# 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. - **Patent:** US 9919813 - **Original title:** Control system and method for a plane change for satellite operations - **Owner:** US Department of Navy - **Granted:** 2018 - **Status:** Active - **Times cited:** 1 - **Field:** aerospace, software ## What it does 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 does NOT 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. ## Real-world examples 1. Autonomous satellite formation flying 2. On-orbit satellite servicing and refueling 3. Space debris inspection missions ## 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. ## Frequently asked questions ### What does How Spacecraft Calculate Maneuvers to Change Orbits Near Another Satellite cover? 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. ### Who owns patent US 9919813? US Department of Navy owns this patent, granted in 2018. ### When does this patent expire? This patent is expected to expire on March 20, 2038, when the invention enters the public domain. ### What is patent US 9919813 cited by? This patent has been cited by 1 later patents that build on its ideas. ### What problem does this patent solve? 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. ### What does this patent NOT cover? Does not cover maneuvers that change both slant and colatitude simultaneously. **Full plain-English explainer:** https://patentbrief.org/patent/us/9919813/fairing-recovery-system **Original patent:** https://patents.google.com/patent/US9919813 --- _Source: PatentBrief — https://patentbrief.org. Patent facts are from public records; the plain-English explanation is PatentBrief's._ ## Related patents Semantically similar inventions in the PatentBrief corpus: - [How Rockets Catch Up to Satellites Faster Using Out-of-Plane Steering](https://patentbrief.org/patent/us/11377237/starship-heat-shield-tiles) — A method for launching rockets to reach a space station or satellite in less than one full orbit by steering the rocket sideways during launch. - [How Satellites Use Split Thrusters to Reach Orbit Faster](https://patentbrief.org/patent/us/11753188/direct-to-cell-starlink) — A method for satellites with electric engines to manage their power usage by staggering when they fire thrusters, allowing them to reach their final orbit more quickly. - [How Space Taxis and Locomotives Move Satellites Between Orbits](https://patentbrief.org/patent/us/11492143/catching-super-heavy-booster) — A modular system using a small 'rendezvous' vehicle to collect satellites and a larger 'locomotive' vehicle to haul them to their final destination in space. - [How Spacecraft Servicing Pods Maneuver and Refuel Other Satellites](https://patentbrief.org/patent/us/11685554/starship-upper-stage) — A specialized robotic pod designed to dock with aging satellites and use a flexible, multi-jointed boom arm to adjust their orbit or velocity. - [How to Launch Spacecraft Using Giant Cannons Instead of Rockets](https://patentbrief.org/patent/us/10427804/starship-stainless-steel-construction) — A method for launching space vehicles into orbit using high-speed impulsive forces like cannons, precisely timed to rendezvous with existing satellites.