A numerical model of a circumstellar debris disk is developed and applied to observations of the circumstellar dust orbiting \beta Pictoris .
The model accounts for the rates at which dust is produced by collisions among unseen planetesimals , and the rate at which dust grains are destroyed due to collisions .
The model also accounts for the effects of radiation pressure , which is the dominant perturbation on the disk ’ s smaller but abundant dust grains .
Solving the resulting system of rate equations then provides the dust abundances versus grain size and over time .
Those solutions also provide the dust grains ’ collisional lifetime versus grain size , and the debris disk ’ s optical depth and surface brightness versus distance from the star .
Comparison to observations then yields estimates of the unseen planetesimal disk ’ s radius , and the rate at which the disk sheds mass due to planetesimal grinding .
The model can also be used to measure or else constrain the dust grain ’ s physical and optical properties , such as the dust grains ’ strength , their light scattering asymmetry parameter , and the grains ’ efficiency of light scattering Q _ { s } .

The model is then applied to optical observations of the edge-on dust disk orbiting \beta Pictoris , and good agreement is achieved when the unseen planetesimal disk is broad , with 75 \lesssim r \lesssim 150 AU .
If it is assumed that the dust grains are bright like Saturn ’ s icy rings ( Q _ { s } = 0.7 ) , then the cross section of dust in the disk is A _ { d } \simeq 2 \times 10 ^ { 20 } km ^ { 2 } and its mass is M _ { d } \simeq 11 lunar masses .
In this case the planetesimal disk ’ s dust production rate is quite heavy , \dot { M } _ { d } \sim 9 M _ { \oplus } /Myr , implying that there is or was a substantial amount of planetesimal mass there , at least 110 earth-masses .
But if the dust grains are darker than assumed , then the planetesimal disk ’ s mass-loss rate and its total mass are heavier .
In fact , the apparent dearth of any major planets in this region , plus the planetesimal disk ’ s heavy mass-loss rate , suggests that the 75 \lesssim r < 150 AU zone at \beta Pic might be a region of planetesimal destruction , rather than a site of ongoing planet formation .