Is the Roche limit used this way?

Is the Roche limit used this way?

We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

Has the Roche limit affect been observed having an effect on an constructed object gravitational wise to cause damage? Could the Roche limit be used to slow an object?

No. The Roche limit refers to the radius at which a satellite which is held together only by its own self gravity is disrupted by tidal forces. Spacecraft are not such satellites, but are much harder to tear apart.

You have asked two different questions, Muze. The title of your question asks whether the Roche limit is dangerous to spacecraft, but the body asks whether the Roche limit has been observed having an effect on an object. The answers to these two very different questions are "no" and "yes".

The main question first: The Roche limit applies to objects that are weakly bound by self gravitation. A good example was Comet Shoemaker-Levy 9, which broke apart into a number of pieces before colliding with Jupiter in 1994. A prior close approach to Jupiter in 1992 tore the comet into pieces thanks to tidal effects. The collision in 1994 was a string of pearls hitting Jupiter.

Spacecraft are held together via welds, nuts and bolts, screws, and inter-atomic and inter-molecular forces. Each of these is many orders of magnitude stronger than is gravitation. The Roche limit doesn't apply to spacecraft as spacecraft aren't held together by gravitation.

Roche limit

In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's gravitational self-attraction. [1] Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit material tends to coalesce. The Roche radius depends on the radius of the first body and on the ratio of the bodies' densities.

The term is named after Édouard Roche (French: [ʁɔʃ] , English: / r ɒ ʃ / ROSH ), who was the French astronomer who first calculated this theoretical limit in 1848. [2]

A Mystery Orbits a Dark Star in ROCHE LIMIT

Roche limit: in astronomy, the minimum distance to which a large satellite can approach its primary body without being torn apart by tidal forces. -Encyclopedia Britannica

The Roche Limit Colony lies at the cusp of an energy anomaly in the Andromeda Galaxy, and on top of a cache of an alien mineral deposit used to make the drug “Recall.” It has become a magnet for greed, crime, a place where people disappear — both because they want to or someone else wants them to. In ROCHE LIMIT, VOLUME 1, the March graphic novel by Michael Moreci (HOAX HUNTERS, HACK/SLASH: SON OF SAMHAIN) and Vic Malhotra (The X-Files: Year Zero, Thumbprint), Sonya Torin wants to find one of those who have disappeared, her sister Bekkah, who came to Roche Limit to help Recall addicts.

Sonya’s only help on the corrupt, lawless colony in finding her sister is Alex Ford, a shifty drug manufacturer with his own set of pursers who are after his Recall formula. As the search for Bekkah leads Sonya deeper into Roche Limit’s underbelly, they move ever closer to a burgeoning spiritual movement with the energy anomaly at its center.

“Both noir and sci-fi are perfect genres to employ for Roche Limit because both have deep underpinnings in existentialism/fatalism,” said writer Moreci in an interview with Comic Bulletin. “I’ve always contended that the best sci-fi examines who we are as humans, particularly in the context of our social mores. Noir is similar, but a bit more personal…. I want to explore that intersection of existentialism and popcorn fiction as only genre fiction can.”

Artist Malhotra inhabits Roche Limit with weary denizens who move through a lived-in, often dilapidated and grimy setting. “I find it really tough to get my imagination going with stories set in sleek sci-fi settings. The sense of history is lost,” he said in the Comics Bulletin interview. “That’s why it’s more fun to draw old buildings rather than new ones or an old tennis shoe rather than a brand new one.”

ROCHE LIMIT, VOLUME 1, the first book in a planned trilogy, will be in comic book stores on March 25 and in bookstores on April 7. It is available for pre-order now.

  • ISBN 978-1-63215-199-5
  • Diamond Comic order code DEC140688
  • 136 pages, paperback, full color
  • $9.99
  • Collects ROCHE LIMIT #1-5
  • Rated Teen Plus (16 and up)
  • In comic book stores March 25, bookstores April 7
  • Retailers, librarians, and reviewers may request a PDF galley from Jennifer de Guzman, Director of Trade Book Sales, [email protected]

Praise for ROCHE LIMIT:

“Moreci and Malhotra are… succeeding at upending expectations of a science fiction story and regaling us with their tale the way they want to tell it. Through great art comes questioning of perception or simply exciting experiences. This artistic team has succeeded at both.” –Keith Dooley, Multiversity Comics

“Moreci’s skilful world-building and Malhotra’s uniquely expressive artwork combine here to create something truly memorable a noir-soaked sci-fi masterclass complete with twists, turns and dramatic, character-driven moments.” –Michael Bettendorf, Comics Bulletin

“This is a series that demands and deserves to be read by any and all sci-fi, comic, and storytelling fans.” –Zac Thompson, Bloody Disgusting

Roche Limit

The Roche limit is named after French astronomy Edouard Roche, who published the first calculation of the theoretical limit, in 1848. The Roche limit is a distance, the minimum distance that a smaller object (e.g. a moon) can exist, as a body held together by its self-gravity, as it orbits a more massive body (e.g. its parent planet) closer in, and the smaller body is ripped to pieces by the tidal forces on it.

Remember how tidal forces come about? Gravity is an inverse-square-law force – twice as far away and the gravitational force is four times as weak, for example – so the gravitational force due to a planet, say, is greater on one of its moon’s near-side (the side facing the planet) than its far-side.

The fine details of whether an object can, in fact, hold up against the tidal force of its massive neighbor depend on more than just the self-gravity of the smaller body. For example, an ordinary star is much more easily ripped to piece by tidal forces – due to a supermassive black hole, say – than a ball of pure diamond (which is held together by the strength of the carbon-carbon bonds, in addition to its self-gravity).

The best known application of Roche’s theoretical work is on the formation of planetary rings: an asteroid or comet which strays within the Roche limit of a planet will disintegrate, and after a few orbits the debris will form a nice ring around the planet (of course, this is not the only way a planetary ring can form small moons can create rings by being bombarded by micrometeorites, or by outgassing).

Roche also left us with two other terms widely used in astronomy and astrophysics, Roche lobe and Roche sphere no surprise to learn that they too refer to gravity in systems of two bodies!

More to explore on Roche limits: Saturn (NASA), Roche Limit (University of Oregon), and Tides and Gravitational Locking.

Check out these Astronomy Cast episodes for more on Roche limits: Tidal Forces, Tidal Forces Across the Universe, and Stellar Roche Limits.

Thread: Mining asteroids. the Roche way?

Just had an interesting idea after reading the entry on Wikipedia (Most deserving homepage IMHO) on the Roche limit. suppose we as a planet started mining asteroids for constructing something-or-other, (stations, orbital towers, dyson sphere, who knows until then?) and had it towed into earth orbit, then to break up the bulk of the material just gently lowered it beyond its Roche limit? Even if its rigidity prevented breakup, I think it would make it easier to break it up and to keep all of its pieces local to each other. Even if over time it spread out into a tiny tiny arc. (Ringlet?)

Then I thought, if we ever decide to explore Titan in more detail, maybe even bring back samples, why not build a small way-station on the far side of Pan from Saturn? It's within its Roche limit, so instead of an orbital elevator to escape pan's gravity well, you'd need only ship it over the horizon before Saturn's tides yanked it off the surface! (Only if Pan is tidally locked with Saturn. Isn't it?)

Anyway, the only education I got with astro-physics is from what I glean off of Wikipedia, so if my trains of thought here are in error, let me know where I went wrong and how? I'm really getting into this field.

At night the stars put on a show for free (Carole King)

I think that you may be seriously underestimating the energy required to get an asteroid into a Roche-limit orbit around the Earth (or other body). You are probably also over-estimating the difficulty in mining the asteroid in-situ.

Aside from that, it is a creative idea.

For volume, you could just assume a sphere. None of them (other than Ceres) are truly spherical, but it should still be good enough for a back of the envelope calculation. For the more potato-shaped asteroids, you could assume an ellipsoid, which would be much more accurate.

AFAIK, density data is not that great for asteroids. It is better for the ones that have moons, but I havn't been able to find enough data to even hazard a guess on average density. I have seen numbers as low as 1.2 g/cm 3 (probably a mostly icy body). For more rocky bodies, you might see densities as high as 3 or 4 g/cm 3 . You best bet would be to just pick a body that we have good numbers for, and use the mass estimate given.

From there, at the speeds we are talking about, it would be perfectly reasonable to use Newtonian mechanics for energy estimates.

Thank you, Saluki. Newtonian mechanics are a way beyond me, though
I'm a neophyte to this sort of thing. What's a good resource where I could dig up the applicable formulae?

Just because I was able to dig up some data on this one, which is around the size you wanted, I did some basic calculations on Dactyl (a moon of Ida) to get you started.

Dactyl is (very) roughly spherical at 1.2 x 1.4 x 1.6 km in diameter. Using the middle figure of 1.4 for a radius, we get a volume of:

V = (4/3)(pi)r 3 = (4/3)(3.14)1.4 3 = 11.5 km 3

I couldn't find density estimates for Dactyl, but the sources say that Dactyl is made of roughly the same material as Ida, and the density estimates for Ida are 2.2 to 2.9 g/cm 3 . Since Dactyl is much smaller than Ida, and probably less compacted, I will take the low number of 2.2. This gives us a mass:

m = 11.5 km 3 (2.2 g/cm 3 )(1 x 10 15 cm 3 /1 km 3 = 25.3 x 10 15 g = 25.3 x 10 12 kg

I will leave the rest to you, but here are some hints:

1. You will first need to accelerate Dactyl to escape the gravity of Ida. Search for "escape velocity".

2. Next, you need to alter the orbit (reduce the energy) of Ida so that it roughly intersects with the orbit of the body you are using for the Roche forces. Search "orbital mechanics" for a discussion of this. A "Hohmann Transfer" may be of use here.

3. Finally, you need to reduce the energy of Ida again so that it is captured by the target planet. Its velocity with respect to the planet would need to be less than the escape velocity of the planet. To get it to the desired orbit, you would need to callculate the correct relative speed for the desired orbit.

Maybe it would be safer and more cost effective to just slam the asteroids onto the moon's surface, then mine out the remains there. Sounds kind of inefficient, though, and that's bound to create a good number of activists. I'll try to work out that formula tonight, Saluki. At work for the time being, and I don't have enough time to devote to it

Roche's limit only applies to objects that are large enough that the tidal forces are enough to overcome the tensile strengh of the material. For a nickel-iron asteroid (the ones worth mining), probably be in the high tens of kilometers across - way too big to move into Earth orbit.

FWIW, we are already mining one asteroid here on Earth. The nickel mine at Sudbury, Ontario, Canada is the site of a huge asteroid impact about 2 billion years ago!

Just because I was able to dig up some data on this one, which is around the size you wanted, I did some basic calculations on Dactyl (a moon of Ida) to get you started.

Dactyl is (very) roughly spherical at 1.2 x 1.4 x 1.6 km in diameter. Using the middle figure of 1.4 for a radius, we get a volume of:

V = (4/3)(pi)r 3 = (4/3)(3.14)1.4 3 = 11.5 km 3

I couldn't find density estimates for Dactyl, but the sources say that Dactyl is made of roughly the same material as Ida, and the density estimates for Ida are 2.2 to 2.9 g/cm 3 . Since Dactyl is much smaller than Ida, and probably less compacted, I will take the low number of 2.2. This gives us a mass:

m = 11.5 km 3 (2.2 g/cm 3 )(1 x 10 15 cm 3 /1 km 3 = 25.3 x 10 15 g = 25.3 x 10 12 kg

I will leave the rest to you, but here are some hints:

1. You will first need to accelerate Dactyl to escape the gravity of Ida. Search for "escape velocity".

2. Next, you need to alter the orbit (reduce the energy) of Ida so that it roughly intersects with the orbit of the body you are using for the Roche forces. Search "orbital mechanics" for a discussion of this. A "Hohmann Transfer" may be of use here.

3. Finally, you need to reduce the energy of Ida again so that it is captured by the target planet. Its velocity with respect to the planet would need to be less than the escape velocity of the planet. To get it to the desired orbit, you would need to callculate the correct relative speed for the desired orbit.

I wouldnt bother trying to stop it in earths orbit. Let the tides tear it apart then do the mining in the belt. Any bits you dont want of your asteroid you can put back into an orbit in the belt.

I would also up the density. Dactyl may be the right size, but I doubt it is the right composition. We dont want carbonates, we want metals. Try a density of 4 or more

Roche limit

Environmentalists today generally prefer to limit roads and block new water projects, even in parched California.

This approach would greatly limit his appeal beyond the Northeast and the west coast.

The argument now is how to limit certain types of plays that banks can make under certain circumstances.

The foremost trendsetter of Scandi-sleek design and New Nordic food knows no limit to its progressive reputation.

Sadly, laws throughout the Middle East—from North Africa to the Gulf—limit the rights of religious minorities and non-believers.

The controlling center of consciousness is the extreme limit of the nares anteri.

They had been permitted to sit up till after the ice-cream, which naturally marked the limit of human indulgence.

Another way of learning such a series by rote, is to limit the extent of the repetitions.

There was no need of Lawrence signaling Dan to come on, for the squad were urging their horses to the limit.

McNeil, his force now augmented by Shaffer's, resolved to push Porter to the limit, and if possible bring him to battle.


The Roche limit typically applies to a satellite's disintegrating due to tidal forces induced by its primary, the body around which it orbits. Parts of the satellite that are closer to the primary are attracted more strongly by gravity from the primary than parts that are farther away this disparity effectively pulls the near and far parts of the satellite apart from each other, and if the disparity (combined with any centrifugal effects due to the object's spin) is larger than the force of gravity holding the satellite together, it can pull the satellite apart. Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Objects resting on the surface of such a satellite would be lifted away by tidal forces. A weaker satellite, such as a comet, could be broken up when it passes within its Roche limit.

Since, within the Roche limit, tidal forces overwhelm the gravitational forces that might otherwise hold the satellite together, no satellite can gravitationally coalesce out of smaller particles within that limit. Indeed, almost all known planetary rings are located within their Roche limit. (Notable exceptions are Saturn's E-Ring and Phoebe ring. These two rings could possibly 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.)

The Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure and rotational splitting are other ways for a comet to split under stress.

The table below shows the mean density and the equatorial radius for selected objects in the Solar System. [ citation needed ]

Primary Density (kg/m 3 ) Radius (m)
Sun 1,408 696,000,000
Earth 5,513 6,378,137
Moon 3,346 1,737,100
Jupiter 1,326 71,493,000
Saturn 687 60,267,000
Uranus 1,318 25,557,000
Neptune 1,638 24,766,000

The equations for the Roche limits relate the minimum sustainable orbital radius to the ratio of the two objects' densities and the radius of the primary body. Hence, using the data above, the Roche limits for these objects can be calculated. This has been done twice for each, assuming the extremes of the rigid and fluid body cases. The average density of comets is taken to be around 500 kg/m 3 .

The table below gives the Roche limits expressed in kilometres and in primary radii. [ citation needed ] The mean radius of the orbit can be compared with the Roche limits. For convenience, the table lists the mean radius of the orbit for each, excluding the comets, whose orbits are extremely variable and eccentric.

Body Satellite Roche limit (rigid) Roche limit (fluid) Mean orbital radius (km)
Distance (km) R Distance (km) R
Earth Moon 9,492 1.49 18,381 2.88 384,399
Earth average comet 17,887 2.80 34,638 5.43 N/A
Sun Earth 556,397 0.80 1,077,467 1.55 149,597,890
Sun Jupiter 894,677 1.29 1,732,549 2.49 778,412,010
Sun Moon 657,161 0.94 1,272,598 1.83 149,597,890 approximately
Sun average comet 1,238,390 1.78 2,398,152 3.45 N/A

These bodies are well outside their Roche limits by various factors, from 21 for the Moon (over its fluid-body Roche limit) as part of the Earth–Moon system, upwards to hundreds for Earth and Jupiter.

The table below gives each satellite's closest approach in its orbit divided by its own Roche limit. [ citation needed ] Again, both rigid and fluid body calculations are given. Note that Pan, Cordelia and Naiad, in particular, may be quite close to their actual break-up points.

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.

The limiting distance to which a satellite can approach without breaking up 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 would lie somewhere between these two extremes, with tensile strength rendering the satellite neither perfectly rigid nor perfectly fluid. For example, a rubble-pile asteroid will behave more like a fluid than a solid rocky one an icy body will behave quite rigidly at first but become more fluid as tidal heating accumulates and its ices begin to melt.

But note that, as defined above, the Roche limit refers to a body held together solely by the gravitational forces which cause otherwise unconnected particles to coalesce, thus forming the body in question. The Roche limit is also usually calculated for the case of a circular orbit, although it is straightforward to modify the calculation to apply to the case (for example) of a body passing the primary on a parabolic or hyperbolic trajectory.

Rigid-satellite calculation Edit

The rigid-body Roche limit is a simplified calculation for a spherical satellite. Irregular shapes such as those of tidal deformation on the body or the primary it orbits are neglected. It is assumed to be in hydrostatic equilibrium. These assumptions, although unrealistic, greatly simplify calculations.

This does not depend on the size of the objects, but on the ratio of densities. This is the orbital distance inside of which loose material (e.g. regolith) on the surface of the satellite closest to the primary would be pulled away, and likewise material on the side opposite the primary will also go away from, rather than toward, the satellite.

Note that this is an approximate result as inertia force and rigid structure are ignored in its derivation.

The orbital period then depends only on the density of the secondary:

where G is the gravitational constant. For example, a density of 3.346 g/cc (the density of our moon) corresponds to an orbital period of 2.552 hours.

Derivation of the formula Edit

In order to determine the Roche limit, 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. Assume that the satellite is in free fall around the primary and that the tidal force is the only relevant term of the gravitational attraction of the primary. This assumption is a simplification as free-fall only truly applies to the planetary center, but will suffice for this derivation. [5]

To obtain this approximation, find the difference in the primary's gravitational pull on the center of the satellite and on the edge of the satellite closest to the primary: [ citation needed ]

The Roche limit is reached when the gravitational force and the tidal force balance each other out. [ citation needed ]

which gives the Roche limit, d , as

The radius of the satellite should not appear in the expression for the limit, so it is re-written in terms of densities.

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

which can be simplified to the following Roche limit:

Roche limit, Hill sphere and radius of the planet Edit

Note : Roche limit and Hill sphere are completely different from each other but are both work of Édouard Roche. [ citation needed ]

Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites whereas Roche limit is the minimum distance to which a satellite can approach its primary body without tidal force overcoming the internal gravity holding the satellite together. [ citation needed ]

Fluid satellites Edit

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.

The calculation is complex and its result cannot be represented in an exact algebraic formula. Roche himself derived the following approximate solution for the Roche limit:

However, a better approximation that takes into account the primary's oblateness and the satellite's mass is:

where c / R is the oblateness of the primary. The numerical factor is calculated with the aid of a computer.

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. [6]

Derivation of the formula Edit

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.

When M is very much bigger than m, this will be close to

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.

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, the form of the surface that satisfies the equipotential condition must be determined.

As the orbit has been assumed circular, the total gravitational force and orbital centrifugal force acting on the main body cancel. That leaves two forces: the tidal force and the rotational centrifugal force. The tidal force 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 FT as given above.

While this force in the rigid model depends only on the radius r of the satellite, in the fluid case, all the points on the surface must be considered, 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. Since the tidal force is linear in Δd, the related potential is proportional to the square of the variable and for m ≪ M we have

Likewise, the centrifugal force has a potential

for rotational angular velocity ω .

We want to determine the shape of the satellite for which the sum of the self-gravitation potential and VT + VC 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 To a first approximation, we can ignore the centrifugal potential VC and consider only the tidal potential VT.

Since the potential VT changes only in one direction, i.e. the direction toward 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 VT 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:

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

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

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 VT is equal to VS plus a constant independent of the variable Δd. By inspection, this occurs when

This equation can 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.

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.

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

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,

Surprisingly, including the centrifugal potential makes remarkably little difference, though the object becomes a Roche ellipsoid, a general triaxial ellipsoid with all axes having different lengths. The potential becomes a much more complicated function of the axis lengths, requiring elliptic functions. However, the solution proceeds much as in the tidal-only case, and we find

The ratios of polar to orbit-direction to primary-direction axes are 1:1.06:2.07.

Roche limit

If a planet and a satellite have identical densities, then the Roche limit is 2.446 times the radius of the planet. Some 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 Metis
, in astronomy, one of the 39 known moons, or natural satellites, of Jupiter.
. Click the link for more information. and Saturn's moon Pan Pan,
in astronomy, one of the named moons, or natural satellites, of Saturn. Also known as Saturn XVIII (or S18), Pan is 12.5 mi (20 km) in diameter, orbits Saturn at a mean distance of 83,000 mi (133,583 km), and has an orbital period of 0.575 earth days.
. Click the link for more information. are examples of natural satellites that survive despite being within their Roche limits&mdashthey hold together largely because of their tensile strength. A weaker body, such as a comet comet
[Gr.,=longhaired], a small celestial body consisting mostly of dust and gases that moves in an elongated elliptical or nearly parabolic orbit around the sun or another star. Comets visible from the earth can be seen for periods ranging from a few days to several months.
. Click the link for more information. , could be broken up when it passes within its Roche limit. For example, comet Shoemaker-Levy 9's decaying orbit around Jupiter passed within its Roche limit in July, 1992, causing it to break into a number of smaller pieces. All known planetary rings are located within the Roche limit, and may be either remnants from the planet's protoplanetary accretion disc that did not amalgamate into satellites or fragments from a body passed within its Roche limit and broke apart.

Thread: Roche limit

That number (2.46) depends on the density of the planet or star. It should also be noted that small objects (man-made objects and rocks) are held together by molecular cohesion, and not gravity, and are not subject to the Roche Limit. Hence, you, who are 1.00 times the Earth&#39s Radius from the cnter of the Earth are not ripped apart by differential gravitation.

The point of the Roche limit is that the difference in gravity that the less massive object feels from the more massive object is different from the closest point between them and the furthest. There is some orbit that is so close that the difference between those two points exceeds the gravity that binds the less massive object together. Note also that if the less massive object is spinning rapidly with an axis near perpendicular to the plane of the orbit, the Roche Limit might be even more distant.

It is said that the Moon will eventually come too close and get broken into rings, but I have the impression that the Sun will vaporize it or rip it away from the Earth first.

Saturn&#39s rings, and the rings of all of the planets that have them are within that planet&#39s Roche Radius. All are believed to have been moons that drifted within the Roche Limit and were then torn apart into rings. The rings will slowly settle into those planets and not exist in the future.

And the Earth&#39s Moon is slowly drifting away from the Earth and will continue to do so until they reach an equilibrium that will coincide with them being doubly resonant.

Figure 7 shows two satellites that some planetary astronomers feel may be undergoing tidal stress.

Figure 7: Satellites Atlas (Jupiter) and Pan (Saturn) (Source).

The following quote from Quora does a nice job describing why satellites like these are hanging together.

Pan and Metis are held together by tensile forces. Tensile strength of a body is the maximum stress it can withstand before being pulled apart by stretching. Had their core been weaker, they would have disintegrated. The tidal forces affecting the bodies is why both the satellites are irregularly shaped. It is presumed that the primary's tidal forces can actually lift an object off the satellites' surface. Naturally, since the satellites are so close to their respective planets, there is massive tidal deceleration at play. This means that the satellites are gradually spiraling towards the primaries, owing to the decay of their orbits. The tidal forces are constantly tugging at the satellites. Pan's surface (as we've discovered from Cassini) consists of a large amount of porous material that it has accreted. The particles are weakly bound by their self-gravity, and had there been no other satellites, would eventually shear out forming large clumps before they disintegrate and the particles join other clumps.

Watch the video: How Close Can Moons Orbit? Understanding the Roche Limit (May 2022).


  1. Tojarn

    It seems to me, what is it it was already discussed.

  2. Kazitaxe

    Understandably, many thanks for your assistance on this matter.

  3. Espen

    I'm sorry, but, in my opinion, they were wrong. Write to me in PM, it talks to you.

  4. Nekazahn

    In my opinion, it is a lie.

  5. Arashijar

    Quite right! The idea is great, I agree with you.

Write a message