However, this is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic. However their rotations are not known or not known enough.

/ 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. {\displaystyle R} A collision occurs between two moons near the Roche limit, shattering both. Review 14 What is unusual about Uranus’s rotation axis? R

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: The Roche limit is reached when the gravitational pull and the tidal force cancel each other out. The Roche limit it basically the point at which differential gravitational forces due to the finte size of an object overcome the forces holding a body together. 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.

μ If satellite and primary are of similar composition, the theoretical limit is about 2 1/2 times the radius of the larger body. 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. The above formulae for the timescale of locking may be off by orders of magnitude, because they ignore the frequency dependence of Take your favorite fandoms with you and never miss a beat. If satellite and primary are of similar composition, the

Using these data, the Roche Limits for rigid and fluid bodies can easily be calculated. (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. m Roche Limit = 2.4 x (Radius of Larger Object) x (Density of the Larger Object/Density of the Smaller Object)^1/3.

The true Roche Limit for a satellite depends on its density and rigidity.

There are two forces on this mass $ u $: the gravitational pull towards the satellite and the gravitational pull towards the primary.

Figure 5: The orbits of Pan at 75% and 50% of its maximum distance from Saturn, compared with Pan's Roche limit and Saturn's Roche limit.

In practice, the densities of most of the inner satellites of giant planets are not known. too small to develop substantial tidal stresses. Note Naiad in particular, which may in fact be quite close to its actual break-up point. Since tidal forces overwhelm gravity within the Roche limit, no large satellite can coalesce out of smaller particles within that limit.

Q Detailed derivation of formulae for calculating the Roche limit,

a .

{\displaystyle Q} The Roche limit is the minimum distance to which a large satellite In these cases (shown in italics), likely values have been assumed, but their actual Roche limit can vary from the value shown. Artificial satellites are

To calculate the "rigid body" Roche limit for a spherical satellite, the cause of the rigidity is neglected but it is assumed that the body does not deform from its spherical shape while being held together only by its own self-gravity.

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. s

The limit was first calculated by the

A large comet collides with a moon near the Roche limit, breaking apart the moon.

The calculation is complex and its result cannot be represented as an algebraic formula.

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