How Spacecraft Calculate Maneuvers to Change Orbits Near Another Satellite

A mathematical method for onboard computers to calculate the precise engine burns needed for one satellite to change its orbital plane while moving relative to another satellite.

What it covers

This patent describes a computational method for a secondary spacecraft to adjust its orbital path relative to a primary spacecraft. It uses a specific mathematical framework called the apocentral coordinate system to simplify the complex geometry of relative motion. By calculating the difference between a pre-maneuver velocity vector and a desired post-maneuver velocity vector, the system determines the exact impulsive velocity change (delta-V) required. This allows an onboard computer to automatically calculate the necessary engine burns to shift either the slant or the colatitude of the orbit without needing ground-based mission control.

What it doesn't cover

• —Does not cover maneuvers that change both slant and colatitude simultaneously.
• —Does not cover orbital changes for spacecraft that are not in a relative orbit around a primary spacecraft.
• —Does not cover non-impulsive propulsion systems like continuous low-thrust electric ion drives.
• —Does not cover maneuvers where the primary spacecraft is in an elliptical rather than circular orbit.

The clever bit

The innovation lies in using the apocentral coordinate system, which aligns the math with the geometry of the relative orbital ellipse itself, making the calculation of plane changes significantly more efficient for onboard processors.

Why it matters

As space becomes more crowded, the ability for satellites to autonomously navigate around each other—known as proximity operations—is becoming critical. This technology reduces the reliance on ground stations for calculating complex maneuvers, which is essential for deep space missions or scenarios where communication latency makes real-time ground control impossible.

Real-world examples

• 1.Autonomous satellite formation flying
• 2.On-orbit satellite servicing and refueling
• 3.Space debris inspection missions