Modeling the meteoroid environment far from the ecliptic plane

TL;DR

This work introduces MEM 3.1, a high-ecliptic-latitude extension of NASA’s Meteoroid Engineering Model that computes finite, volume-averaged spatial density and encounter geometry for observers far from the ecliptic. It derives a robust off-ecliptic framework using dimensionless coordinates $s$ and $\xi$, four encounter geometries, and velocity components in cylindrical coordinates, with a Python implementation released publicly. The model expands the heliocentric range to $4.6$ au, fixes a speed-averaging bug, and adds parallelization, enabling faster, more general risk assessments for solar-observation missions like Solaris. Comparative analyses against MEM 3.0 and IRAS zodiacal-light data show near-ecliptic agreement but reveal a sharper ecliptic concentration in MEM, indicating areas for refining orbital-population distributions. Overall, MEM 3.1 provides a practical tool for evaluating meteoroid risk at high latitudes and beyond the near-Earth region, with clear paths for generalizations and future validation against observations.

Abstract

We describe a new version (numbered 3.1) of NASA's Meteoroid Engineering Model (MEM) in which we extend the model to handle locations that lie more than a few degrees in latitude off the ecliptic plane. We provide our algorithms for computing the spatial density and directionality of meteoroids far from the ecliptic and discuss their applications. In particular, we demonstrate how correct modeling of the out-of-ecliptic environment is critical for accurately assessing the risk posed by meteoroids to solar observation missions such as Solaris.

Figures (7)

• Figure 1: Volume of integration, with one quadrant cut away in order to show the cross section. In this illustration ${r=0.5}$, ${\beta=0.4}$, and ${d=0.1}$; normally, $d$ will be relatively small compared to $r$.
• Figure 2: Number density ($\eta$) of a single particle on an orbit with ${a=1}$, ${e=0.5}$, and ${i=0.3}$ radians. Heliocentric distance has been decomposed into an ecliptic component (${\rho = r \cos \beta}$) and an out-of-ecliptic component (${z = r \sin \beta}$). In the top panel, we use eq. \ref{['eq:limd0']} to calculate $\eta$; it is not possible to show the full range of values in this case, as eq. \ref{['eq:limd0']} is unbound near the edges of the depicted region. In the bottom panel, we use eq. \ref{['eq:nrbd']}, selecting a fairly large value of ${d = 0.1 r}$ in order to better illustrate the differences between the two approaches. The dashed line in the lower panel shows the limits on the orbiting particle's position.
• Figure 3: The four possible encounter geometries between a target (black circle) and a meteoroid with orbital elements ${a=3}$ au, ${e=0.8}$, and ${i = 60^\circ}$. The target is 1.28 au from the Sun and is separated from the ecliptic plane by 0.8 au. The arrowheads indicate the meteoroid's direction of motion as it intercepts the target.
• Figure 4: The flux of meteoroids larger than 1 $\upmu$g relative to the ISS, averaged over 10 sample state vectors using MEM 3.0 and MEM 3.1. The flux is binned by azimuth and elevation angle in the velocity-normal-binormal (VNB) reference frame, and therefore the flux is quoted per steradian. The bottom panel shows the difference between the two sets of results.
• Figure 5: The vertical profile of zodiacal brightness observed by IRAS at ${25 \upmu}$m wavelength and a solar elongation angle of $90^\circ$ and that corresponding to MEM's meteoroid orbits. In addition to the overall brightness profile, we also show the contribution from each of MEM's populations (top); in the lower panel, we normalize each population separately. The IRAS profile was extracted from Fig. 2 of nesvorny10, mirrored across $0^\circ$, and averaged. The units of relative brightness are arbitrary.