edge, but hitherto it has been impossible to model the formation process fully owing to a lack of computational power. Here we report a hybrid simulation in which the viscous spreading of Saturn's rings beyond the Roche limit (the distance beyond which the rings are gravitationally unstable) gives rise to the small moons. The moonlets' mass distribution and orbital architecture are reproduced. The current confinement of the main rings and the existence of the dusty F ring are shown to be direct consequences of the coupling of viscous evolution and satellite formation. Saturn's rings, like a mini protoplanetary disk, may be the last place where accretion was recently active in the Solar System, some 10(6)-10(7) yr ago.

The birth of Saturn's baby moons

Simulations show that Saturn's nearby moons, after forming on the outskirts of the planet's main rings, get pushed clear of them. This model reproduces the moons' orbital locations and remarkably low densities. A population of Saturn's smaller moons contrasts dramatically with the regular moons of the giant planets. Moons like Saturn's Enceladus and Jupiter's Europa orbit in the equatorial plane of their host planet and are thought to have finished their accretion at about the same time as the planets, 4.5 billion years ago. Saturn's icy moonlets are much younger, formed less than 10 million years ago, and as their spectra resemble those of the main rings it has been suggested that they formed by accretion at the rings' edges. A new hybrid numerical simulation of the Saturn system supports this idea, suggesting that the moons formed via viscous spreading of Saturn's main rings beyond the Roche limit (the distance beyond which rings are gravitationally unstable, about 140,000 km from Saturn). After the moons' formation, the edge of the ring migrated inward.

The stability of ultra-compact planetary systems

Aims. We investigate the dynamical stability of compact planetary systems in the CoRoT discovery space, i.e., with orbital periods of less than 50 days, including a detailed study of the stability of systems, which are spaced according to Hill’s criteria. Methods. The innermost fictitious planet was placed close to the Roche limit from the star (MStar = 1 MSun) and all other fictitious planets are lined up according to Hill’s criteria up to a distance of 0.26 AU, which corresponds to a 50 day period for a Sun-massed star. For the masses of the fictitious planets, we chose a range of 0.33–17 mEarth, where in each simulation all fictitious planets have the same mass. Additionally, we tested the influence of both the semi-major axis of the innermost planet and of the number of planets. In a next step we also included a gas giant in our calculations, which perturbs the inner ones and investigated their stability. Results. With numerous integrations of many different configurations we could show that long-time stable motion is possible for up to 10 planets with 17 mEarth within a distance of 0.26 AU. Further investigations show that the fictitious planets remain stable under certain circumstances even if a close-in gas giant is present.

The thermal emission of the young and massive planet CoRoT-2b at 4.5 and 8 μm

We report measurements of the thermal emission of the young and massive planet CoRoT-2b at 4.5 and 8 <i>μ<i/>m with the <i>Spitzer<i/> Infrared Array Camera (IRAC). Our measured occultation depths are 0.510<i>±<i/>0.042% at 4.5 and 0.41<i>±<i/>0.11% at 8 <i>μ<i/>m. In addition to the CoRoT optical measurements, these planet/star flux ratios indicate a poor heat distribution on the night side of the planet and agree better with an atmosphere free of temperature inversion layer. Still, such an inversion is not definitely ruled out by the observations and a larger wavelength coverage is required to remove the current ambiguity. Our global analysis of CoRoT, <i>Spitzer<i/>, and ground-based data confirms the high mass and large size of the planet with slightly revised values (<i>M<i/><sub>p<sub/> = 3.47<i>±<i/>0.22 <i>M<sub>J<sub/><i/>, <i>R<i/><sub>p<sub/> = 1.466<i>±<i/>0.044 <i>R<sub>J<sub/><i/>). We find a small but significant offset in the timing of the occultation when compared to a purely circular orbital solution, leading to = -0.00291<i>±<i/>0.00063 where <i>e<i/> is the orbital eccentricity and <i>ω<i/> is the argument of periastron. Constraining the age of the system to at most a few hundred Myr and assuming that the non-zero orbital eccentricity does not come from a third undetected body, we modeled the coupled orbital-tidal evolution of the system with various tidal <i>Q<i/> values, core sizes, and initial orbital parameters. For = 10<sup>5<sup/>-10<sup>6<sup/>, our modeling is able to explain the large radius of CoRoT-2b if <i>≤<i/> 10 through a transient tidal circularization and corresponding planet tidal heating event. Under this model, the planet will reach its Roche limit within 20 Myr at most.

Writing at the Roche Limit: Order and Entropy in W. G. Sebald's Die Ringe des Saturn

This essay argues that W. G. Sebald's Die Ringe des Saturn is centered thematically and structurally around a dynamic system in which entropy and order, dispersion and coalescence, operate in a delicate balance. Sebald alludes to just such a balanced system in the reference to the physical‐astronomical concept of the Roche limit contained in one of his epigraphs to this text. Just as the Roche limit designates a boundary at which two powerful gravitational forces hold each other in check, Sebald's text is structured around an equilibrium between decomposition and (re‐)organization. The more positive, constructive aspects of this text have often been overlooked due to Sebald's critique of traditional rationalist principles of order. His narrative, however, presents alternative ordering strategies, such as repetition, periodicity, co‐incidence (understood literally), and convergence as counter‐measures to decline and fragmentation. This reading thus calls more broadly for a revision of the widely held view of Sebald's text as a manifestation of nihilism or cultural pessimism.

TIDAL AND MAGNETIC INTERACTIONS BETWEEN A HOT JUPITER AND ITS HOST STAR IN THE MAGNETOSPHERIC CAVITY OF A PROTOPLANETARY DISK

We present a simplified model to study the orbital evolution of a young hot Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model takes into account the disk locking of stellar spin as well as the tidal and magnetic interactions between the star and the planet. We focus on the orbital evolution starting from the orbit in the 2:1 resonance with the inner edge of the disk, followed by the inward and then outward orbital migration driven by the tidal and magnetic torques as well as the Roche-lobe overflow of the tidally inflated planet. The goal in this paper is to study how the orbital evolution inside the magnetospheric cavity depends on the cavity size, planet mass, and orbital eccentricity. In the present work, we only target the mass range from 0.7 to 2 Jupiter masses. In the case of the large cavity corresponding to the rotational period ~ 7 days, the planet of mass >1 Jupiter mass with moderate initial eccentricities (>~ 0.3) can move to the region < 0.03 AU from its central star in 10^7 years, while the planet of mass <1 Jupiter mass cannot. We estimate the critical eccentricity beyond which the planet of a given mass will overflow its Roche radius and finally lose all of its gas onto the star due to runaway mass loss. In the case of the small cavity corresponding to the rotational period ~ 3 days, all of the simulated planets lose all of their gas even in circular orbits. Our results for the orbital evolution of young hot Jupiters may have the potential to explain the absence of low-mass giant planets inside ~ 0.03 AU from their dwarf stars revealed by transit surveys.

Length scales and size distributions in dynamic fragmentation

The shatter of a cherished wine glass on impact with the kitchen tile, the spallation in the high-energy collision of atomic nuclei, the fragmentation of the Shoemaker-Levi comet on passage of the Roche limit of the Jovian gravitational field, collectively span vast length scales, yet are each examples of dynamic fragmentation with a number of commonalities. In the above examples, as well as many other dynamic fragmentation events, the consequence is the breakage of the body into some number of fragments that are distributed over size. At the heart of a satisfactory theory is the prediction of the number of fragments and the statistical distribution of these fragments over size. A theory based on energy principles is found to provide length scales that govern both the characteristic fragment size and the distribution spread. Fundamental failure and fracture properties of the material are central in determining the nature of the fragment size distribution. Fragment size distributions can range from relatively tight exponential functions to power-law relations spanning a number of decades in fragment size. The fragment distribution and the dynamic fracture processes leading to power-law distributions bear striking similarities to hydrodynamic turbulence. Onset of fracture asymptotes to a range of length scales in which destruction is self-similar and fractal, requiring that consequences, including the fragment size distributions, exhibit a power-law dependence on the length scale. The theory is described and supporting experimental evidence is provided.

Radiation pressure and pulsation effects on the Roche lobe

Several observational pieces of evidence indicate that specific evolutionary channels which involve Roche lobe overflow are not correctly accounted for by the classical Roche model. We generalize the concept of Roche lobe in the presence of extra forces (caused by radiation pressure or pulsations). By computing the distortion of the equipotential surfaces, we are able to evaluate the impact of these perturbing forces on the stability of Roche-lobe overflow (RLOF). Radiative forces are parametrized through the constant reduction factor that they impose on the gravitational force from the radiating star (neglecting any shielding in case of large optical thickness). Forces imparted by pulsations are derived from the velocity profile of the wind that they trigger. We provide analytical expressions to compute the generalized Roche radius. Depending on the extra force, the Roche-lobe radius may either stay unchanged, become smaller, or even become meaningless (in the presence of a radiatively- or pulsation-driven wind). There is little impact on the RLOF stability.

THE ULTRAVIOLET SPECTRUM AND PHYSICAL PROPERTIES OF THE MASS DONOR STAR IN HD 226868 = Cygnus X-1

We present an examination of high resolution, ultraviolet spectroscopy from Hubble Space Telescope of the photospheric spectrum of the O-supergiant in the massive X-ray binary HD 226868 = Cyg X-1. We analyzed this and ground-based optical spectra to determine the effective temperature and gravity of the O9.7 Iab supergiant. Using non-local thermodynamic equilibrium (non-LTE), line blanketed, plane parallel models from the TLUSTY grid, we obtain T_eff = 28.0 +/- 2.5kK and log g > 3.00 +/- 0.25, both lower than in previous studies. The optical spectrum is best fit with models that have enriched He and N abundances. We fit the model spectral energy distribution for this temperature and gravity to the UV, optical, and IR fluxes to determine the angular size of and extinction towards the binary. The angular size then yields relations for the stellar radius and luminosity as a function of distance. By assuming that the supergiant rotates synchronously with the orbit, we can use the radius - distance relation to find mass estimates for both the supergiant and black hole as a function of the distance and the ratio of stellar to Roche radius. Fits of the orbital light curve yield an additional constraint that limits the solutions in the mass plane. Our results indicate masses of 23^{+8}_{-6} M_sun for the supergiant and 11^{+5}_{-3} M_sun for the black hole.

Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity

White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to estimate the number of LISA-resolved galactic binaries that will undergo either SMT or UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary differential equations and compute the corresponding gravitational waveforms. Finally, we discuss in general terms the possible fate of binaries that undergo UMT and construct approximate Newtonian equilibrium configurations of merged WDNS remnants. We use these configurations to assess plausible outcomes of our future, fully relativistic simulations of these systems. If sufficient WD debris lands on the NS, the remnant may collapse, whereby the gravitational waves from the inspiral, merger, and collapse phases will sweep from LISA through LIGO frequency bands. If the debris forms a disk about the NS, it may fragment and form planets.

The equilibrium of rubble-pile satellites: The Darwin and Roche ellipsoids for gravitationally held granular aggregates

Many new small moons of the giant planets have been discovered recently. In parallel, satellites of several asteroids, e.g., Ida, have been found. Strikingly, a majority of these new-found planetary moons are estimated to have very low densities, which, along with their hypothesized accretionary origins, suggests a rubble internal structure. This, coupled to the fact that many asteroids are also thought to be particle aggregates held together principally by self-gravity, motivates the present investigation into the possible ellipsoidal shapes that a rubble-pile satellite may achieve as it orbits an aspherical primary. Conversely, knowledge of the shape will constrain the granular aggregate's orbit—the closer it gets to a primary, both primary's tidal effect and the satellite's spin are greater. We will assume that the primary body is sufficiently massive so as not to be influenced by the satellite. However, we will incorporate the primary's possible ellipsoidal shape, e.g., flattening at its poles in the case of a planet, and the proloidal shape of asteroids. In this, the present investigation is an extension of the first classical Darwin problem to granular aggregates. General equations defining an ellipsoidal rubble pile's equilibrium about an ellipsoidal primary are developed. They are then utilized to scrutinize the possible granular nature of small inner moons of the giant planets. It is found that most satellites satisfy constraints necessary to exist as equilibrated granular aggregates. Objects like Naiad, Metis and Adrastea appear to violate these limits, but in doing so, provide clues to their internal density and/or structure. We also recover the Roche limit for a granular satellite of a spherical primary, and employ it to study the martian satellites, Phobos and Deimos, as well as to make contact with earlier work of Davidsson [Davidsson, B., 2001. Icarus 149, 375–383]. The satellite's interior will be modeled as a rigid-plastic, cohesion-less material with a Drucker–Prager yield criterion. This rheology is a reasonable first model for rubble piles. We will employ an approximate volume-averaging procedure that is based on the classical method of moments, and is an extension of the virial method [Chandrasekhar, S., 1969. Ellipsoidal Figures of Equilibrium. Yale Univ. Press, New Haven] to granular solid bodies.

Did Saturn's rings form during the Late Heavy Bombardment?

The origin of Saturn's massive ring system is still unknown. Two popular scenarios—the tidal splitting of passing comets and the collisional destruction of a satellite—rely on a high cometary flux in the past. In the present paper we attempt to quantify the cometary flux during the Late Heavy Bombardment (LHB) to assess the likelihood of both scenarios. Our analysis relies on the so-called “Nice model” of the origin of the LHB [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459–461; Morbidelli, A., Levison, H.H., Tsiganis, K., Gomes, R., 2005. Nature 435, 462–465; Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466–469] and on the size distribution of the primordial trans-neptunian planetesimals constrained in [Charnoz, S., Morbidelli, A., 2007. Icarus 188, 468–480]. We find that the cometary flux on Saturn during the LHB was so high that both scenarios for the formation of Saturn rings are viable in principle. However, a more detailed study shows that the comet tidal disruption scenario implies that all four giant planets should have comparable ring systems whereas the destroyed satellite scenario would work only for Saturn, and perhaps Jupiter. This is because in Saturn's system, the synchronous orbit is interior to the Roche Limit, which is a necessary condition for maintaining a satellite in the Roche Zone up to the time of the LHB. We also discuss the apparent elimination of silicates from the ring parent body implied by the purity of the ice in Saturn's rings. The LHB has also strong implications for the survival of the saturnian satellites: all satellites smaller than Mimas would have been destroyed during the LHB, whereas Enceladus would have had from 40% to 70% chance of survival depending on the disruption model. In conclusion, these results suggest that the LHB is the “sweet moment” for the formation of a massive ring system around Saturn.

Effect of Coriolis force on the shapes of rotating stars and stars in binary systems

In this paper an attempt has been made to determine the effect of Coriolis force on the shapes of Roche equipotential surfaces of rotating stars and stars in binary systems. Equations of Roche equipotential surfaces have been obtained for rotating and binary stars which take into account the effects of Coriolis force besides the centrifugal and gravitational forces. Shapes of Roche equipotentials and values of Roche limits are obtained for different values of angular velocity of rotation for rotating stars and for different values of mass ratios for the binary stars. The obtained results have been compared with the corresponding results in which the effect of Coriolis force has not been considered.

Tidal excitation of elliptical instability in the Martian core: Possible mechanism for generating the core dynamo

We propose a causal relationship between the creation of the giant impact basins on Mars by a large asteroid, ruptured when it entered the Roche limit, and the excitation of the Martian core dynamo. Our laboratory experiments indicate that the elliptical instability of the Martian core can be excited if the asteroid continually exerts tidal forces on Mars for ∼20,000 years. Our numerical experiments suggest that the growth‐time of the instability was 5,000–15,000 years when the asteroid was at a distance of 50,000–75,000 km. We demonstrate the stability of the orbital motion of an asteroid captured by Mars at a distance of 100,000 km in the presence of the Sun and Jupiter. We also present our results for the tidal interaction of the asteroid with Mars. An asteroid captured by Mars in prograde fashion can survive and excite the elliptical instability of the core for only a few million years, whereas a captured retrograde asteroid can excite the elliptical instability for hundreds of millions of years before colliding with Mars. The rate at which tidal energy dissipates in Mars during this period is over two orders of magnitude greater than the rate at which magnetic energy dissipates. If only 1% of the tidal energy dissipation is partitioned to the core, sufficient energy would be available to maintain the core dynamo. Accordingly, a retrograde asteroid is quite capable of exciting an elliptical instability in the Martian core, thus providing a candidate process to drive a core dynamo.

Tidal disruptions: II. A continuum theory for solid bodies with strength, with applications to the Solar System

We present a comprehensive theory for the breakup conditions for ellipsoidal homogeneous secondary bodies subjected to the tidal forces from a nearby larger primary: for materials ranging from purely fluid ones, to granular rubble-pile gravel-like ones, and to those with either cohesive or granular strength including cohesive rocks and metals. The theory includes but greatly extends the classical analyses given by Roche in 1847, which dealt only with fluids, and also our previous analysis [Holsapple, K.A., Michel, P., 2006. Icarus 183, 331–348], which dealt only with solid but non-cohesive bodies. The results here give the distance inside of which breakup must occur, for both a steadily orbiting satellite and for a passing or impacting object. For the fluid bodies there is a single specific shape (a “Roche Ellipsoid”) that can be in equilibrium at any given distance from a primary, and especially only one shape that can exist at the overall minimum distance ( d / R ) ( ρ / ρ p ) 1 / 3 = 2.455 , the classical well-known “Roche limit.” In contrast, solid bodies can exist at a given distance from a primary with a range of shapes. Here we give multiple plots of the minimum distances for various important combinations of body shape, spin, mass density, and the strength parameters characterized by an angle of friction and cohesive strength. Such results can be used in different ways. They can be used to estimate limits on strengths and mass densities for orbiting bodies at a known distance and shape. They can be used to determine breakup distances for passing bodies with an assumed strength and shape. They can be used to constraint physical properties such as bulk density of bodies with a known shape that were known to breakup at a given distance. A collection of approximately 40 satellites of the Solar System is used for comparison to the theory. About half of those bodies are closer than the Roche fluid limit and must have some cohesion and/or friction angle to exist at their present orbital distance. The required solid strength for those states is determined. Finally, we apply the theory to the break up of the SL9 comet at close approach with Jupiter. Our results make clear that the literature estimates of its bulk density depend markedly on unknown parameters such as shape, orientation and spin, and most importantly, material strength characterization.

Tidal barrier and the asymptotic mass of proto gas-giant planets

AbstractAlthough late stage gap formation reduces the surface density in the vicinity of protoplanets, simulations suggest gas may continue to leak through the protoplanets tidal barrier, replenishing the gas supply and allowing protoplanets to acquire masses comparable to or larger than that of Jupiter. Global gas depletion is a possible explanation for gaseous planets with lower masses in weak-line T-Tauri disks and ice giants in our own solar system, but it is unlikely to have stalled the growth of multiple systems around nearby stars that contain relatively low-mass, close-in planets along with more massive and longer period companions. Here, we suggest a potential solution. We show that supersonic infall of surrounding gas onto a protoplanet is only possible interior to both its Bondi and Roche radii. Although the initial Bondi radius is much smaller than its Roche radius, the former overtakes the latter during its growth. Thereafter, a positive pressure gradient is required to induce the gas to enter the Roche lobe of the protoplanet and flow is significantly reduced. We present the results of analysis and numerical simulations to show that the accretion rate increases rapidly with the ratio of the protoplanets Roche to Bondi radii. Based on these results we suggest that in regions with low geometric aspect ratios gas accretion is quenched, resulting in relatively low protoplanetary masses.

Infrared Emission from the Dusty Disk Orbiting GD 362, an Externally Polluted White Dwarf

We report Spitzer Space Telescope photometry between 3.6 microns and 24 microns and spectroscopy between 5 microns and 15 microns of GD 362, a white dwarf with an effective temperature near 10,000 K that displays a remarkably high concentration of metals in its photosphere and a thermal infrared excess. We approximately reproduce both the infrared continuum and the very strong 10 micron silicate emission feature with a model of an orbiting dusty disk which is flat out to 50 stellar radii and warped between 50 and 70 stellar radii. The relatively small amount of cold material implied by the weak 24 mircon flux argues that the disk lies within the Roche radius of the star, and we may be witnessing a system where an asteroidal-size body has been tidally destroyed. If so, determination of the photospheric metal abundances may measure the bulk composition of an extrasolar minor planet.

Tidal Barrier and the Asymptotic Mass of Proto–Gas Giant Planets

Extrasolar planets found with radial velocity surveys have masses ranging from several Earth to several Jupiter masses. While mass accretion onto protoplanetary cores in weak-line T-Tauri disks may eventually be quenched by a global depletion of gas, such a mechanism is unlikely to have stalled the growth of some known planetary systems which contain relatively low-mass and close-in planets along with more massive and longer period companions. Here, we suggest a potential solution for this conundrum. In general, supersonic infall of surrounding gas onto a protoplanet is only possible interior to both of its Bondi and Roche radii. At a critical mass, a protoplanet's Bondi and Roche radii are equal to the disk thickness. Above this mass, the protoplanets' tidal perturbation induces the formation of a gap. Although the disk gas may continue to diffuse into the gap, the azimuthal flux across the protoplanets' Roche lobe is quenched. Using two different schemes, we present the results of numerical simulations and analysis to show that the accretion rate increases rapidly with the ratio of the protoplanet's Roche to Bondi radii or equivalently to the disk thickness. In regions with low geometric aspect ratios, gas accretion is quenched with relatively low protoplanetary masses. This effect is important for determining the gas-giant planets' mass function, the distribution of their masses within multiple planet systems around solar type stars, and for suppressing the emergence of gas-giants around low mass stars.

A Simplified Theoretical Treatment and Simulated Experimental Calculation of the Roche Limit

First calculated theoretically in 1850 by French mathematician Eduardo Roche, the Roche limit is the approximate distance from a Jovian planet beyond which moons are found. Within this distance, tidal forces (differential gravitational forces) are stronger than the gravitational binding forces between particles so moons cannot form and instead rings are found. Tidal forces are the differences in gravitation force exerted on different parts of an object due to being different distances from the source. This paper presents a simulation of a scientific experiment. First, a simple expression for the Roche limit, the boundary between the distances from a Jovian planet that the ring systems and moons are found, is derived. A computer simulation of an observation is then used to test the expression “experimentally.”