🔭 astrophysics

Low-Energy Round-Trip Trajectories to Near-Earth Objects using Low Thrust

This paper presents a streamlined hybrid methodology combining the Sun-Earth circular restricted three-body problem and the heliocentric two-body problem to efficiently design low-energy, round-trip trajectories for Near-Earth Objects using low-thrust propulsion, enabling rapid preliminary mission design across broad NEO populations without heavy optimization.

Original authors: Alessandro Beolchi, Mauro Pontani, Kathleen Howell, Chiara Pozzi, Sean Swei, Elena Fantino

Published 2026-03-31

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CC BY 4.0

Original authors: Alessandro Beolchi, Mauro Pontani, Kathleen Howell, Chiara Pozzi, Sean Swei, Elena Fantino

Original paper licensed under CC BY 4.0 (http://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

Imagine you are planning a road trip, but instead of driving a car across a continent, you are piloting a spaceship traveling from Earth to a wandering asteroid and back again.

For decades, planning these trips has been like trying to navigate a maze while blindfolded. You have to calculate every turn, every speed change, and every fuel burn with extreme precision. If you miss a calculation by a tiny bit, you might miss the asteroid entirely or run out of fuel.

This paper introduces a new, smarter way to plan these cosmic road trips, specifically for "Near-Earth Objects" (NEOs)—those asteroids and comets that wander close to our planet. The authors have developed a method that finds low-energy, fuel-efficient round-trip paths using a mix of celestial mechanics and low-thrust engines.

Here is the breakdown of their method using simple analogies:

1. The Two Maps: The "Swing" and the "Highway"

To get from Earth to an asteroid, the authors use two different "maps" (mathematical models) and stitch them together:

The Swing (The Three-Body Problem): Near Earth, the gravity of the Sun and the Earth are both pulling on the ship. It's like being on a playground swing set where two people are pushing you from different sides. The authors use the natural "swings" (called Libration Points or L1 and L2) created by this tug-of-war. These are like invisible ramps or slides in space. Instead of fighting gravity with a massive engine blast, the spaceship "slides" down these natural ramps to escape Earth's neighborhood.
The Highway (The Two-Body Problem): Once the ship is far enough away from Earth, the Sun's gravity takes over completely. Now, the ship is just driving on a highway around the Sun. The authors calculate a simple elliptical path (like a racetrack) that intersects with the asteroid's own racetrack.

The Magic Trick: They don't try to solve the whole trip at once. They calculate the "outbound" trip (Earth to Asteroid) and the "inbound" trip (Asteroid back to Earth) separately, like planning the drive there and the drive home on two different pieces of paper. Then, they look for a match where the two pieces fit together perfectly.

2. The "Low-Thrust" Engine: The Slow and Steady Tortoise

Most traditional space missions use chemical rockets (like the ones on the Space Shuttle). These are like sprinting: you blast off with a huge burst of speed, then coast for a long time. They are fast but burn a lot of fuel.

This paper focuses on Low-Thrust propulsion (like ion engines). Imagine a tortoise that never stops walking. It moves very slowly, but it keeps pushing forward for months or years.

The Problem: It's hard to plan a trip with a tortoise because you can't just "jump" to a new speed; you have to gradually accelerate.
The Solution: The authors first plan the trip as if it were a sprint (using "impulsive" jumps). Then, they use a special algorithm to "stretch" those jumps into long, smooth, continuous pushes. It's like taking a jagged, bumpy path and smoothing it out into a gentle, continuous slope. This saves a massive amount of fuel.

3. The "Parking Lot" Strategy

One of the coolest features of this method is the use of Libration Points as "parking lots."
Imagine you are driving to a friend's house, but you don't know exactly when they will be home. Instead of driving back and forth, you park your car in a special spot near the house where the car naturally wants to stay put (a Libration Point orbit). You can wait there for weeks or months with almost no fuel. When your friend is ready, you hop back in and drive home.
This allows for flexible missions. You could visit one asteroid, park at the "space station" (Libration point), wait for a better window, and then visit a different asteroid without needing a new launch from Earth.

4. The Results: More Options, Less Fuel

The authors tested this method on 80 different asteroids.

The Volume: They found over 2 million different round-trip possibilities.
The Efficiency: Compared to traditional methods (like the NASA NHATS study), their method offers:
- Wider windows: You don't have to launch on a specific day; you have a whole season to choose from.
- Lower energy: The "launch energy" required is much lower, meaning you can launch smaller, cheaper rockets.
- Fuel savings: By using the low-thrust "tortoise" approach, the total fuel needed is significantly less than traditional chemical rockets, even for difficult targets like the asteroid Apophis.

Why Does This Matter?

Think of space exploration as a new frontier.

Old Way: You need a giant, expensive truck (chemical rocket) to carry heavy fuel just to get to the store (the asteroid).
New Way: You have a small, efficient electric car (low-thrust) that uses the natural currents of the ocean (gravity) to glide there. You can carry more scientific equipment or resources because you aren't carrying so much fuel.

This paper provides a blueprint for a future where we can easily send robotic missions to asteroids to study them, mine resources, or even deflect them if they threaten Earth. It turns the chaotic, difficult math of space travel into a modular, flexible, and fuel-efficient system.

In a nutshell: They found a way to use the universe's natural "slides" and "highways" to send a slow-but-steady spaceship to an asteroid and back, saving fuel and giving mission planners much more freedom to choose when to go.

1. Problem Statement

Near-Earth Objects (NEOs) are critical targets for scientific exploration, resource utilization, and planetary defense. While previous studies have cataloged accessible NEOs and designed one-way transfers, there is a significant gap in systematic strategies for designing low-energy, round-trip missions (Earth–NEO–Earth) that utilize low-thrust propulsion.

Existing methods often rely on:

Patched-Conics (PC): Which ignore the complex dynamics near Earth and miss low-energy pathways.
Optimization-Intensive Procedures: Which are computationally expensive and difficult to scale for large populations of targets.
One-Way Focus: Many studies focus solely on outbound transfers or do not systematically address the return leg.

The challenge is to develop a modular, scalable framework that leverages the natural dynamics of the Sun-Earth system to generate thousands of feasible round-trip trajectories with low launch energy ( $C_3$ ) and low propellant consumption, specifically for unmanned missions.

2. Methodology

The authors propose a hybrid dynamical framework combining the Sun-Earth Circular Restricted Three-Body Problem (CR3BP) and the Sun-Spacecraft Two-Body Problem (2BP). The methodology operates in a planar approximation (focusing on low-inclination NEOs) and follows a modular, non-iterative design process.

A. Dynamical Model & Transition

CR3BP (Near Earth): Used to model motion within the Earth's sphere of influence, specifically utilizing Libration Points ( $L_1$ and $L_2$ ).
2BP (Heliocentric): Used for the transfer between Earth and the NEO.
Transition Sphere (TC): A boundary (radius $\approx$ 2.77 million km) where trajectories switch between the two models.
Key Structures:
- Manifold Trajectories (MTs): Unstable/stable invariant manifolds of periodic Lyapunov orbits (PLOs) around $L_1/L_2$ . These act as natural "gateways" for low-energy departure and arrival.
- Transit Orbits (TOs): Direct trajectories connecting the parking orbit (or Earth surface) to the TC, offering faster transfers than MTs.

B. Target Selection

The study filters the NASA JPL Small-Body Database to select 80 NEOs with orbital elements close to Earth's (perihelion $\ge$ 0.9 au, aphelion $\le$ 1.1 au, inclination $\le$ 5°).
This filtering ensures the NEOs' orbits intersect naturally with the MTs and TOs generated by the CR3BP model.

C. Trajectory Design Strategy

The round-trip mission is constructed by independently computing Outbound and Inbound segments and then combining them:

Outbound Leg: Earth $\to$ TC (via MT or TO) $\to$ Heliocentric Ellipse $\to$ NEO Rendezvous.
Inbound Leg: NEO Departure $\to$ Heliocentric Ellipse $\to$ TC (via MT or TO) $\to$ Earth.
Combination: The two legs are patched together based on mission constraints (departure epoch, stay time, total duration).
Impulsive to Low-Thrust Conversion:
- Initial solutions are calculated as impulsive maneuvers (Lambert arcs).
- A dedicated Finite-Thrust Lambert Solver converts these impulses into continuous low-thrust arcs.
- The algorithm iteratively adjusts thrust arcs and coast phases to match the impulsive boundary conditions while minimizing mass ratio mismatch.

3. Key Contributions

Systematic Round-Trip Framework: First method to systematically generate large ensembles of round-trip trajectories by independently solving outbound and inbound legs and patching them, avoiding complex global optimization.
Hybrid Dynamics: Successfully integrates CR3BP manifold dynamics (for Earth escape/return) with 2BP heliocentric transfers, uncovering low-energy paths missed by standard patched-conic methods.
Modularity: The approach allows for flexible mission architectures, such as using Libration Point orbits as "parking stations" for multi-target missions or crewed staging.
Low-Thrust Implementation: Provides a robust algorithm to convert impulsive solutions into low-thrust trajectories without losing the temporal flexibility of the initial design.
Scalability: Capable of processing large NEO populations (80 targets) to produce millions of trajectory options.

4. Results

The method was applied to a population of 80 NEOs over a 5-year departure window (2035–2040).

Solution Space: The study generated ~2 million distinct round-trip trajectories to 11 accessible NEOs.
Performance Metrics:
- Launch Energy ( $C_3$ ): Significantly lower than NASA's NHATS (Near-Earth Object Human Space Flight Accessible Targets Study) benchmarks. For example, for 1991 VG, $C_3$ was 0.239 km²/s² (this work) vs. 2.985 km²/s² (NHATS).
- Total $\Delta v$ : Comparable to NHATS for rendezvous/departure, but achieved with much lower launch energy.
- Mission Duration: Longer durations (due to low-energy transfers) but offering wider temporal flexibility.
Low-Thrust Efficiency:
- When converting impulsive solutions to low-thrust (using a 240 mN, 1700 s $I_{sp}$ thruster), the launch mass decreased compared to chemical propulsion equivalents.
- Example (1991 VG): Chemical launch mass (NHATS) = 797 kg; Low-thrust launch mass (this work) = 663 kg.
Case Study (Apophis): Even for a target outside the primary low-energy population (Apophis, with higher eccentricity), the method produced a low-energy solution ( $C_3 \approx 0.066$ ) that, despite higher $\Delta v$ , resulted in a lower launch mass (847 kg) than the NHATS chemical solution (901 kg) due to the efficiency of low thrust.

5. Significance

Mission Flexibility: The method enables the design of complex architectures, such as multi-NEO visits using Libration Point orbits as intermediate staging points, which is impossible with standard patched-conic methods.
Cost Reduction: By drastically reducing $C_3$ (launch energy) and $v_\infty$ (return hyperbolic excess speed), the method lowers the required launch vehicle capability and propellant mass, making missions more feasible for small satellites and CubeSats.
Strategic Value: It provides a "library" of pre-computed trajectories for rapid mission planning, essential for future planetary defense and resource extraction missions.
Future Outlook: While currently planar, the framework is designed to be extended to 3D high-fidelity models, supporting the next generation of deep-space exploration infrastructure (e.g., Gateway).

In conclusion, this paper presents a transformative approach to NEO mission design, shifting from high-energy, optimization-heavy searches to a modular, dynamics-driven strategy that maximizes the utility of low-thrust propulsion for sustainable, low-cost round-trip exploration.