Simulation of Bouncing Mechanics on asteroids
with Smooth Particle Hydrodynamics
In 2014, I performed a study of lander impacts on asteroids for my BSc thesis at the University of Tuebingen in collaboration with the DLR. Our setup was tailored to simulate the impact of the Hayabusa-2 lander MASCOT on the asteroid 1999 JU3 to determine the effect of the impact on the asteroid’s surface as well as the likelihood of the asteroid’s gravitational field capturing the lander. Extracts from my thesis have been included on this page to give an overview of the project.
The Hayabusa 2 Project
In 2003, JAXA (Japan Aerospace Exploration Agency) launched the Hayabusa spacecraft, which returned to Earth in 2010, having collected material samples of the near-Earth S-type asteroid Itokawa. In late 2014, JAXA launched the succession mission Hayabusa 2 which arrived at its destination, the C-type asteroid 1999 JU3, in 2018 and is scheduled to return to Earth in December 2019.
1999 JU3 is a near-Earth Apollo Asteroid discovered in 1999 by the LINEAR (Lincoln Near
Earth Asteroid Research) project. It has a diameter of 0.9 km and consists of material that
has remained almost unchanged for the past 4.5 billion years. After its arrival, Hayabusa 2
observed the complete surface of 1999 JU3, before selecting touch-down points. Several small
rovers (MINERVA2) were released alongside MASCOT. Hayabusa 2 itself collected samples
from the surface in a so-called ’touch-and-go’ approach as well as sub-surface material samples
from a crater created by an impactor.
Hayabusa 2 (artistic depiction).
MASCOT STM-1 in 2011.
The MASCOT Lander
The asteroid lander MASCOT was developed by DLR in cooperation with CNES (Centre national d’études spatiales) and JAXA. MASCOT successfully landed on near-Earth asteroid 1999 JU3 in 2018 by descending from the unmanned spacecraft Hayabusa 2. After its arrival on the asteroid surface (impact velocity ≈ 0.1 ms ) it could change its position twice by hopping. The lander itself has a mass of m = 10 kg and dimensions of 0.3 × 0.32 × 0.185 m3 . We assume regolith covers the entire surface of the asteroid.
MASCOT’s main objective on the asteroid surface was the mapping of 1999 JU3’s geomorphology, the analysis of the structure texture and composition of the regolith along with the study of the asteroid surface’s thermal, mechanical and magnetic properties. MASCOT operated for more than 10 hours. Its findings are still being analysed.
Smooth Particle Hydrodynamics
SPH was first introduced by Lucy (1977) and Gingold and Monaghan (1977). Since then, this widely used numerical tool has been extensively improved. Attempts to find ways to further reduce noise and inaccuracies are still ongoing. SPH was developed to solve the hydrodynamic equations for compressible flows and has been used for a variety of astrophysical problems, such as the collapse of molecular clouds, accretion discs, planet formation, and collisions of asteroids to name only a few.
The basic idea behind SPH is the transformation of a system of coupled partial differential equations into a system of ordinary differential equations via kernel interpolation. The SPH method does not require a grid to calculate spatial derivatives. Instead, the fluid is divided into discrete mass packages, referred to as particles. Each particle carries quantities representing the fluid element, such as mass, momentum, energy, and velocity. The particles move like point masses according to the Lagrangian form of the equation of motion used and are able to interact with each other by exchanging momentum and energy, whereby the smoothing length h determines the range of this interaction.
Visualization of SPH particles describing a fluid. The smoothing length h for one specific particle marked in red is indicated by the circle.
Sketch of the lander impact geometry.
A typical simulation output is shown in the figure below. The colour coding represents different types of material. SPH particles of type 1 represent the lander, SPH particles of type 1 represent the asteroid surface, and SPH particles of type 2 generate a fixed outer boundary.
(Note: Not all simulations were carried out with a fixed outer boundary. If the simulation runtime is long enough for density waves to propagate through the entire regolith material, the presence or absence of a fixed boundary will result in different numerical effects.)
Visualization of the simulation setup with paraSPH.
Summary of Results
Even for initial velocities of the order of 50 m/s, surface
deformations happen on relatively small scales.
Deformation of Asteroid Surface
Using unrealistic parameters (e.g. initial projectile velocities between 3 m/s and 50 m/s instead of 0.1 m/s and target densities around 400 kg/m^3 instead of 1280 kg/m^3) we find that even in these worst case scenarios the damage to the asteroid surface is negligible and the lander will not burrow into the material but bounce off instead.
Movement of Lander on Asteroid Surface
Using realistic parameters (an initial projectile velocity of 0.1 m/s, a target density of 1280 kg/m3 , and 10% of Earth’s gravitational field) we find that the lander does not sink into the asteroid surface. Instead, it bounces off but is captured by the gravitational field of the asteroid, meaning it does not escape and fly off into space. Our simulations show a series of bounces on the surface as illustrated by the figure to the right. Due to the short duration of the project and the computational expenses of each run, longer simulations could not be carried out. However, we note that the bounce height decreases with each bounce, indicating that the lander will eventually come to rest.
(Note: Longer simulations are subjected to numerical effects once the density waves have traversed through the entire target. Reflection of waves can then occur which leads to an oscillation of the surface. This is a numerical effect and not realistic but leads to the seemingly sharp decrease of bounce height after the second impact as well as the slightly increased bounce height after the 5th bounce. Unfortunately, limited time and computer resources did not enable us to increase the target size to minimise this effect.)
Height of the lander’s centre of mass above the
asteroid’s surface as a function of time.
Six impacts were simulated.
Impact of a horizontally elongated rectangle with an
initial velocity of -10 m/s in y-direction.
Impact of a rectangle with an initial velocity of -10 m/s
Impact of a rotated lander with an initial velocity of -3 m/s in y-direction.
Impact of a rotated lander with an initial velocity of -13.5 m/s in y-direction.
Impact of a rotated lander with an initial velocity of -50 m/s in y-direction.