⚡ electrical engineering

Trajectory Generation for Multiple Atmospheric Passes Aeroassisted Orbital Plane Change

This paper proposes a fuel-efficient aeroassisted maneuver strategy for high lift-to-drag ratio spacecraft that achieves significant orbital inclination changes in low Earth orbit by iteratively combining multiple atmospheric passes with constant bank angles and post-exit three-impulse corrections, thereby substantially reducing fuel consumption compared to traditional purely propulsive methods.

Original authors: Zenan Zhong, Ming Yang, Songyan Wang, Tao Chao

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zenan Zhong, Ming Yang, Songyan Wang, Tao Chao

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

Spacecraft have long relied on powerful rocket engines to change their paths in orbit, burning precious fuel to tilt their trajectory or shift their altitude. This method works, but it is expensive and limits how much equipment a mission can carry, as every kilogram of fuel is a kilogram of cargo that cannot be transported. A more efficient alternative exists for vehicles designed with a high ability to glide: using the atmosphere itself as a tool. By dipping into the thin air surrounding Earth, a spacecraft can use aerodynamic forces to slow down, turn, or change its tilt without firing its engines. This concept, known as aeroassisted orbital transfer, has been studied for decades, yet applying it to make large changes in a spacecraft's orbital tilt over multiple passes through the atmosphere has remained a complex challenge. The difficulty lies in balancing the intense heat and pressure of reentry with the precise need to exit the atmosphere at the exact right speed and angle to set up the next maneuver.

Researchers at the Harbin Institute of Technology have developed a new method to solve this problem, creating a step-by-step plan for spacecraft to perform multiple atmospheric dips to change their orbital plane while saving significant amounts of fuel. Instead of trying to control the vehicle with complex, constantly shifting commands during the fiery reentry, the team proposed a simpler strategy: the spacecraft enters the atmosphere at a fixed angle and holds its banking angle—the tilt of its wings or body—at the maximum possible limit. This steady, predictable flight path allows the vehicle to use the air to steer itself efficiently. The real work of fine-tuning the orbit happens in the vacuum of space between these dips. The researchers designed a specific sequence of three engine burns to occur in the empty space above the atmosphere, correcting the spacecraft's path so that it returns to the air for the next pass with the exact speed and angle needed to continue the process.

The study focuses on a scenario where a spacecraft needs to change the tilt of its orbit, a common requirement for satellites that need to cover different parts of the Earth. The team simulated a vehicle starting in a circular orbit 450 kilometers above the ground. They calculated a safe "corridor" for reentry, defining the precise speeds and angles that would allow the craft to dip into the atmosphere, survive the heat and pressure, and bounce back out without burning up or falling too deep. They found that by holding a constant bank angle of 65 degrees and entering at a specific shallow angle, the spacecraft could repeatedly enter and exit the atmosphere. Between each dip, the spacecraft would coast in space, fire its engines three times to adjust its path, and then dive back in. This cycle could be repeated until the desired change in orbital tilt was achieved.

Through detailed computer simulations, the researchers demonstrated that this multi-pass approach is far more fuel-efficient than traditional methods that rely solely on rocket thrust. In their tests, the spacecraft was able to change its orbital inclination by nearly 19 degrees using this aerodynamic technique. The simulations showed that the heat generated during these passes stayed well within safe limits, never exceeding the maximum temperature the vehicle's materials could withstand. The fuel savings were substantial; the total amount of energy required for the maneuver was significantly lower than what would be needed to achieve the same result using only rocket engines. The study also provided a way to predict how many atmospheric dips would be needed to reach a specific target, allowing mission planners to estimate the fuel cost and time required for such a journey before it even begins.

One of the key findings was that the efficiency of this method depends heavily on the vehicle's ability to glide. The researchers compared spacecraft with different aerodynamic capabilities and found that those with a higher lift-to-drag ratio—meaning they can glide farther for every unit of drag they experience—performed much better. A vehicle with a lift-to-drag ratio of 2.4, for instance, showed a clear advantage in fuel savings, whereas a vehicle with a lower ratio of 1.6 offered no fuel benefit over traditional rocket maneuvers. This suggests that for this technique to be practical, the spacecraft must be designed specifically to glide efficiently. The study also highlighted that the timing and direction of the engine burns in space are critical; a small error in the three-impulse sequence could prevent the spacecraft from hitting the atmosphere correctly for the next pass.

The researchers validated their approach by running thousands of simulations on a standard computer, confirming that the trajectory generation method works consistently. They showed that even with the strict limits on heat and pressure, the spacecraft could successfully complete the cycle of dipping and exiting the atmosphere multiple times. The method proved robust enough to handle the complex physics of Earth's gravity and atmospheric density, which vary with altitude. By breaking the problem down into a simple atmospheric phase and a precise space phase, the team created a reliable framework for planning these missions. While the current work relies on computer models, the results suggest that this strategy could be a viable option for future missions where saving fuel is a priority, such as for large satellite constellations or deep-space probes that need to adjust their orbits after arriving at their destination. The study concludes that by combining the natural forces of the atmosphere with carefully timed engine burns, spacecraft can achieve major orbital changes that were previously too costly to attempt.

Technical Summary: Trajectory Generation for Multiple Atmospheric Passes Aeroassisted Orbital Plane Change

Problem Statement
This research addresses the challenge of adjusting the orbital inclination of high lift-to-drag ratio spacecraft in Low Earth Orbit (LEO). Traditional purely propulsive maneuvers for significant plane changes are fuel-intensive. While Aeroassisted Orbital Transfer (AOT) offers a fuel-saving alternative by utilizing atmospheric drag and lift, existing methods face limitations. Current approaches often rely on complex numerical optimizations for in-atmosphere control, struggle with the physical mechanisms of impulse effects, and require the a priori selection of the number of atmospheric passes ( $N$ ), which can lead to infeasible solutions if chosen incorrectly. Furthermore, single-exo-atmospheric impulse strategies limit precise control over reentry parameters for each pass.

Methodology
The paper proposes a trajectory generation scheme that separates the control problem into a simplified in-atmosphere phase and an optimized exo-atmospheric phase.

Simplified In-Atmosphere Control:
- The spacecraft maintains a constant angle of attack and a maximum constant bank angle ( $\sigma_{max}$ ) during atmospheric flight.
- This strategy simplifies the guidance law, maximizes cross-range capability, and ensures conservative thermal/structural margins.
- A profile-based method is used to determine feasible reentry parameters (velocity $V_{entry}$ $V_{e n t r y}$ and flight path angle $\gamma_{entry}$ $γ_{e n t r y}$ ). This involves:
  - Backward integration from the exit condition to establish a ballistic entry boundary.
  - Forward integration to enforce strict path constraints: stagnation point heating rate ( $\dot{Q}$ ), total heat load ( $Q$ ), dynamic pressure ( $q$ ), and sensed acceleration ( $G$ ).
  - Selection of the optimal $\gamma_{entry}$ and $V_{entry}$ that satisfy these constraints while minimizing the deorbit impulse cost and maximizing orbital plane change capability.
Exo-Atmospheric Optimization (Three-Impulse Strategy):
- To ensure consistent reentry conditions across multiple passes, the paper introduces a three-impulse maneuver strategy for the space phase between atmospheric exits and subsequent reentries.
- The impulses are:
  1. An energy-boost impulse ( $\Delta V^{(1)}$ ) applied immediately after exit to adjust energy.
  2. A transfer impulse ( $\Delta V^{(2)}$ ) applied at a specific transfer angle to control the Flight Path Angle (FPA) for the next entry.
  3. A velocity adjustment impulse ( $\Delta V^{(3)}$ ) applied at the atmospheric boundary to match the target reentry velocity.
- This is formulated as a low-dimensional optimization problem (minimizing total impulse magnitude) using Particle Swarm Optimization (PSO), reducing the complexity from 12 variables to 3.
Trajectory Generation and Estimation:
- The full trajectory consists of a deorbit segment, $N$ repeated entry/exit cycles, and a final Hohmann transfer to return to the target circular orbit.
- A predictive method is developed to estimate the "reachable zone" (achievable inclination and RAAN changes) as a function of the number of passes, using quadratic and linear models fitted to simulation data.

Key Contributions
The authors identify four primary contributions:

Novel Trajectory Scheme: A framework that strategically separates simplified atmospheric flight control from optimized exo-atmospheric impulses, avoiding complex in-atmosphere optimization.
Systematic Reentry Parameter Selection: A deterministic, profile-based method to select feasible $V_{entry}$ and $\gamma_{entry}$ that explicitly account for atmospheric exit conditions and all critical path constraints.
Efficient Three-Impulse Model: A low-dimensional optimization model for planning transfers between passes, effectively handling the boundary-value problem while ensuring repeatable reentry interfaces.
Predictive Capability Estimation: A method to estimate the achievable orbital plane change and impulse costs based on the number of passes, aiding in preliminary mission design.

Simulation Results
Simulations were conducted for a spacecraft with a maximum lift-to-drag ratio ( $C_{L/D}^{max}$ ) of 2.4, starting from a 450 km circular orbit with 45° inclination.

Constraint Satisfaction: The generated trajectories successfully maintained altitude between 70 km and 700 km, keeping stagnation point heating rates below 2 MW/m² and total heat loads below 800 MJ/m².
Inclination Change: The method achieved an orbital inclination change of approximately 19° using a positive bank angle configuration.
Impulse Distribution: The velocity adjustment impulse for the first entry was ~70 m/s, while subsequent energy compensation impulses averaged ~20 m/s. Range control impulses remained below 1 m/s.
Efficiency: The transfer efficiency ( $\eta = \Delta V_{AOT} / \Delta V_{pure}$ ) reached a maximum of approximately 0.7, indicating a 30% reduction in fuel consumption compared to pure propulsive maneuvers.
Lift-to-Drag Ratio Impact: Comparisons with spacecraft having lower $C_{L/D}$ (1.6 and 2.0) showed that higher lift-to-drag ratios yield greater inclination changes and better transfer efficiency. A $C_{L/D}$ of 1.6 showed no fuel-saving advantage over pure propulsion.
Estimation Accuracy: The proposed estimation method for reachable zones showed good agreement with actual simulation results for inclination changes, with minor discrepancies in RAAN estimation.

Significance and Claims
The paper claims that the proposed multi-pass aeroassisted maneuver method significantly reduces fuel consumption compared to traditional purely propulsive orbital transfer methods, even under strict path constraints and a simplified control strategy (constant bank angle). By decoupling the complex atmospheric dynamics from the optimization of exo-atmospheric impulses, the method provides a tractable and deterministic approach to planning repeated orbital plane changes. The authors assert that this approach validates the fuel-saving potential of aerodynamically assisted maneuvers for high $L/D$ spacecraft in LEO.

The study concludes by noting that future work will address practical engineering factors, such as finite thrust constraints and the dynamic characteristics of attitude control, to further enhance the method's engineering applicability and robustness.

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