  Meteoroids impacting the Earth atmosphere are commonly classified using the
PE criterion. This criterion was introduced to support the identification of
the fireball type by empirically linking its orbital origin and composition
characteristics. Additionally, it is used as an indicator of the meteoroid
tensile strength and its ability to penetrate the atmosphere. However, the
level of classification accuracy of the PE criterion depends on the ability to
constrain the value of the input data, retrieved from the fireball observation,
required to derive the PE value. To overcome these uncertainties and achieve a
greater classification detail we propose a new formulation using scaling laws
and dimensionless variables that groups all the input variables into two
parameters that are directly obtained from the fireball observations. These two
parameters, ${\alpha}$ and ${\beta}$, represent the drag and the mass loss
rates along the luminous part of the trajectory, respectively, and are linked
to the shape, strength, ablation efficiency, mineralogical nature of the
projectile, and duration of the fireball. Thus, the new formulation relies on a
physical basis. This work shows the mathematical equivalence between the PE
criterion and the logarithm of $2{\alpha}{\beta}$ under the same PE-criterion
assumptions. We demonstrate that $log(2{\alpha}{\beta})$ offers a more general
formulation which does not require any preliminary constraint on the meteor
flight scenario and discuss the suitability of the new formulation for
expanding the classification beyond fully disintegrating fireballs to larger
impactors including meteorite-dropping fireballs. The reliability of the new
formulation is validated using the Prairie Network meteor observations.
