Non-Propulsive Payload Deployment for Efficient On-Orbit Servicing of Mega-Constellations

This paper proposes a Non-Propulsive Payload Deployment (NPD) architecture for on-orbit servicing of mega-constellations, which significantly reduces fuel consumption by ejecting micro-payloads to autonomously rendezvous with targets, while introducing a phase-based algorithm and analytical formulas that enable efficient, low-error scheduling and planning for large-scale constellations like Starlink Gen2.

The Gist

The Big Problem: The "Heavy Backpack" Dilemma

Imagine you are a delivery driver (the Service Spacecraft) tasked with refueling 100 different cars (the Target Satellites) scattered across a massive parking lot in space.

Currently, the standard way to do this is to drive your heavy truck to the first car, refuel it, drive to the second, refuel it, and so on. The problem is that your truck is heavy. Every time you stop and start, you burn a huge amount of fuel just to move your own weight. If you have to visit 1,000 cars, you would need a fuel tank bigger than the truck itself. This is why scientists think servicing massive groups of satellites (mega-constellations) is impossible with current methods—it would cost too much fuel.

The New Solution: The "Sniper Bullet" Strategy

The authors propose a new idea called Non-Propulsive Payload Deployment (NPD).

Instead of driving the heavy truck to every single car, imagine your truck has a special launcher on the back.

1. The Truck (Service Spacecraft): It stays in a high orbit, acting as a stable launch platform. It doesn't need to move much.
2. The Bullets (Micro-Payloads): The truck shoots out tiny, lightweight "bullets" (micro-spacecraft).
3. The Mission: Each bullet flies out on its own, finds its specific target car, and refuels it.

Because the bullets are tiny, they need very little fuel to fly. The heavy truck only uses a tiny bit of energy to eject the bullets. This saves a massive amount of fuel compared to moving the whole truck.

The Hidden Challenge: The "Recoil" Effect

There is a catch. When you shoot a gun, the gun kicks back (recoil).

• Every time the truck shoots a bullet, the truck gets a tiny push in the opposite direction.
• If you shoot 100 bullets, those tiny pushes add up. The truck slowly starts drifting off its intended path.
• If the truck drifts too much, the next bullet might miss its target.

This creates a complex math puzzle: How do you schedule the shots so the truck doesn't drift too far, while still hitting all the targets?

The Smart Shortcut: The "Phase-Based" Algorithm

Solving this puzzle perfectly for 100+ targets would take a supercomputer days to calculate. The authors developed a clever shortcut called a Phase-Based Approximation Algorithm.

Think of it like this: Instead of calculating the exact wobble of the truck after every single shot, the algorithm assumes the truck's path is still mostly a perfect circle. It uses a simple rule: "Shoot the next bullet when the target is exactly opposite you."

• The Result: This shortcut is incredibly fast. It cuts the calculation time by 90% (from hours to seconds) while still being accurate enough that the "miss" is less than 1%. It's like using a rough map to get to a destination quickly, rather than measuring every single step.

The "Magic Formula"

The paper also found a simple formula to predict how much fuel the truck needs.

• They discovered that the total "kick" the truck feels is the main factor.
• They created a formula that says: Total Fuel Needed = (Standard Flight Fuel) + (Half of the Total Kick).
• This formula is so accurate (within 2% error) that mission planners can use it on a napkin to estimate if a mission is possible, without needing complex computer simulations.

The Starlink Test Case

To prove this works, the authors tested their idea on a real-world scenario: the Starlink Gen2 constellation (a massive group of internet satellites).

• The Old Way (O2M): To refuel 120 satellites, the traditional method would need a massive amount of fuel. In fact, for a quick 10-day mission, it would be physically impossible because the fuel tank would need to be larger than the truck itself.
• The New Way (NPD): Using the "bullet" strategy, the truck uses less than 1/50th of the fuel required by the old method.
• Bonus Speed: By staying in a slightly higher orbit, the truck can use the Earth's natural gravity quirks (called J2 perturbation) to drift sideways and reach different rows of satellites quickly. This allows the truck to service multiple "lanes" of traffic without burning extra fuel.

Summary

This paper introduces a way to service thousands of satellites by shooting tiny, fuel-efficient drones from a stationary mother ship. It solves the math problem of the ship drifting away by using a fast, smart shortcut and a simple formula. The result is a system that is 50 times more fuel-efficient than current methods, making it possible to maintain the massive satellite networks of the future.

Technical Summary

Technical Summary: Non-Propulsive Payload Deployment for Efficient On-Orbit Servicing of Mega-Constellations

Problem Statement
The paper addresses the critical challenge of servicing mega-constellations in Low Earth Orbit (LEO). While On-Orbit Servicing (OOS) is established for individual geosynchronous assets, the prevailing assumption is that servicing mega-constellations (comprising hundreds or thousands of dispersed satellites) is infeasible. Conventional architectures, such as One-to-Many (O2M), require a Service Spacecraft (SSc) to perform multiple rendezvous maneuvers. Due to the rocket equation, the propellant required scales exponentially with the velocity change ($\Delta v$) and the mass of the SSc. For large constellations, the cumulative $\Delta v$ requirements render traditional servicing economically unviable and fundamentally limit scalability. Furthermore, existing Non-Propulsive Payload Deployment (NPD) concepts have largely focused on attitude dynamics, neglecting the complex scheduling problem caused by cumulative orbital perturbations from successive payload ejections.

Methodology
The authors propose a novel NPD architecture where an SSc ejects micro-payload spacecraft (PSc) into transfer orbits. The PScs then autonomously rendezvous with Target Spacecraft (TSc). Since only the minimal mass of the PSc requires propulsion for the final approach, total fuel consumption is drastically reduced. However, each ejection imparts a recoil velocity to the SSc, perturbing its orbit and altering the initial conditions for subsequent deployments.

To resolve the resulting scheduling problem, the paper develops a phase-based approximation algorithm:

1. Dynamic Modeling: A coupled dynamics model is established where the SSc's orbit is treated as a piecewise function, updated instantaneously after each ejection based on momentum conservation.
2. Approximation Strategy: Recognizing that the SSc's orbit remains near-circular with low eccentricity after ejections, the authors approximate the transfer strategy using Hohmann transfer principles. They assume a phase difference of $\pi$ between departure and arrival positions, simplifying the optimization of ejection and rendezvous times.
3. Analytical Derivation: The authors derive a closed-form analytical formula for the maximum required ejection velocity ($\Delta v_{max}$). This formula expresses $\Delta v_{max}$ as the sum of the standard Hohmann transfer velocity and half of the total cumulative recoil velocity ($\Delta v_r$) accumulated from all previous ejections.

Key Results
Numerical simulations were conducted for constellations exceeding 100 satellites, including a case study of the Starlink Gen2 constellation. The results demonstrate:

• Computational Efficiency: The proposed phase-based approximation algorithm reduces computation time by over 90% compared to a greedy optimization approach (Algorithm 1), while maintaining ejection velocity errors below 1%.
• Analytical Accuracy: The derived analytical formula for $\Delta v_{max}$ yields a maximum relative error of less than 2% within near-Earth orbital regimes (altitude differences < 2000 km), provided the total payload mass is less than half the SSc mass.
• Fuel Efficiency: In a comparative analysis with a conventional O2M architecture for a 120-satellite constellation, the NPD system consumed less than 1/50 of the propellant required by the traditional method. For a 10-day mission, NPD used only 30.8 kg of maneuvering propellant compared to 1636.6 kg for O2M (which required a 100-day window).
• Multi-Plane Servicing: By operating at a higher altitude, the SSc utilizes $J_2$ perturbation to induce nodal precession. This allows the SSc to drift to adjacent orbital planes for sequential servicing. The NPD system achieved a plane transfer in 10.8 days, whereas the O2M method would require 213.6 days for the same drift.

Significance and Claims
The paper claims that the NPD architecture fundamentally shifts the paradigm for mega-constellation servicing by decoupling the service vehicle's mass from the propulsion requirements of individual rendezvous maneuvers. The primary contributions are:

1. Scalability: The proposed algorithm enables near-real-time mission planning for large-scale constellations, overcoming the computational intractability of previous high-dimensional optimization problems.
2. Predictive Capability: The analytical formula provides a rapid, reliable method for evaluating deployment capabilities and fuel requirements without intensive numerical iteration.
3. Operational Viability: The study demonstrates that efficient, multi-plane servicing is achievable with negligible propellant consumption, making sustained OOS for mega-constellations a feasible alternative to costly batch replacements.

The authors conclude that this approach addresses the prohibitive fuel consumption barrier, enabling a scalable infrastructure for next-generation orbital maintenance.