### Abstract

The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws - one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.

Original language | English (US) |
---|---|

Pages (from-to) | 334-345 |

Number of pages | 12 |

Journal | Icarus |

Volume | 164 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2003 |

### Fingerprint

### Keywords

- Asteroids
- Collisional evolution

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

**Steady-state size distributions for collisional populations : Analytical solution with size-dependent strength.** / O'Brien, David P.; Greenberg, Richard J.

Research output: Contribution to journal › Article

*Icarus*, vol. 164, no. 2, pp. 334-345. https://doi.org/10.1016/S0019-1035(03)00145-3

}

TY - JOUR

T1 - Steady-state size distributions for collisional populations

T2 - Analytical solution with size-dependent strength

AU - O'Brien, David P.

AU - Greenberg, Richard J.

PY - 2003/8/1

Y1 - 2003/8/1

N2 - The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws - one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.

AB - The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws - one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.

KW - Asteroids

KW - Collisional evolution

UR - http://www.scopus.com/inward/record.url?scp=0042430210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042430210&partnerID=8YFLogxK

U2 - 10.1016/S0019-1035(03)00145-3

DO - 10.1016/S0019-1035(03)00145-3

M3 - Article

AN - SCOPUS:0042430210

VL - 164

SP - 334

EP - 345

JO - Icarus

JF - Icarus

SN - 0019-1035

IS - 2

ER -