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A systematic investigation of the gravity dependence of static and dynamic angles of repose from 0.01g to 1g

This study utilizes controlled avalanche experiments on the China Space Station to demonstrate that while the static angle of repose remains constant across gravity levels from 0.01g to 1g, the dynamic angle of repose increases with gravity up to approximately 0.16g before saturating, a behavior attributed to a gravity-dependent rolling friction coefficient that significantly improves models of regolith on small Solar System bodies.

Original authors: Meiying Hou, Ke Cheng, Tuo Li, Xiaohui Cheng, Sen Yang, Zhihong Qiao, Xiang Li, Dengming Wang, Ke Chen, Raphael Blumenfeld

Published 2026-08-28

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CC BY 4.0

Original authors: Meiying Hou, Ke Cheng, Tuo Li, Xiaohui Cheng, Sen Yang, Zhihong Qiao, Xiang Li, Dengming Wang, Ke Chen, Raphael Blumenfeld

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Gravity is the invisible hand that shapes the world of loose, granular materials, from the sand on a beach to the dust covering the surface of an asteroid. When you pour sand into a pile, it naturally forms a cone with a specific steepness. This steepness, known as the angle of repose, is a fundamental property that tells scientists how stable a pile of material will be. If the slope is too steep, the material slides down; if it is gentle enough, it stays put. This concept is critical for anyone planning to build on the Moon, drive a rover on Mars, or land a spacecraft on a small asteroid, where the ground is often a loose layer of rock and dust. For decades, scientists have debated how this angle changes when gravity weakens. Some computer models suggested the angle stays the same, while others hinted it might get steeper or shallower depending on how the particles interact. The answers have been elusive because creating a stable, low-gravity environment on Earth is incredibly difficult, and previous short-duration experiments could not capture the full picture.

To solve this puzzle, a team of researchers took their experiment to space, specifically to the China Space Station. They needed a way to create a steady, artificial gravity that could be dialed down to levels far weaker than Earth's, simulating the conditions found on asteroids and moons. They used a specialized centrifuge, a spinning device that generates gravity by rotation, mounted inside a research rack. Inside this machine, they placed a small, transparent box filled with dry zirconium oxide spheres, tiny glass-like beads about one millimeter in diameter. The setup allowed them to control the gravity from a very weak 0.01 times Earth's gravity up to slightly more than Earth's own gravity. By carefully moving a wall inside the box, they could trigger the beads to avalanche, either very slowly to mimic a gentle slide or very quickly to simulate a rapid collapse. High-speed cameras, using a clever system of mirrors to see around corners in the tight space, recorded every movement of the beads as they settled into new piles.

The results revealed a surprising split in behavior between how the material behaves when it is almost still versus when it is moving. When the beads were allowed to settle very slowly, the angle of the pile remained exactly the same, regardless of how weak the gravity became. It held steady at about 22.4 degrees. This finding confirms a long-held belief that the basic friction between two stationary particles is an intrinsic property of the material itself and does not change just because gravity gets weaker. However, the story changed completely when the beads were allowed to tumble and slide rapidly. In these dynamic situations, the angle of the pile did not stay constant. As the gravity dropped from Earth's level down to about 0.16 times Earth's gravity, the angle decreased only slightly. But once the gravity fell below that threshold, entering the range typical of small asteroids, the angle dropped much more sharply, settling at roughly 19.6 degrees.

To understand why this happened, the researchers turned to computer simulations that mimicked the exact conditions of their space experiment. These simulations pointed to a specific physical mechanism: the way particles roll against one another. When gravity is strong, the weight of the particles presses them together firmly, creating a significant resistance to rolling. As gravity weakens, this pressing force diminishes, and the resistance to rolling drops dramatically. The researchers found that this rolling resistance, which acts like a brake on moving particles, follows a specific rule where it weakens as gravity gets weaker. This reduction in rolling resistance allows the particles to slide and settle into a flatter, more spread-out pile when gravity is very low. The study provides the first direct experimental proof that this rolling effect is the key driver behind the changing shape of granular piles in low gravity.

These findings offer a clearer picture of how the surfaces of asteroids and other small bodies in the solar system behave. The fact that the angle of repose changes so significantly in very low gravity means that models used to predict landslides, the stability of landing sites, and the formation of surface features on asteroids need to be updated. The research suggests that the transition from Earth-like gravity to asteroid-like gravity is not a smooth, gradual shift but involves a distinct change in how the material flows. By isolating this effect in a controlled space environment, the team has provided a reliable data set that engineers and scientists can use to design safer missions and better understand the geology of our solar system's smallest worlds.

Technical Summary: A Systematic Investigation of the Gravity Dependence of Static and Dynamic Angles of Repose from 0.01g to 1g

Problem Statement
The angle of repose (AOR) is a fundamental parameter for characterizing granular materials, essential for modeling landforms on the Moon, Mars, and asteroids. While the dependence of AOR on gravity is critical for predicting regolith behavior in extraterrestrial environments and assessing risks for planetary exploration (e.g., landing site stability, rover mobility, and excavation), experimental data in this domain is scarce and contradictory. Previous studies utilizing drop towers, parabolic flights, and rotating drums have yielded inconsistent results, with some reporting an increase in AOR under reduced gravity and others reporting a decrease or no dependence. Furthermore, prior experiments were largely restricted to lunar (~~0.16g) and Martian (~~0.38g) gravity levels, leaving the critical asteroid gravity range (0.01g – 0.16g) largely unexplored. Additionally, isolating the effects of rolling friction from cohesion and electrostatic forces in short-duration experiments has proven difficult.

Methodology
To address these gaps, the authors conducted a systematic investigation aboard the China Space Station (CSS) using a variable-gravity research rack.

Experimental Setup: A controlled avalanche-box apparatus was installed on a centrifuge within the Wentian module. The chamber (150mm × 30mm × 60mm) contained dry zirconium oxide spheres (1mm diameter, 5.89 g/cm³) to ensure negligible cohesive and electrostatic forces.
Gravity Range: The centrifuge generated stable artificial gravity ranging from $g = 0.01$ to $g > 1.40$ (Earth's gravity).
Procedure: A standardized preparation protocol ensured consistent initial packing fractions ( $0.571 \pm 0.003$ ). The experiment involved retracting a movable baffle at varying speeds ( $v_0$ from 0.01 mm/s to 300 mm/s) to distinguish between quasi-static piling and rapid free-collapsing regimes.
Data Acquisition: High-speed cameras captured the collapse process via a folded optical path system.
Corrections:
- Geometric Mapping: A coordinate transformation was applied to map the centrifuge's radial gravitational field to a rectangular Cartesian system to correct for systematic deviations compared to Earth-based uniform gravity.
- Coriolis Force: Control experiments were performed with clockwise (CW) and counter-clockwise (CCW) rotations. The study determined that CCW rotation provided more reliable dynamic AOR measurements, as CW rotation significantly reduced effective pressure on the pile due to the Coriolis force.
Simulation: Discrete Element Method (DEM) simulations were conducted to mimic the experimental geometry and conditions. These simulations incorporated a gravity-dependent rolling friction coefficient ( $\mu_r = k \cdot g^{1/3}$ ) derived from theoretical analysis of contact asymmetry.

Key Results

Quasi-Static AOR: The quasi-static angle of repose remained effectively constant at $22.4^\circ \pm 0.4^\circ$ across the entire gravity range (0.01g to 1.40g). This confirms that the static friction coefficient is an intrinsic material property independent of gravity.
Dynamic AOR: In contrast, the dynamic AOR exhibited a systematic dependence on gravity:
- Saturation Regime: For effective gravity $g > 0.16$ , the dynamic AOR was relatively constant at approximately $20.8^\circ \pm 0.2^\circ$ .
- Transition Regime: As gravity decreased below $g \approx 0.16$ , the dynamic AOR decreased more pronouncedly.
- Low-Gravity Regime: Approaching the asteroid regime ( $g \approx 0.01$ ), the dynamic AOR dropped to $19.6^\circ \pm 0.4^\circ$ .
- Power Law: The decrease in the dynamic AOR at low gravity fits a power law relationship: $\theta - 19.10 \sim g^{0.52}$ .
Mechanism: DEM simulations confirmed that this behavior is driven by the gravity dependence of the rolling friction coefficient ( $\mu_r$ ). As gravity decreases, interparticle normal forces weaken, leading to a reduction in $\mu_r$ (scaling as $g^{1/3}$ ), which facilitates particle rolling and reduces the dynamic angle of repose.

Significance and Claims
The authors claim this study provides the first experimental evidence of the effect of rolling friction on the dynamic angle of repose at low gravity. The findings resolve long-standing discrepancies in the literature by identifying a transition-like behavior in granular dynamics near lunar gravity ( $g \approx 0.16$ ). The paper posits that previous studies failed to observe this decrease because they focused primarily on gravity levels above lunar gravity.

The results offer new insights into low-gravity granular dynamics, suggesting that the reduction of rolling friction under weak interparticle contact forces is a fundamental characteristic of granular materials. This discovery is presented as essential for improving models of regolith behavior on small Solar System bodies (asteroids, moons, Mars) and for informing the design and risk assessment of future deep-space exploration missions, including in-situ resource utilization, planetary base construction, and rover mobility. The authors also note a parallel between this transition and the "Brazil-nut effect" observed in vibrated granular media under reduced gravity, suggesting a common underlying physical mechanism.

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