NationMaster - Encyclopedia: Roche limit

Consider an orbiting mass of fluid held together by gravity, here viewed from above the orbital plane. Far from the Roche limit the mass is practically spherical.

Closer to the Roche limit the body is deformed by tidal forces.

Within the Roche limit the mass's own gravity can no longer withstand the tidal forces, and the body disintegrates.

Particles closer to the primary move more quickly than particles farther away, as represented by the red arrows.

The varying orbital speed of the material eventually causes it to form a ring.

The Roche limit, sometimes referred to as the Roche radius, is the distance within which a celestial body held together only by its own gravity will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. The term is named after Édouard Roche, the French astronomer who first calculated this theoretical limit in 1848. Image File history File links drawn by Theresa Knott File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Drawn by Theresa Knott File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... Image File history File links Drawn by Theresa Knott File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Drawn by Theresa Knott (Nate the Stork) 13:39, 5 Sep 2004 (UTC) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Drawn by Theresa Knott File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Gravity is a force of attraction that acts between bodies that have mass. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... Look up coalescence in Wiktionary, the free dictionary. ... Ã‰douard Albert Roche (1820-1883) was a French scientist. ... A giant Hubble mosaic of the Crab Nebula, a supernova remnant. ... 1848 (MDCCCXLVIII) was a leap year starting on Saturday of the Gregorian calendar. ...

Typically, the Roche limit applies to a satellite disintegrating due to tidal forces induced by its primary, the body about which it orbits. Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Jupiter's moon Metis and Saturn's moon Pan are examples of such satellites, which hold together because of their tensile strength. In extreme cases, objects resting on the surface of such a satellite could actually be lifted away by tidal forces. A weaker satellite, such as a comet, could be broken up when it passes within its Roche limit. MILSTAR:A communication satellite A satellite is any object that orbits another object (which is known as its primary). ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... Moons of the Solar System scaled to Earths Moon A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... For other uses, please see Satellite (disambiguation) A satellite is an object that orbits another object (known as its primary). ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Atmospheric pressure 0 kPa Metis (mee-tÉ™s, IPA: , Greek ÎœÎ®Ï„Î¹Ï‚), or Jupiter XVI, is the innermost member of the Jupiters small inner moons and thus Jupiters innermost moon. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Atmosphere none Pan (pan, Greek Î Î¬Î½) is a moon of Saturn, named after the god Pan. ... Tensile strength measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ... Comet Hale-Bopp A comet is a small body in the solar system that orbits the Sun and (at least occasionally) exhibits a coma (or atmosphere) and/or a tail â€” both primarily from the effects of solar radiation upon the comets nucleus, which itself is a minor body composed...

Since tidal forces overwhelm gravity within the Roche limit, no large satellite can coalesce out of smaller particles within that limit. Indeed, almost all known planetary rings are located within their Roche limit (Saturn's E-Ring being a notable exception). They could either be remnants from the planet's proto-planetary accretion disc that failed to coalesce into moonlets, or conversely have formed when a moon passed within its Roche limit and broke apart. A planetary ring is a ring of dust and other small particles orbiting around a planet in a flat disc-shaped region. ... The full set of rings The rings of Saturn are a series of planetary rings that orbit the planet Saturn. ... Artists conception of a binary star system with one black hole and one main sequence star An accretion disc (or accretion disk) is a structure formed by material falling into a gravitational source. ...

(Note that the Roche limit should not be confused with the concept of the Roche lobe or Roche sphere, which are also named after Édouard Roche. The Roche lobe describes the limits at which an object which is in orbit around two other objects will be captured by one or the other. The Roche sphere approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits.) A three-dimensional representation of the Roche potential in a binary star with a mass ratio of 2, in the co-rotating frame. ... A Hill sphere approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits. ... Gravity is a force of attraction that acts between bodies that have mass. ... See lists of astronomical objects for a list of the various lists of astronomical objects in Wikipedia. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

1 Determining the Roche limit
- 1.1 Rigid satellites
  - 1.1.1 Derivation of the formula
- 1.2 Fluid satellites
  - 1.2.1 Derivation of the formula
2 Roche limits for selected examples
3 See also
4 References
5 External links

Determining the Roche limit

The Roche limit depends on the rigidity of the satellite. At one extreme, a completely rigid satellite will maintain its shape until tidal forces break it apart. At the other extreme, a highly fluid satellite gradually deforms leading to increased tidal forces, causing the satellite to elongate, further compounding the tidal forces and causing it to break apart more readily. Most real satellites are somewhere between these two extremes, with internal friction, viscosity, and tensile strength rendering the satellite neither perfectly rigid nor perfectly fluid. Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. ... The pitch drop experiment at the University of Queensland. ...

Rigid satellites

To calculate the rigid body Roche limit for a spherical satellite, the cause of the rigidity is neglected but the body is assumed to maintain its spherical shape while being held together only by its own self-gravity. Other effects are also neglected, such as tidal deformation of the primary, rotation of the satellite, and its irregular shape. These somewhat unrealistic assumptions greatly simplify the Roche limit calculation. A sphere (< Greek ÏƒÏ†Î±Î¯ÏÎ±) is a perfectly symmetrical geometrical object. ...

The Roche limit, $d$ , for a rigid spherical satellite orbiting a spherical primary is

$d = Rleft( 2;frac {rho_M} {rho_m} right)^{frac{1}{3}}$ ,

where $R$ is the radius of the primary, $ρ M$ is the density of the primary, and $ρ m$ is the density of the satellite. Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... Density, or volumic mass (ISO 31), is a measure of mass per given unit volume. ...

Notice that if the satellite is more than twice as dense as the primary (as can easily be the case for a rocky moon orbiting a gas giant) then the Roche limit will be inside the primary and hence not relevant.

Derivation of the formula

In order to determine the Roche limit, we consider a small mass $u$ on the surface of the satellite closest to the primary. There are two forces on this mass $u$ : the gravitational pull towards the satellite and the gravitational pull towards the primary. Since the satellite is already in orbital free fall around the primary, the tidal force is the only relevant term of the gravitational attraction of the primary. Free fall in its strictest sense is the condition of acceleration which is due only to gravity. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

The gravitational pull $F G$ on the mass $u$ towards the satellite with mass $m$ and radius $r$ can be expressed according to Newton's law of gravitation. Image File history File links A copy of the now misnamed GFDL image Image:Roche limit (two spheres). ... The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. ...

$F_G = frac{Gmu}{r^2}$

The tidal force $F T$ on the mass $u$ towards the primary with radius $R$ and a distance $d$ between the centers of the two bodies can be expressed as Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

$F_T = frac{2GMur}{d^3}$ .

The Roche limit is reached when the gravitational pull and the tidal force cancel each other out.

$F_G = F_T ;$

$frac{Gmu}{r^2} = frac{2GMur}{d^3}$ ,

which quickly gives the Roche limit, $d$ , as

$d = r left( 2;frac{M}{m} right)^{frac{1}{3}}$

However, we don't really want the radius of the satellite to appear in the expression for the limit, so we re-write this in terms of densities.

For a sphere the mass $M$ can be written as

$M = frac{4pirho_M R^3}{3}$ where

R

is the radius of the primary.

And likewise

$m = frac{4pirho_m r^3}{3}$ where

r

is the radius of the satellite.

Substituting for the masses in the equation for the Roche limit, and cancelling out $4π / 3$ gives

$d = r left( frac{ 2 rho_M R^3 }{ rho_m r^3 } right)^{1/3}$ ,

which can be simplified to the Roche limit:

$d = Rleft( 2;frac {rho_M} {rho_m} right)^{frac{1}{3}}$ .

Fluid satellites

A more accurate approach for calculating the Roche Limit takes the deformation of the satellite into account. An extreme example would be a tidally locked liquid satellite orbiting a planet, where any force acting upon the satellite would deform it (into a prolate spheroid). Tidal locking makes one side of an astronomical body always face another, like the Moon facing the Earth. ... In mathematics, a spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ...

The calculation is complex and its result cannot be represented as an algebraic formula. The Roche Limit is given by

$d approx 2.423Rleft( frac {rho_M} {rho_m} right)^{1/3}$

The numerical factor is calculated with the aid of a computer. Historically, Roche himself derived a similar formula with the numerical factor 2.44.

The fluid solution is appropriate for bodies that are only loosely held together, such as a comet. For instance, comet Shoemaker-Levy 9's decaying orbit around Jupiter passed within its Roche limit in July 1992, causing it to fragment into a number of smaller pieces. On its next approach in 1994 the fragments crashed into the planet. Shoemaker-Levy 9 was first observed in 1993, but its orbit indicated that it had been captured by Jupiter a few decades prior. [1] Hubble Space Telescope image of Comet Shoemaker-Levy 9, taken on May 17, 1994. ... 1992 (MCMXCII) was a leap year starting on Wednesday. ... 1994 (MCMXCIV) was a common year starting on Saturday of the Gregorian calendar, and was designated as the International Year of the Family and the International Year of the Sport and the Olympic Ideal by United Nations. ...

Derivation of the formula

As the fluid satellite case is more delicate than the rigid one, the satellite is described with some simplifying assumptions. First, assume the object consists of incompressible fluid that has constant density $ρ m$ and volume $V$ that do not depend on external or internal forces.

Second, assume the satellite moves in a circular orbit and it remains in synchronous rotation. This means that the angular speed $ω$ at which it rotates around its center of mass is the same as the angular speed at which it moves around the overall system barycenter. In astronomy, synchronous rotation is a planetological term describing a body orbiting another, where the orbiting body takes as long to rotate on its axis as it does to make one orbit; and therefore always keeps the same hemisphere pointed at the body it is orbiting. ...

The angular speed $ω$ is given by Kepler's third law: Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ...

$omega^2 = G , frac{M + m}{d^3}$

The synchronous rotation implies that the liquid does not move and the problem can be regarded as a static one. Therefore, the viscosity and friction of the liquid in this model do not play a role, since these quantities would play a role only for a moving fluid. The pitch drop experiment at the University of Queensland. ... Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. ...

Given these assumptions, the following forces should be taken into account:

The force of gravitation due to the main body;
the centrifugal force in the rotary reference system; and
the self-gravitation field of the satellite.

Since all of these forces are conservative, they can be expressed by means of a potential. Moreover, the surface of the satellite is an equipotential one. Otherwise, the differences of potential would give rise to forces and movement of some parts of the liquid at the surface, which contradicts the static model assumption. Given the distance from the main body, our problem is to determine the form of the surface that satisfies the equipotential condition. Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ...

Radial distance of one point on the surface of the ellipsoid to the center of mass

As the orbit has been assumed circular, we know that the total gravitational force and centrifugal force acting on the main body cancel. Therefore, the force that affects the particles of the liquid is the tidal force, which depends on the position with respect to the center of mass (already considered in the rigid model). For small bodies, the distance of the liquid particles from the center of the body is small in relation to the distance d to the main body. Thus the tidal force can be linearized, resulting in the same formula for F_T as given above. While this force in the rigid model depends only on the radius r of the satellite, in the fluid case we need to consider all the points on the surface and the tidal force depends on the distance Δd from the center of mass to a given particle projected on the line joining the satellite and the main body. We call Δd the radial distance (see the picture). Since the tidal force is linear in Δd, the related potential is proportional to the square of the variable and for $mll M$ we have Image File history File links Roche_delta. ... Image File history File links Roche_delta. ...

$V_T = - frac{3 G M }{2 d^3}Delta d^2 ,$

We want to determine the shape of the satellite for which the sum of the self-gravitation potential and $V T$ is constant on the surface of the body. In general, such a problem is very difficult to solve, but in this particular case, it can be solved by a skillful guess due to the square dependence of the tidal potential on the radial distance Δd

Since the potential V_T changes only in one direction (i.e. the direction to the main body), the satellite can be expected to take an axially symmetric form. More precisely, we may assume that it takes a form of a solid of revolution. The self-potential on the surface of such a solid of revolution can only depend on the radial distance to the center of mass. Indeed, the intersection of the satellite and a plane perpendicular to the line joining the bodies is a disc whose boundary by our assumptions is a circle of constant potential. Should the difference between the self-gravitation potential and V_T be constant, both potentials must depend in the same way on Δd. In other words, the self-potential has to be proportional to the square of Δd. Then it can be shown that the equipotential solution is an ellipsoid of revolution. Given a constant density and volume the self-potential of such body depends only on the eccentricity ε of the ellipsoid: In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis) that lies on the same plane. ... (This page refers to eccentricity in mathematics. ...

$V_s = V_{s_{0}} + G pi rho_m cdot f (epsilon) cdot Delta d^2,$

where $V_{s_0}$ is the constant self-potential on the intersection of the circular edge of the body and the central symmetry plane given by the equation Δd=0.

The dimensionless function f is to be determined from the accurate solution for the potential of the ellipsoid

$f(epsilon) = frac{1 - epsilon^2}{epsilon^3} cdot left[ left(3-epsilon^2 right) cdot mathrm{arsinh} left(frac{epsilon}{sqrt{1-epsilon^2}} right) -3 epsilon right]$

and, surprisingly enough, does not depend on the volume of the satellite.

The graph of the dimensionless function f which indicates how the strength of the tidal potential depends on the eccentricity ε of the ellipsoid

Although the explicit form of the function f looks complicated, it is clear that we may and do choose the value of ε so that the potential V_T is equal to V_S plus a constant independent of the variable Δd. By inspection, this occurs when Image File history File links Download high-resolution version (905x665, 7 KB) Created with Gnuplot by CWitte. ... Image File history File links Download high-resolution version (905x665, 7 KB) Created with Gnuplot by CWitte. ...

$frac{2 G pi rho_M R^3}{d^3} = G pi rho_m f(epsilon)$

This equation can easily be solved numerically. The graph indicates that there are two solutions and thus the smaller one represents the stable equilibrium form (the ellipsoid with the smaller eccentricity). This solution determines the (eccentricity of) the tidal ellipsoid as a function of the distance to the main body. The derivative of the function f has a zero where the maximal eccentricity is attained. This corresponds to the Roche limit.

The derivative of f determines the maximal eccentricity. This gives the Roche limit.

More precisely, the Roche limit is determined by the fact that the function f, which can be regarded as a (nonlinear) measure of the force squeezing the ellipsoid towards a spherical shape, is bounded so that there is an eccentricity at which this contracting force becomes maximal. Since the tidal force increases when the satellite approaches the main body, it is clear that there is a critical distance at which the ellipsoid is torn up. Image File history File links Download high-resolution version (907x686, 5 KB) Created with Gnuplot by CWitte. ... Image File history File links Download high-resolution version (907x686, 5 KB) Created with Gnuplot by CWitte. ...

The maximal eccentricity can be calculated numerically as the zero of the derivative of f' (see the diagram). One obtains

$epsilon_textrm{max}approx 0{.}86$

which corresponds to the ratio of the ellipsoid axes 1:1.95. Inserting this into the formula for the function f one can determine the minimal distance at which the ellipsoid exists. This is the Roche limit,

$d approx 2{,}423 cdot R cdot sqrt[3]{ frac {rho_M} {rho_m} } ,.$

Roche limits for selected examples

The table below shows the mean density and the equatorial radius for selected objects in our solar system. Major features of the Solar System (not to scale): The Sun, the eight planets, the asteroid belt containing the dwarf planet Ceres, outermost there is the dwarf planet Pluto (the dwarf planet Eris not shown), and a comet. ...

Primary	Density (kg/m³)	Radius (m)
Sun	1408	696,000,000
Jupiter	1326	71,492,000
Earth	5513	6,378,137
Moon	3346	1,738,100
Saturn	687.3	60,268,000
Uranus	1318	25,559,000
Neptune	1638	24,764,000

Using these data, the Roche Limits for rigid and fluid bodies can easily be calculated. The average density of comets is taken to be around 500 kg/m³. The Sun is the star of our solar system. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Earth (IPA: , often referred to as the Earth, Terra, the World or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... Adjective lunar Bulk silicate composition (estimated wt%) SiO2 44. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Atmospheric characteristics Atmospheric pressure 120 kPa Hydrogen 83% Helium 15% Methane 1. ... Atmospheric characteristics Surface pressure â‰«100 MPa Hydrogen - H2 80% Â±3. ... Comet Hale-Bopp A comet is a small body in the solar system that orbits the Sun and (at least occasionally) exhibits a coma (or atmosphere) and/or a tail â€” both primarily from the effects of solar radiation upon the comets nucleus, which itself is a minor body composed...

The table below gives the Roche limits expressed in metres and in primary radii. The true Roche Limit for a satellite depends on its density and rigidity.

Body	Satellite	Roche limit (rigid)		Roche limit (fluid)
Body	Satellite	Distance (km)	R	Distance (km)	R
Earth	Moon	9,496	1.49	18,261	2.86
Earth	average Comet	17,880	2.80	34,390	5.39
Sun	Earth	554,400	0.80	1,066,300	1.53
Sun	Jupiter	890,700	1.28	1,713,000	2.46
Sun	Moon	655,300	0.94	1,260,300	1.81
Sun	average Comet	1,234,000	1.78	2,374,000	3.42

If the primary is less than half as dense as the satellite, the rigid-body Roche Limit is less than the primary's radius, and the two bodies may collide before the Roche limit is reached.

How close are the solar system's moons to their Roche limits? The table below gives each inner satellite's orbital radius divided by its own Roche radius. Both rigid and fluid body calculations are given. Note Pan and Naiad in particular, which may be quite close to their actual break-up points. Atmosphere none Pan (pan, Greek Î Î¬Î½) is a moon of Saturn, named after the god Pan. ... A simulated view of Naiad orbiting Neptune with The Sun in the distance. ...

In practice, the densities of most of the inner satellites of giant planets are not known. In these cases (shown in italics), likely values have been assumed, but their actual Roche limit can vary from the value shown.

Primary	Satellite	Orbital Radius vs. Roche limit
Primary	Satellite	(rigid)	(fluid)
Sun	Mercury	104:1	54:1
Earth	Moon	41:1	21:1
Mars	Phobos	172%	89%
Mars	Deimos	451%	234%
Jupiter	Metis	~186%	~94%
	Adrastea	~188%	~95%
	Amalthea	175%	88%
	Thebe	254%	128%
Saturn	Pan	142%	70%
	Atlas	156%	78%
	Prometheus	162%	80%
	Pandora	167%	83%
	Epimetheus	200%	99%
	Janus	195%	97%
Uranus	Cordelia	~154%	~79%
	Ophelia	~166%	~86%
	Bianca	~183%	~94%
	Cressida	~191%	~98%
	Desdemona	~194%	~100%
	Juliet	~199%	~102%
Neptune	Naiad	~139%	~72%
	Thalassa	~145%	~75%
	Despina	~152%	~78%
	Galatea	153%	79%
	Larissa	~218%	~113%
Pluto	Charon	12.5:1	6.5:1

class="preview" id="pv88"> The Sun is the star of our solar system. ... Note: This article contains special characters. ... Earth (IPA: , often referred to as the Earth, Terra, the World or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... Adjective lunar Bulk silicate composition (estimated wt%) SiO2 44. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... Phobos (IPA or , Greek Î¦ÏŒÎ²Î¿Ï‚: Fright), is the larger and innermost of Mars two moons (the other being Deimos), and is named after Phobos, son of Ares (Mars) from Greek Mythology. ... Deimos (IPA or ; Greek Î”ÎµÎ¯Î¼Î¿Ï‚: Dread), is the smaller and outermost of Marsâ€™ two moons, named after Deimos from Greek Mythology. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Atmospheric pressure 0 kPa Metis (mee-tÉ™s, IPA: , Greek ÎœÎ®Ï„Î¹Ï‚), or Jupiter XVI, is the innermost member of the Jupiters small inner moons and thus Jupiters innermost moon. ... Atmospheric pressure 0 kPa Adrastea (IPA: , ad-ra-stee-a, Greek Î‘Î´ÏÎ¬ÏƒÏ„ÎµÎ¹Î±) is the second of Jupiters known moons (counting outward from the planet). ... Atmospheric pressure 0 kPa Amalthea (am-É™l-thee-É™, IPA: , Greek Î‘Î¼Î¬Î»Î¸ÎµÎ¹Î±) is the third moon of Jupiter (in order of distance from the planet), and the fifth in order of discovery, hence its Roman numeral designation of Jupiter V. It was discovered on September 9, 1892 by Edward Emerson Barnard using... Atmospheric pressure 0 kPa Thebe (thee-bee, IPA ; Greek Î˜Î®Î²Î·) is the fourth of Jupiters known moons by distance from the planet. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Atmosphere none Pan (pan, Greek Î Î¬Î½) is a moon of Saturn, named after the god Pan. ... Atmospheric pressure 0 kPa Atlas (at-lus, Greek Î†Ï„Î»Î±Ï‚) is a moon of Saturn. ... Prometheus (proe-mee-thee-us, Greek Î ÏÎ¿Î¼Î·Î¸ÎÎ±Ï‚) is a moon of Saturn. ... Pandora (pan-dor-a, Greek Î Î±Î½Î´ÏŽÏÎ±) is a moon of Saturn. ... Epimetheus (ep-i-mee-thee-us, Greek Î•Ï€Î¹Î¼Î·Î¸ÎµÏÏ‚) is a moon of Saturn. ... Janus (jay-nus, Greek Î™Î±Î½ÏŒÏ‚) is a moon of Saturn. ... Atmospheric characteristics Atmospheric pressure 120 kPa Hydrogen 83% Helium 15% Methane 1. ... Atmospheric pressure 0 kPa Cordelia (kor-dee-lee-a) is the innermost moon of Uranus. ... Atmospheric pressure 0 kPa Ophelia (o-fee-lee-a) is a moon of Uranus. ... Bianca orbiting Uranus There is also an asteroid called 218 Bianca. ... Atmospheric pressure 0 kPa Cressida (kres-i-da) is a moon of Uranus. ... Atmospheric pressure 0 kPa Desdemona (dez-di-moe-na) is a moon of Uranus. ... Atmospheric pressure 0 kPa Juliet (jew-lee-et ) is a moon of Uranus. ... Atmospheric characteristics Surface pressure â‰«100 MPa Hydrogen - H2 80% Â±3. ... A simulated view of Naiad orbiting Neptune with The Sun in the distance. ... A simulated view of Thalassa orbiting Neptune. ... A simulated view of Despina orbiting Neptune Despina (des-pee-na or des-pye-na; Latin DespÅ“na from Greek Î”ÎµÏƒÏ€Î¿Î¯Î½Î·) is the third known moon of Neptune. ... A simulated view of Galatea orbiting Neptune Galatea (gal-a-tee-a, Greek Î“Î±Î»Î±Ï„ÎµÎ¯Î±) is the fourth known moon of Neptune, named after Galatea, one of the Nereids of Greek legend. ... A simulated view of Larissa orbiting Neptune Larissa (la-ris-a, Greek Î›Î¬Ïá¿‘ÏƒÎ±) is the fifth of Neptunes known moons. ... Atmospheric characteristics Atmospheric pressure 0. ... Media:Example. ...

References

Édouard Roche: La figure d'une masse fluide soumise à l'attraction d'un point éloigné, Acad. des sciences de Montpellier, Vol. 1 (1847-50) p. 243

External links

Detailed derivation of formulae for calculating the Roche limit

Categories: Celestial mechanics | Space science | Gravity Image File history File links LinkFA-star. ...

Results from FactBites:

Roche Limit: Why Do Comets Break Up? (742 words)
	Earth’s Roche limit for comets is 34,700 km or 5.43 radii and for asteroids, 19,000 km or 2.98 radii.
	Jupiter’s limit for comets is 242,000 km or 3.38 radii and for asteroids is 133,000 km or 1.86 radii.
	Saturn’s limit for comets is 164.000 km or 2.72 radii and for asteroids is 90.200 km or 1.50 radii.

More results at FactBites »

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Contents

Rigid satellites

Derivation of the formula

Fluid satellites

Derivation of the formula

Roche limits for selected examples

See also

References

External links