A model of the heliocentric dust ring on Venus orbit

TL;DR

This work builds a dynamical model of the circumsolar dust ring on Venus’s orbit to quantify particle distribution, velocity, and density and to estimate spacecraft impact risk. It employs two initialization schemes (IC1 and IC2) and long multi-millennial integrations with a Radau integrator, including non-gravitational forces, to reveal ring evolution and its implications for a mission like BepiColombo. The model indicates the ring persists for at least several millennia, remains concentrated near Venus’s orbit, and exhibits a modest debris flux that is comparable to the interplanetary background, signifying a low risk for gravity-assisted spacecraft. The study also discusses major uncertainties and outlines pathways for refinement with future observations and alternative size-distribution models, underscoring the need for data to constrain azimuthal variations and the ring’s origin.

Abstract

A heliocentric dust ring on Venus orbit was discovered following observations by the Helios spacecraft, and then confirmed thanks to observations by STEREO and the Parker Solar Probe. The impact risk it poses needs to be evaluated for any spacecraft crossing the ring. This study aims to provide a first model of the dust ring, in terms of distribution of particles (including size distribution), velocity, density of the ring, and deduce a first estimation of the impact risk to spacecrafts crossing the ring. We seek to describe the orbits of dust particles in the ring. We explore a first simple model, that leads us to propose a second, more elaborate, model. This model is then populated by particles that we integrate for 2000 years. We demonstrate that the dust ring will persist over the next 2000 years, only slightly extending radially and perpendicularly to the Venus orbital plane. We show that particles tend to accumulate at Venus orbit, but that along it the differences in density is negligible. We compute the number of particles we can expect to find in the ring. Finally, as an example, we apply this model to Bepi-Colombo to obtain a first estimate of the impact flux in function of radius and mass, for radii between 2 $μ$m and 2 cm (i.e. for masses between 10^-2 kg and 10^-14 kg). We also present the impact velocity and direction of impacts with respect to Bepi-Colombo. We are able to conclude that the ring seems to present a low risk for spacecrafts using Venus as a gravity assist.

Figures (19)

• Figure 1: Schematics describing the orbits taken into account for the first model of the dust ring. The dashed grey lines show the outline of the dust ring on the interior and the exterior. The red (dash dot) and blue (dash dot dot) lines represent the two orbits chosen to have maximum and minimum values of eccentricity. All eccentricities here are highly exaggerated for ease of representation.
• Figure 2: Histograms of the distribution of the longitude of ascending node ($\Omega$) and of the distribution of the argument of perihelion ($\omega$) after the end of the integration (2000 years) of IC1. For the distribution of the argument of perihelion, the continuous red line in the middle is the value of the mean, the dotted orange line on the left corresponds to the value of the mean minus three standard deviation, and the dashed green line on the right shows the value of the mean plus three standard deviation.
• Figure 3: Schematics describing the computation of maximum inclination. The horizontal black line represents the orbital plane of Venus (at inclination $i_V$, in green), the dash-dot green line is the ecliptic, and the dashed blue line represents the orbit in the ring with the maximum inclination possible. The limit in height of the ring is represented through the dotted red line. A simple trigonometric equation allowed us to compute $\delta i$, the red angle. None of the angles represented here are to scale with the actual values.
• Figure 4: Histogram of the distribution of the particles on the $r$ values. The data in blue ('IC'; solid outline) are the initial conditions, meaning they represent the particles before the integration (IC2). The data in orange (dotted outline) represent the same particles but 6000 years later. The black line in the middle represents Venus at the end of the integration. The dashed lines around it underline the theoretical limits of the ring, as described in Sect. \ref{['sec:data']}.
• Figure 5: Histogram of the distribution of the particles on the $h$ values. This figure is similar to Fig. \ref{['fig:evol_r']} and uses the same legend.