Sesquinary Catastrophe: Runaway Moon Erosion

• Sesquinary catastrophe is a runaway collisional cascade in which ejecta from small, close-in moons escape and later re-impact at velocities that cause net mass loss.
• The mechanism leverages differential precession and orbital excitation to amplify small differences between ejecta and source, resulting in high-speed, erosive collisions.
• Its applications span planetary moons like Deimos and Saturnian moonlets to minor planets orbiting white dwarfs, providing insights into debris disk formation and re-accretion dynamics.

Sesquinary catastrophe is a runaway collisional erosion process in which ejecta launched from a small body escape that body, remain bound to the central gravitating primary, and later re-impact the source at velocities high enough to produce net mass loss rather than reaccretion. In planetary science, the mechanism was identified for small, close-in moons on dynamically excited orbits, where differential precession between the source moon and its ejecta drives high-speed returns; the expected end-state is destruction into debris followed by re-accretion onto a dynamically colder orbit (Ćuk et al., 2023). Subsequent work has used the mechanism to reconcile Deimos’s plausibly excited past with its presently cool orbit and has extended the framework to minor planets orbiting white dwarfs, where analogous re-impact cascades can operate exterior to the Roche radius (Anand et al., 17 Dec 2025, Veras et al., 7 Jul 2025).

1. Terminology and conceptual scope

In the relevant literature, “sesquinary” describes impact ejecta launched from a satellite that escape that satellite’s gravity, go onto their own planetocentric orbits, and later re-impact the same satellite. Ordinary cratering and secondary cratering are therefore distinct from sesquinary phenomena: primary craters are made by impactors unrelated to the target, whereas secondary craters are made by sub-orbital ejecta that fall back without escaping the target’s gravity (Ćuk et al., 2023).

A sesquinary catastrophe is the destabilized limit of this process. Instead of gentle reaccretion, returning ejecta collide at velocities sufficiently large that each impact excavates and liberates more mass than it reaccretes, producing a self-amplifying erosion sequence. The 2023 formulation describes a runaway erosion or disruption of a small, close-in moon on a dynamically excited orbit; the 2025 Deimos study reframes the same process as a runaway collisional cascade that converts the moon into a Roche-exterior debris disk and then into a dynamically cool, porous body through re-accretion (Ćuk et al., 2023, Anand et al., 17 Dec 2025).

The mechanism is not restricted to Mars. The same logic has been applied to Saturnian resonant moonlets, Neptune’s Naiad, Jupiter’s Thebe, and minor planets orbiting white dwarfs. This suggests that sesquinary catastrophe is best understood as a generic dynamical-collisional instability of low-escape-speed bodies whose returning ejecta can be kinematically amplified by orbital excitation and secular misalignment (Veras et al., 7 Jul 2025).

2. Dynamical mechanism of runaway re-impact

The canonical sequence begins with an impact or mutual collision that produces ejecta. A fraction of the ejecta escape the source moon with speed at least the moon’s escape speed,

$v_{\rm esc,m} = \sqrt{\frac{2 G M_m}{R_m}},$

but remain bound to the central planet because $v_{\rm esc,m} \ll v_k$ for close-in moons, where

$v_k = \sqrt{\frac{G M_p}{a_m}}.$

The escaping fragments enter planet-bound orbits whose semimajor axis, eccentricity, and inclination differ only slightly from those of the source, so the fragments initially “inherit” the moon’s dynamical state (Ćuk et al., 2023).

The crucial amplification arises from differential precession. In the Solar System formulation, the longitude of ascending node and argument of periapse precess at rates controlled by the primary’s oblateness:

$n = \sqrt{\frac{G M_p}{a^3}},$

$$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$

$$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$

Even tiny differences in $a$, $e$, and $i$ between the source and the ejecta therefore cause their nodes and periapses to shear apart. Encounters then occur after apsidal and/or nodal misalignment, so the re-impact velocity is dominated not by the launch speed but by the orbital excitation of the source orbit (Ćuk et al., 2023).

The characteristic encounter speed scales as

$v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$

and the impact speed is

$v_{\rm esc,m} \ll v_k$0

For the smallest moons, $v_{\rm esc,m} \ll v_k$1, so gravitational focusing is a minor correction. Once impacts are erosive rather than accretive, the moon loses mass, more ejecta are created, and the process accelerates into a runaway (Ćuk et al., 2023).

The Deimos-specific formulation adds an explicit positive-feedback channel through the mass dependence of the return time. Using

$v_{\rm esc,m} \ll v_k$2

the authors simplify the timescale to

$v_{\rm esc,m} \ll v_k$3

As erosion lowers $v_{\rm esc,m} \ll v_k$4, $v_{\rm esc,m} \ll v_k$5 shortens and impact cadence accelerates, reinforcing the runaway (Anand et al., 17 Dec 2025).

3. Quantitative diagnostics and instability thresholds

The primary susceptibility metric in the 2023 and white-dwarf formulations is

$v_{\rm esc,m} \ll v_k$6

The paper adopts $v_{\rm esc,m} \ll v_k$7 for rubble piles and $v_{\rm esc,m} \ll v_k$8 for cohesive or strong bodies. A necessary condition for susceptibility is therefore

$v_{\rm esc,m} \ll v_k$9

All else equal, small, low-density moons close to the planet are more vulnerable because $v_k = \sqrt{\frac{G M_p}{a_m}}.$0 is small while $v_k = \sqrt{\frac{G M_p}{a_m}}.$1 is large (Ćuk et al., 2023).

The Deimos study uses a related but differently named parameter,

$v_k = \sqrt{\frac{G M_p}{a_m}}.$2

with typical sesquinary re-impact speeds scaling as

$v_k = \sqrt{\frac{G M_p}{a_m}}.$3

Using N-body simulations with collisional fragmentation and a semi-analytical model calibrated to those simulations, the authors find a formal threshold near $v_k = \sqrt{\frac{G M_p}{a_m}}.$4 for strengthless targets, but adopt $v_k = \sqrt{\frac{G M_p}{a_m}}.$5 as the conservative disruption threshold because of uncertainties in material strength, radiation forces on small debris, and numerical artifacts (Anand et al., 17 Dec 2025).

The Deimos work also gives an explicit angle-averaged cratering mass-loss law in terms of $v_k = \sqrt{\frac{G M_p}{a_m}}.$6:

$v_k = \sqrt{\frac{G M_p}{a_m}}.$7

From the N-body runs, the normalized distribution of $v_k = \sqrt{\frac{G M_p}{a_m}}.$8 is well fit by a log-normal probability density

$v_k = \sqrt{\frac{G M_p}{a_m}}.$9

with shape $n = \sqrt{\frac{G M_p}{a^3}},$0 and scale $n = \sqrt{\frac{G M_p}{a^3}},$1 (Anand et al., 17 Dec 2025).

The re-impact timescale in the 2023 study is

$n = \sqrt{\frac{G M_p}{a^3}},$2

with

$n = \sqrt{\frac{G M_p}{a^3}},$3

Short $n = \sqrt{\frac{G M_p}{a^3}},$4 values accelerate runaway onset; long $n = \sqrt{\frac{G M_p}{a^3}},$5 can permit survival despite large nominal $n = \sqrt{\frac{G M_p}{a^3}},$6 values (Ćuk et al., 2023).

4. Deimos and the Martian-moon problem

The Deimos application is motivated by a specific tension. In impact-generated circum-Martian disk scenarios, multiple inner moons form interior to Mars’s synchronous radius and subsequently interact via disk torques and tides. As inner moons migrate, they can encounter mean-motion resonances with Deimos, raising Deimos’s eccentricity and inclination well above modern values. Yet Deimos today is dynamically cool, with $n = \sqrt{\frac{G M_p}{a^3}},$7 and $n = \sqrt{\frac{G M_p}{a^3}},$8 relative to the local Laplace plane (Anand et al., 17 Dec 2025).

The sesquinary catastrophe is proposed as the mechanism that resolves this tension. If Deimos or its precursor were driven to sufficiently large $n = \sqrt{\frac{G M_p}{a^3}},$9, it would undergo a runaway collisional cascade, break apart into a Roche-exterior debris disk, and later re-accrete into a dynamically cool body. Using N-body simulations with collisional fragmentation, the paper argues that breakup occurs for $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$0 on timescales of $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$1 years. In accelerated piecewise sequences at $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$2 with $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$3 and $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$4, Deimos rapidly loses mass and passes a tipping point near $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$5–$$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$6 of its initial mass, beyond which the cascade rapidly completes (Anand et al., 17 Dec 2025).

The argument depends on Roche geometry. The standard fluid Roche limit is

$$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$7

For Mars and Deimos-like material, $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$8 is a few $$\frac{d\Omega}{dt} = -\frac{3}{2} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{\cos i}{(1 - e^2)^2},$$9 (approximately $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$0–$$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$1), well interior to Deimos’s orbit at $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$2. Deimos fragments therefore form a Roche-exterior, planetocentric debris disk that is dynamically stable and can collisionally damp and re-accrete (Anand et al., 17 Dec 2025).

The paper further argues that tides cannot erase excitation quickly enough. The order-of-magnitude eccentricity damping rate due to tides raised on the satellite is

$$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$3

For a small, porous Deimos, even optimistic choices of $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$4–$$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$5 yield eccentricity damping times far exceeding $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$6–$$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$7 years for $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$8, which is orders of magnitude slower than the few $$\frac{d\omega}{dt} = \frac{3}{4} J_2 n \left(\frac{R_p}{a}\right)^2 \frac{(5\cos^2 i - 1)}{(1 - e^2)^2}.$$9 years destruction times found for the sesquinary catastrophe (Anand et al., 17 Dec 2025).

The inferred end-state is a porous sand-pile moon assembled from fine debris. The paper explicitly connects this expectation to Deimos’s smooth surface and to recent ephemeris and moment-of-inertia fits consistent with near-uniform density bodies. This suggests that Deimos’s low eccentricity and inclination need not forbid strong past excitation; instead, strong excitation may have been self-limiting because it triggered destruction and re-accretion (Anand et al., 17 Dec 2025).

5. Other Solar System manifestations

The 2023 survey concludes that the large majority of small close-in moons in the Solar System have orbits that are immune to sesquinary catastrophe, but several notable exceptions illuminate the controlling physics. For Saturn’s resonant moonlets, large nominal $a$0 values do not always imply destruction because resonances can keep ejecta co-aligned and re-impacts slow. Methone, for example, has $a$1 and $a$2 yr, yet its $a$3 corotation resonance with Mimas allows low-speed reaccretion; Anthe behaves similarly in $a$4 corotation, while Pallene, with $a$5 and $a$6 yr, may survive because of its long timescale and possible departure from resonance (Ćuk et al., 2023).

By contrast, Naiad and Thebe illustrate environments where resonance protection is weak or absent. Naiad has $a$7 and $a$8 yr; because its $a$9 resonance with Thalassa affects inclination but does not confine debris, its survival implies substantial internal strength, consistent with independent Roche-limit arguments. Thebe has $e$0 and $e$1 yr; its persistence and faint gossamer ring suggest ongoing but modest erosion, which the paper interprets as evidence that a higher effective threshold, around $e$2, may apply for Jupiter’s inner moons (Ćuk et al., 2023).

Mars’s moons also appear in the 2023 stability analysis. Present values from the paper’s table give Phobos $e$3 and $e$4 yr, and Deimos $e$5 and $e$6 yr, both below the rubble-pile threshold. The derived constraints are

$e$7

for Phobos and

$e$8

for Deimos if long-lived rubble-pile stability is required. Sustained larger values over Myr would trigger sesquinary cascades, disfavoring prolonged high-excitation past orbits unless strength or other protection intervened (Ćuk et al., 2023).

6. Extension to minor planets orbiting white dwarfs

The white-dwarf generalization preserves the same core logic but shifts the dynamical scale dramatically. For a white dwarf of mass $e$9,

$i$0

Near the white-dwarf Roche radius, orbital speeds are hundreds of km s$i$1, so even modest orbital excitation yields $i$2 for kilometer-scale rubble piles. The key “danger zone” is $i$3–$i$4 rubble-pile Roche radii, corresponding to periods of approximately $i$5–$i$6 hours for a fiducial $i$7 white dwarf (Veras et al., 7 Jul 2025).

The rubble-pile Roche radius used in the paper is

$i$8

with $i$9 for a non-spinning body and $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$0 for synchronous spin. Inside roughly $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$1, classical tidal disruption dominates; outside roughly $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$2, orbital speed and differential precession slow enough that sesquinary timescales lengthen. Between these limits, returning ejecta impacts are fast enough and frequent enough to be erosive, implying destruction on $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$3–$v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$4 yr timescales (Veras et al., 7 Jul 2025).

Apsidal and nodal misalignment are again essential. In white-dwarf systems, stellar oblateness and magnetic precession are usually too slow, whereas general relativity sets a robust floor on apsidal precession:

$v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$5

Nearby massive planets can further accelerate both apsidal and nodal precession on $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$6–$v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$7 yr timescales. The paper therefore argues that misalignment is effectively inevitable in the relevant orbital regime (Veras et al., 7 Jul 2025).

The destruction timescale is estimated as $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$8 a few $v_{\rm rel} \sim v_k \sqrt{e^2 + \sin^2 i},$9, where

$v_{\rm esc,m} \ll v_k$00

The paper also recasts $v_{\rm esc,m} \ll v_k$01 in terms of $v_{\rm esc,m} \ll v_k$02 and emphasizes the steep scaling $v_{\rm esc,m} \ll v_k$03. The astrophysical consequence is that debris discs around white dwarfs may be in a state of semi-continuous replenishment, because parent bodies exterior to the Roche radius can still be collisionally destroyed well inside typical disc-lifetime estimates (Veras et al., 7 Jul 2025).

7. Nonstandard catastrophe-theoretic extension and principal uncertainties

A separate 2025 paper, "Apocalypsis and Apocalyptic Events: The Morphogenetic Ontology of Synchronized Catastrophes" (Martinez, 29 Oct 2025), does not explicitly define “sesquinary catastrophe.” It instead formalizes local catastrophes, synchronized apocalyptic events, and Apocalypsis as a topological meta-singularity generated by the coherent alignment of local singularities into a global structure of collapse. Consistent with that paper’s ontology, a sesquinary catastrophe can be rigorously defined as a partial, intermediate-order synchronized collapse: a multi-subsystem singular event in which at least two but not all subsystems synchronize and cross their catastrophe sets at the same control time, producing a connected cascade within a proper subset of the catastrophe graph (Martinez, 29 Oct 2025).

In that proposed usage, the relevant objects are the coupled potential

$v_{\rm esc,m} \ll v_k$04

the coupled critical set

$v_{\rm esc,m} \ll v_k$05

and the coupled discriminant

$v_{\rm esc,m} \ll v_k$06

A sesquinary catastrophe occurs when the control trajectory hits a multi-singular stratum of codimension $v_{\rm esc,m} \ll v_k$07 in the coupled discriminant, while the triggered connected component $v_{\rm esc,m} \ll v_k$08 of the catastrophe graph satisfies

$v_{\rm esc,m} \ll v_k$09

or lies below a chosen global threshold $v_{\rm esc,m} \ll v_k$10. This is explicitly presented as a proposed definition rather than established terminology (Martinez, 29 Oct 2025).

The mainstream scientific meaning of the term remains the planetary-science and celestial-mechanics usage. The principal uncertainties there are material strength, fragmentation physics, and non-gravitational forces. The Deimos study notes that cohesive strength likely shifts the practical threshold upward from the formal $v_{\rm esc,m} \ll v_k$11 to $v_{\rm esc,m} \ll v_k$12, that radiation and Lorentz forces can modulate the available impactor flux, and that a lower size cutoff of roughly $v_{\rm esc,m} \ll v_k$13 m limits direct modeling of mm–cm dust. The white-dwarf application likewise assumes rubble-pile, low-cohesion bodies and treats ejecta as ballistic test particles; radiation pressure, sublimation forces, and magnetic drag are neglected in the re-impact calculation, although the authors argue that the very large orbital speeds make this conservative for impact timing and velocity (Anand et al., 17 Dec 2025, Veras et al., 7 Jul 2025).

Across these domains, the central conclusion is stable: sesquinary catastrophe functions as a self-limiting mechanism for dynamical excitation. When orbital excitation raises returning-ejecta impacts above the erosive threshold, the source body is driven toward destruction, debris generation, dynamical cooling, and eventual re-accretion on a less excited orbit (Ćuk et al., 2023).